Coherent anti-Stokes Raman scattering: Spectroscopy and microscopy

Vibrational Spectroscopy 55 (2011) 1–37

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Review

Coherent anti-Stokes Raman scattering: Spectroscopy and microscopy Fouad El-Diasty Physics Department, Faculty of Science, Ain Shams University, Khalifa Mamoon, Abbasia, Cairo 11566, Egypt

a r t i c l e

i n f o

Article history: Received 5 May 2009 Received in revised form 2 September 2010 Accepted 22 September 2010 Available online 1 October 2010 Dedicated to Professor Nayel Barakat. Keywords: CARS Coherent anti-Stoke Raman spectroscopy Raman scattering Raman microscopy

a b s t r a c t In this review the basis, recent developments and applications of coherent anti-Stokes Raman scattering (CARS) in the fields of spectroscopy and microscopy are dialed with. The nonlinear susceptibility of the investigated molecule induced by pump and Stokes laser beams employed in the CARS technique is discussed. The relation between the nonlinear susceptibility, the different CARS laser intensities and the phase matching condition between them is also presented. The structure of CARS spectrum is analyzed as a function of the physical characteristics of the different employed lasers. This includes laser half widths, interference effects, cross-coherence and saturation of the resultant CARS signal by stimulated Raman scatter process (SRS). The different broadening mechanisms for CARS spectral line such as pressure and Doppler broadening are demonstrated. The recent progress in CARS for the in situ reaction flame diagnosis due to its suitability for detection of vibrational–rotational excited gas molecules present in the electronic ground state is discussed. CARS diagnosis for liquid- and solid-phases including the progress in polymeric materials is considered. The applications of CARS microscopy are reviewed in the view of its recent advances to study chemical and biological systems. © 2010 Elsevier B.V. All rights reserved.

Contents 1. 2.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bases of CARS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. CARS characteristic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Calculation of CARS susceptibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Structure of CARS spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1. Physical spectrum of CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2. Influence of laser characteristics on CARS spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Theoretical CARS spectra for selected molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Calculation of hydrogen spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Calculation of nitrogen CARS spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advances in CARS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Advances in CARS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Determination of inhomogeneous broadening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Time-resolved two color single-beam CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. High spectral resolution multiplex CARS spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Non-resonant wavepacket using a single ultrashort pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5. Generation of blue coherent radiation by SRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.6. Time-resolved femtosecond CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.7. Time- and frequency-resolved fs-CARS for quantum computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.8. CARS with frequency-shifted and shaped pulses from a photonic-crystal fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. CARS for gases, flames and combustion diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Nano-optical method of background suppression in CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Combination of CARS and photo-acoustic spectroscopy for gas detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. Flame thermometry by femtosecond CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4. Errors of spatial averaging in CARS temperature measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E-mail address: [email protected]. 0924-2031/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.vibspec.2010.09.008

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F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

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3.2.5. Dephasing kinetics of molecular hydrogen rotational transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6. Triple-pump and dual-pump CARS for combustion diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7. Resonant CARS for measuring species concentration and temperature profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8. CARS for non-equilibrium pulsed ns discharge investigation at atmospheric pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.9. CARS and laser-induced fluorescence in flame measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.10. VCRS and DBB-RCARS for diagnosis of fuel-rich sooting flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. CARS for liquid diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1. Nonlinear Raman probe for local structures in liquids and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2. Dephasing in time-resolved fs-CARS from molecules in liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3. Femtosecond CARS in liquid phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4. Mesoscopic local structures in ionic liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5. CARS and mesoporous silica aerogels host for gas- and liquid-phase sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6. SCARS and fifth order Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. CARS for solids diagnoses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. CARS on carbon nanotubes and thin films excited through surface plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. CARS to study polymeric materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3. Dynamical interactions between ␴- and ␲-electrons in organic molecules by CARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. CARS in biological researches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advances in CARS microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Recent CARS microscopy investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. CARS microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. Live cell imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3. CARS tissue imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4. Focus-engineered CARS for imaging chemical interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5. Multimodal CARS microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.6. Polarization and interferometric polarization CARS microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Since the first Raman and Krishnan [1] experimental studies (1928) on inelastic light scattering in water and alcohol vapors and Raman scattering, as spectroscopic technique, is massively developed. The filtered mercury arc excitation sources are used with very exposure times to achieve acceptable signal levels, allowing investigation of the vibrational spectrum of excited molecules. Because each molecule having its specific molecular bonds, the analysis of the scattered wave spectrum provides a unique molecular signature. This can be used in biological imaging, as it will be seen latter in Section 4, for generating contrast without exogenous labels. The scattering process occurs via a “virtual state” which is not an electronically excited state of the system. The Raman signal is considerably enhanced if the incident light is resonant with an energy level of the molecule. This is called resonant Raman scattering (RRS) and can be many orders of magnitude larger than its ordinary nonresonant analog. Raman effect has experienced two periods of growth and interest [2]: • in the 1960s with the advent of the laser as an intense monochromatic (coherent) light source, • in the 1980s with advances in detector, filter and tunable laser technology. According to Myers [3], spontaneous Raman scattering signals are linear in the incident intensity but two photons are involved, one is being spontaneously generated. A net vibrational transition is achieved through “virtual” excitation and de-excitation of higher energy states. The scattering phenomenon may be described in terms of a simple quantum picture of energy exchange between the incident quanta of radiation and the scattering molecule. In elastic collision, involving no exchange of energy, the frequency of the scattered photon remains unchanged, giving rise to Rayleigh scattering. In inelastic collision, energy is transferred from the photon to the molecule, so that the photon will be scattered

19 19 20 20 20 21 21 22 23 23 24 24 24 24 24 25 25 26 26 27 27 28 29 29 30 34 34 35 35

with lower energy and frequency (longer wavelength), giving rise to Stokes radiation. In other case, energy is transferred from the molecule to the photon, so that the scattered radiation is at higher frequency (shorter wavelength), so-called anti-Stokes radiation. Coherent anti-Stokes scattering is known since study of nonlinear phenomena of crystal structures by Mark and Terhune [4] in 1965. With development of high-peak-power pulsed dye laser in 1970s, CARS became potentially attractive for non destructive in situ measurements of species’ concentrations and temperature in flames. It allows also determination of the population density difference between vibrational energy levels with high spatial and temporal resolution. The superiority of CARS over the incoherent spontaneous Raman process derives from its high signal generation efficiency and the fact that the CARS signal emerges as coherent laser-like beam. Furthermore, CARS signals are often orders of magnitude stronger than those produced by spontaneous Raman scattering. For flame diagnosis, CARS radiation is collected over such a small solid angle leading to separation of the CARS signal from the incident laser beam and also efficiently rejects fluorescence and/or luminescence background, resulting in efficient CARS signal detection. In brief, the mean characteristics of CARS are [5]: 1. Rich spectroscopic information can be obtained, more than in spontaneous Raman scattering, due to dispersive line shapes. 2. Insensitive to fluorescence interference by virtue of blue shift of signal relative to pump beam, except when two-photon induced autofluorescence is presented. 3. Excellent spatial resolution (<1 mm) for flame spectroscopy and low resolution of the order or 200 nm in microscopy. 4. Good time resolution (∼100 fs). 5. Excellent spectral resolution (0.03–1 cm−1 on an ordinary setup, 10−3 cm−1 in special applications using CW sources). 6. Extremely luminous (105 –1010 ) more intense than normal Raman scattering.

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In the same time, CARS has a few disadvantages which are: 1. Presence of the non-resonant background, which limits the detectivity at value of ppm to 1% depending on thermodynamic conditions and species studied. 2. Sensitive to laser instabilities as the other techniques. 3. Subject to saturation at the higher laser power density levels (1010 W/cm2 or more). For these reasons, CARS is often preferred to normal Raman scattering for the following measurements: 1. Study of reactive media, plasma, gas laser amplifiers, etc. 2. Analysis of sooting flames or investigation of flows near solid obstacles (as close as 50 ␮m to the surface). 3. High resolution spectroscopy. 4. Resonance-enhanced Raman spectroscopy of gases and liquids. In the following sections, the nonlinear susceptibility of the investigated medium will be discussed as a function of both the different CARS laser intensities and the phase matching condition between them. A complete expression for CARS susceptibility derived quantum mechanically is given involving the expectation value of the electric dipole-moment generated by the third power laser electric field through solving the equation of motion for the density matrix “Liouville equation” using time-dependent perturbation theory. Consequently, the structure of CARS spectrum as a function of the physical characteristics of the CARS laser sources and its influence on the resultant CARS signal, including laser halfwidths, interference effects, cross-coherence and saturation by stimulated Raman scatter process (SRS), are presented. The different broadening mechanisms for CARS spectral line which play role in CARS process such as pressure and Doppler broadening have to be connected. A part is devoted to calculate theoretical CARS spectra for a few selected gas molecules which have been treated experimentally such as hydrogen and nitrogen molecules.

[6]. The resonant part of susceptibility  + i is contributed by the closet vibro-rotational resonances. Whereas NR is a slowly varying non-resonant term, contributed by the electrons and remote resonances. The (3) is resonantly increased at the Raman angular frequency of the molecule; ωR = ω1 − ω2 . In coherent anti-Stokes Raman scattering and through the third-order nonlinear susceptibility of the medium a nonlinear coherently interaction between two pump beams at frequency ωp , ωp , and a Stokes laser beam tuned at a frequency ωs induces a polarization which generates the CARS radiation. Intense signals are produced at resonance if the difference between pump and Stokes beams matches a Raman active transition of the medium, i.e., ωo = ωp − ωs . So the overlapping of the three interacting laser beams produces a coherent scattered signal at the anti-Stokes frequency ωAs , i.e.,

2. Bases of CARS spectroscopy

ωAs = ωp + ωp − ωs

The wave equation of the electrical field E with angular frequency ω propagating in a third-order nonlinear medium and in the z-direction is given by (1)

where k (=nω/c) is the propagation constant, c is the speed of light in vacuum, n is the linear refractive index of the medium, and ε0 is the permittivity of vacuum. P(3) (ω) is the third-order component of the nonlinear polarization PNL of the molecule at the angular frequency ω. Suppose two laser beams of frequency ω1 and ω2 are injected simultaneously then 1  (3) P (ω)e−iωj t + · · ·, 2 3

PNL =

(3)

In case of degenerate CARS with ωp = at

2.1. CARS characteristic parameters

∂2 E(ω) ω2 + kE(ω) = 2 P (3) (ω) 2 ∂z c ε0

Fig. 1. Diagram of the coherent anti-Stokes Raman scattering (CARS) process.

(2)

ωAs = 2ωp − ωs

 2 P (3) (ω1 ) = (3) N(ω1 )E(ω1 )E(ω2 ) ,  2 P (3) (ω2 ) = (3) N(ω2 )E(ω2 )E(ω1 ) , P (3) (ω3 ) = (3) N(ω3 )E 2 (ω1 )E ∗ (ω2 ),

here ω3 = 2ω1 − ω2 , and N is the density of the molecules, while (3) is the third-order nonlinear susceptibility per molecule. The latter can be expressed in Bloembergen’s notation  =  + i + NR

(4)

The principle of CARS is displayed in an energy transition, Fig. 1, with two real energy levels |˛, |ˇ and two virtual energy levels |, |ı. By absorbing the first pump photon with frequency ωp the molecule which exists in the ground energy level |˛, will be pumped to a virtual level |. A photon tuned to frequency ωs induces transition of molecule to the rotational–vibrational level |ˇ. As the molecule absorbs the second pump photon at frequency ωp it will be introduced to undergo transition to a higher virtual level |ı. By the emission of anti-Stokes photon with frequency ωAs , the molecule will return back to the ground energy level |˛. The vibrational and rotational selection rules for CARS process are identical to those for spontaneous Raman scattering [7,8], where the special case of the diatomic molecules provides:



j=1

where

ωp , one utilizes a CARS signal

 = 1,  = 0,

j = +2 S-branch j = 0 Q-branch j = −2 O-branch j = ±2 O-,S-branch



vibrational CARS rotational CARS

where  and j are vibration and rotational quantum numbers respectively. The vibrational excited molecule in the Q-branch ( = 1, j = 0) gives more signal than that in case of O- ( = 1, j = − 2) or S-branch ( = 1, j = + 2). Therefore most of the CARS experiments use the very intense Q-branch.

4

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

The classical description of the coherent anti-Stokes Raman scattering is that, three electric fields from pump- and Stokesbeams hitting the matter to produce a resulting field where ¯ z , t) = E(¯

1 ¯ ¯ [E¯ p (¯z , ωp )ei(kp z−ωp t) + E¯ p (¯z , ωp )ei(kp z−ωp t) 2 ¯

+ E¯ s (¯z , ωs )ei(ks z−ωs t) + · · ·]

(5)

where the k-vectors of all involved waves have only a z-component and all fields are polarized into x-direction. This strong resultant electric field induces a third-order polarization in the medium, which is the source of the anti-Stokes wave with frequency ωAs . The nonlinear response of the matter to the incident laser fields is written in the form of a polarization density power-series in E¯ (P¯ in Coulomb m/m−3 ) as follows: P¯ = P¯ (1) + P¯ (2) + P¯ (3) + · · · = ε0 (1) E¯ + ε0 (2) E¯ · E¯ + ε0 (3) E¯ · E¯ · E¯ + · · ·

(6)

(n)

is the susceptibility tensor of rank n + 1. The normal where linear electric susceptibility (1) characterizes the index of refraction and the absorption of light by the medium, and also Rayleigh and spontaneous Raman scattering. The typical value of |(1) | in gases and plasma is 10−3 . The second-order susceptibility (2) term generates wave fields with 2ωp , ωp ± ωS , hyper-Raman-scattering and parametric oscillations. This term of susceptibility vanishes in a medium with inversion symmetry (isotropic media) such as gases, plasmas, liquids, and in central symmetric crystals. The second nonlinear term, which is non-zero for all media, is responsible for generating the lowest order nonlinear effect in plasma, third harmonic generation, field induced second harmonic generation (SHG), optical Kerr effect, and coherent Raman phenomena including CARS. On other hand, the third-order susceptibility (3) is a fourth-rank tensor characterized by four distinct frequencies and polarization, and it contains 34 = 81 elements. In an isotropic medium, the number of independent tensor elements is reduced from 81 to 3. In frequency-degenerate CARS (ωp = ωp ), there are

Fig. 2. Phase mismatch affecting the CARS process, Ref. [11].

Fig. 3 schematically illustrates the geometry of the commonly employed different phase-matching schemes. The simplest to employ and at the same time generates high CARS signals is collinear CARS, Fig. 3a. But this geometry lacks in its spatial resolution. Focused collinear CARS geometry has an improved resolution (multiple of Rayleigh length), if tight focusing, with a lens of a short focal length, is realized. The most generally used CARS geometry is the BoxCARS in the planer, Fig. 3b, or folded version, Fig. 3c. The letter version provides sufficient spatial resolution and simplified detection means, but a comparatively reduced signal, while still satisfying the phase matching requirements.

only two independent elements, where the typical value of (3) is 10−23 m2 /V2 [9,10]. The CARS signal intensity that generated in a matter by the incident laser fields can be determined by taking Eq. (5) in consideration, and substitution of the nonlinear polarization in Maxwell’s equations neglecting magnetization and currents due to free charges. However, the time averaged CARS signal intensity is given by [10]: IAs =

2 N2 ωAs

16ε20 c 4

2

[(3) (ωp − ωs )] Ip2 Is L2

sin2 (kL/2) (kL/2)

2

(7)

where Ip and Is are the pump and Stokes wave intensities, L is the interaction length, N is the molecular number density and k is the phase mismatch, which can be expressed as k = k¯ p + k¯ p − k¯ s − k¯ As

(8)

Concerning Eq. (7), the CARS signal intensity is proportional to laser beam intensities and it also is proportional to N2 . The dependence of the CARS signal on the phase mismatch is illustrated in Fig. 2 [11]. If a good phase matching is achieved, k = 0 (in case of gases) and the CARS intensity varies quadratically with the interaction length; because in general k = / 0 (case of solids), so the CARS intensity reaches a succession of progressive weaker maxima. This means that the phase matching condition may limit the CARS signal intensity for longer path length. Therefore, phase matching of CARS beams is the impulse for CARS process, participates photons with a momentum: k¯ As = k¯ p + k¯ p − k¯ s

(9)

Fig. 3. The commonly employed different phase-matching schemes in CARS processes: (a) collinear CARS, (b) BoxCARS, and (c) folded BoxCARS.

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

5

The folded BoxCARS configuration permits a large angular separation of the input laser frequencies, and hence the CARS beam is completely spatially separated from the incident laser beams. In this approach, the ωp beam is spilt into two components which are crossed at a half-angle of ˛. The Stokes ωs beam is introduced at angle producing a phase-matched CARS signal at angle . The appropriate phase-matching angles are related obeying the following simple geometric considerations [12]:

are:

ns ωs sin = nAs ωAs sin 

It has an average value for the observant M where

ns ωs cos = nAs ωAs cos  = 2np ωp cos ˛

(10) (11)

where ns , np and nAs are the refractive indices of the medium under study at frequencies ωs , ωp and ωAs . CARS spectra are recorded as a function of ωs with fixed ωp . This can be achieved by two different methods; the first method is scanning CARS, in which scanning in frequency narrow-band ωs dye laser is needed while detecting the CARS signal by means of a photo multiplier tube mounted behind a set of filters. Furthermore, the spectral resolution is determined by the line-widths of the two lasers those providing the frequencies ωp , ωs . The second method is broad band CARS which is based on employing a broad band ωs dye laser and resolving the resultant spectrum on an optical multichannel analyzer. The efficiency is in general determined by the resolution of the detection system. In broad band CARS the rotational molecular structures are often obscured, while in the scanning CARS the rotational transitions are resolved by tuning the lasers to the appropriate line widths. Scanning CARS is an important technique for identification of molecules and also simplifying temperature measurements, especially in a thermal equilibrium condition and stable media like the pyrolysis laminar flames. On the another hand, the use of a broad band dye laser allows a single-shot detection of the full spectrum, which corresponds to about 10 ns interrogation time, whereas averaging these single-shot spectra is usually adopted to improve statistics. For temperature diagnostics on non-equilibrium systems and in case of turbulent media, the broad band CARS with its inherent time advantage would be utilized.

2.2. Calculation of CARS susceptibility The damped harmonic oscillator serves as a model for the classical calculation of CARS susceptibility (3) , where the medium is polarized in a nonlinear fashion by the intense electromagnetic field, Eq. (5) [9]. This approach connects (3) to the macroscopic properties of molecules and the resultant expression depends on the bulk susceptibility of the medium. In other words, susceptibility can be derived quantum mechanically (connecting (3) to the microscopic properties of molecules), in a more rigorous approach. Such approach involves the computation of the expectation value of the electric dipole moment induced by a third power field. The technique is to solve the equation of motion for the density matrix “Liouville-equation” using time-dependent perturbation theory. Because (3) , is a nonlinear third-order effect, so a third-order perturbation expansion is required. Detailed expressions for (3) have been derived in different articles [5,13–16]. For gross and homogeneous ensemble of gas molecules, the use of the wave function |  in appropriate Hilbert space to describe the state of a quantum mechanical system gives only the probability distribution of the individual systems of that ensemble over the possible states, on a condition that the method does not determine the exact state for each individual system. For a system of gas molecules ensemble in the state | i , the probability pi conditions



0 ≤ pi ≤ 1,

pi = 1

(12)

i

where the density operator (statistical operator) is defined as: =



pi |

i 

i|

(13)

i

M =



pi 

i |M|

i

= Sp( M)

(14)

i

M sets the theoretical quantum expectation form in the net state | i  of the ensemble and the statistical averaging over the expectation values. The time evaluation for this ensemble under the action of the Hamiltonian operator , is described by the Liouville-equation of the form: i¯h

d (t) = [H, (t)] dt

(15)

The stationary solution in a thermodynamic equilibrium for an equilibrated density operator H (Boltzmann’s distribution) is =



H 1 exp − Z kT





 H 

Z = Sp exp −

,

kT

(16)

where the normalization factor Z is a states sum term. For a system of gas molecules in a coherent field, the Hamiltonian operator for a molecule is given by H(t) = H0 + V (t)

(17)

where H0 is the Hamiltonian for an unperturbed isolated molecule and V(t) is the dipole interaction energy:



¯ V (t) = −P¯ · E(t) =−

Pi Ei (t)

(18)

i

P¯ is an electric dipole-moment operator and E(t) is the electric field of the coherent radiation. The mutual interaction of molecules takes into consideration an additional relaxation – Hamiltonian operator HR (t); coupling this dynamic system with the calculation of a dissipative process, yields: H(t) = H0 + V (t) + HR (t)

(19)

Substituting Eq. (19) into Eq. (15) yields: i¯h

d (t) = [H0 + V (t) + HR (t), (t)] dt

(20)

So, the Liouville-equation (Eq. (20)) could be rewritten as i¯h

d (t) = [H0 , (t)] + [V (t), (t)] + [HR (t), (t)] dt

(21)

whereas, the last term can take the following form [16], [HR (t), (t)] = R (t)

(22)

where R is considered as a relaxation (damping) matrix and it is determined by stochastic processes such as spontaneous emission of light and the collisions between molecules. Approximations made on the collision mechanisms lead to a simple expression for the damping terms: (1) Impact approximation assumes that the time duration of collision is smaller than the time interval between two collisions and also smaller than the typical interaction time between

6

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

Fig. 4. The interference of a Raman line with the non-resonant background.

molecules and radiation fields. This approximation is valid for diluted media such as gases. (2) Isolated line approximation assumes that there are no overlapping or close-by lines, such that the probability of a collision transfer from one line to the other would be appreciable. Also the coupling by a relaxation among the off-diagonal matrix elements can be neglected [5,16]. This assumption is allowable when the distance between neighboring lines is greater than the inelastic collision frequency, so it leads to the fact that the energy transfer between the rotational levels is very improbable. With all the above approximations, the damping term in Eq. (21) can be written as



(n)

(t) =

∞ n  P

···

˛,ˇ m=0 −∞

 V (tp )

∞  m

{K + (tq+1 , tq )

−∞

q=1

n−m

×

p−1

d ˛˛ |R = − ˛˛ ˛˛ + dt d |R = − ˛ˇ ˛ˇ , dt ˛ˇ

˛ˇ =



i¯h

K

−

  (tp , tp+1 )U(tp+1



W˛ˇ = Wˇ˛ exp

˛= / ˇ

E˛ + Eˇ



kT

(26)

where E˛ and Eˇ are energy levels of initial and final transitions, respectively, kB is Boltzmann constant and T is the absolute temperature. After this suitable transformation, the dissipative term of Eq. (21) becomes the first two terms of Liouville’s equation. Moreover, the representation of the density operator as a power series in a perturbation expansion is (t) = (0) (t) + (1) (t) + (2) (t) + · · ·

(27)

while the individual terms according to [13] in a general representation are:

 − tp )}

 dt1 . . . dtm . . . dt1 . . . dtn−m M

where (0) = W˛ˇ ˇˇ

−

V (tq ) (0) U(tq+1 − tq )}{K + (t1 , t0 )U(t1 − t0 )|˛ ˛ˇ ˇ|K − (t0 , t1 )U(t1 − t0 ) i¯h

(23)

˛= / ˇ

1 e ( ˛˛ + ˇˇ + ˛ˇ ) 2

following expression for W˛ˇ :

(24) (25)

where ˛ˇ is related to the reciprocal of the finite life time of state e |˛ as a result of spontaneous emission and inelastic collisions. ˛ˇ

is the full broadening of the absorption line between states |˛ and |ˇ, caused by phase-interrupting elastic collisions; W˛ˇ is the transition probability via inelastic collisions between states |˛ and |ˇ. Because of this principle, the microscopic reversibility gives the

 ˛,ˇ

(28)

(0)

|˛ ˛ˇ is the initial value of the density matrix

element at t = t0 , which is given in case of a thermodynamic equilibrium described by the Boltzmann’s distribution. The (tq )’s and (tq )’s are the times of various interactions between the molecules and the radiation fields. Through the summation over m, all the interactions distribution at the Kit and Bra sides of 0 (0) will be realized. The operator forms all the time directions of interactions on the  Kit side relative to them on the Bra side. K+ (tq+1 , tq ) and K − (tq , tq+1 ) are propagation terms carrying the wave function during the time between interactions at tq and tq+1 , and between interactions at  tq and tq+1 . The expression [. . .]M denotes an average over the statistical parameters of the molecules ensemble (collision, thermal  velocity). U(tq+1 − tq ) and U(tp+1 − tp ) are unit-step distributions, which maintain casualty for interactions occurring on the left and right hand sides of (0) . Reversible Feynmann diagrams provide a

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

useful technique for keeping track of the large number of terms arising in a perturbation solution as well as utilizing interactive methods of the succession of (0) (t). The expression of (3) (t) represents a sum of altogether 96 terms. This 96 contributors correspond to 96 Feynmann-diagrams, 16 of them are attached to Raman resonant processes. The remaining 80 terms are corresponding to non-resonant contributions. Taking Eq. (14) into consideration, the macroscopic CARS thirdorder polarization P¯ (3) (t), through a statistical average for the ¯ can molecular dipole-moments (3) (t) with the density matrix P, be determined [16]: P¯ (3) (t)

¯ = nSp( (3) (t)P)  (3) (t)P¯ ˇ˛ n

(29)

˛ˇ

˛,ˇ

here “n” is the gas molecules density. Comparing of Eq. (29) with the results of the classical calculation gives a quantum expression for (3) the susceptibility ijkl (ωAs ; ωp , −ωs , ωp ). This expression is divided (3)

= ˛As ij,˛ˇ

=

(3) ijkl

(30)

(3)

grams, NR is related to the 80 non-resonant diagrams. When the frequency-index-symmetry is taken into account then, (3) (ω, ; ω1 , ω2 , ω3 ) 1 ,j2 ,j3

ij1 ,j2 ,j3 (ω, ; ω1 , ω2 , ω3 ) = Pij

(31)

where P here is for the simultaneous permutation of the angular frequencies ω1 , ω2 , ω3 and the indices j1 , j2 , j3 . Therefore, the (3) Raman resonant part of ijkl can be expressed as [17]: (3)

(3)

R

ijkl,˛,ˇ

(ωAs ; ωp , −ωs , ωp )

˛ˇ

=

n  3

8¯h ε0

×

˛ˇ

1 ωˇ˛ − ωp + ωs − i ˇ˛

Pi,˛ı Pj,ıˇ ωı˛ − ωAs − i ı˛



×



(0)

(3)

R

ijkl



(0) −  )

Pk,ˇ Pl,˛ ωˇ − ωs + i ˇ

+



+



Pl,ˇ Pk,˛

Pl,ˇ Pk,˛ ωˇ + ωp + i ˇ

 + [j − l]

anti-Stokes, ˛As , polarizability matrix elements are introduced ij,˛ˇ as



=

1 h ¯ 



Pk,ˇ Pl,˛ ω˛ − ωp



Pk,ˇ Pl,˛ ω˛ − ωp

+

+

Pl,ˇ Pk,˛



ω˛ + ωs Pl,ˇ Pk,˛ ωˇ + ωp



n 3

8¯h ε0

˛ˇ

(0)

(0)

˛˛ − ˇˇ

ωˇ˛ − ωp + ωs − i ˇ˛

(˛As ˛s + ˛As ˛s ) ij,˛ˇ kl,ˇ˛ il,˛ˇ kj,ˇ˛



dˇ˛ d˝



= ij

2

 ω 4 s

ε20

2c

|˛sij,ˇ˛ |2

(36)

where c is the velocity of light in vacuum. If all the field polarizations (3) (3) are the same (i = k = j = l), the scalar value R of the tensor R is,

   nε0 2c 4  dˇ˛

4¯h2

ωs

d˝ ˛ˇ

ijkl

 ˇ˛ ωˇ˛ − ωp + ωs − i ˇ˛

2.3. Structure of CARS spectra

ω˛ + ωs − i ˛

The Raman resonant part includes summation of all Raman transitions ωˇ˛ in the scan range of ωp − ωs . For the other terms [j − l], the exchange of indices j and l is equivalent. For frequencies ωp , ωs and ωAs away from electronic transitions for the molecule (normal CARS), the imaginary part due to a photo resonance can be neglected. From [7,17], the Stokes, ˛skl,ˇ˛ , and

1 h ¯

(ωAs ; ωp , −ωs , ωp )

The CRAS susceptibility for a particular Raman transition results in a Lorentz profile and it is proportional to the population difference  ˇ˛ of the participated energy levels.

(32)

˛skl,ˇ˛ =

(34)

ωıˇ + ωAs

(37)

ωıˇ + ωAs + i ıˇ

ω˛ − ωp − i ˛



Because the frequencies ωp , ωs and ωAs are different from the transition frequencies of the molecules, the matrix elements of Stokes and anti-Stokes polarizability in the scan range ωp − ωs are considered constant and approximately equal. The differential cross-section of the spontaneous Raman scattering is given by [12,18]:

(3)

ı

Pk,ˇ Pl,˛

Pj,˛ı Pi,ıˇ

and the resonant part of the CARS susceptibility follows the expression:

R (ωp − ωs ) =



Pj,˛ı Pi,ıˇ

(0)

( ˛˛ −  )

(0) −( ˇˇ

+

+

ωıˇ + ωAs

(35)

(ωAs ; ωp , −ωs , ωp )

(3)

ijkl (ωAs ; ωp , −ωs , ωp ) =

ωıˇ − ωp

h ¯

Pj,˛ı Pi,ıˇ

+

ωı˛ − ωAs ≈ ωıˇ − ωp , ωˇ − ωs ≈ ω˛ − ωp , ωˇ + ωp ≈ ω˛ + ωs

=

while R includes the contribution of the 16 Raman resonant dia-



1  Pi,˛ı Pj,ıˇ ı

(3) R (ωAs ; ωp , −ωs , ωp ) ijkl

+ NR

Pi,˛ı Pj,ıˇ



and taking into account that ω˛ + ωs = ωˇ + ωp ωı˛ − ωAs = ωıˇ − ωp . In the scan range of CARS, ωp − ωs ≈ ωˇ˛ , according to [17] it follows directly that:

(3)

=

7

ωı˛ − ωAs

ı

to a resonant term R and non-resonant term NR , where (3) ijkl (ωAs ; ωp , −ωs , ωp )

1 h ¯



 (33)

Study the characteristics of the CARS spectra are carried out with respect to the physical characteristics of the scattering medium and the laser light sources. It comprises the interference effect and the influence of the macroscopic parameters (pressure and temperature) on the spectral width of the Raman transitions. It also presents the cross-coherence and the saturation by Raman scattering. 2.3.1. Physical spectrum of CARS The spectral width of the scattered radiation is determined by the pumping laser line widths convolution, thus the CARS spectrum line shape is the spectral profile of CARS nonlinear process conversion efficiency. The line shape (physical spectrum) of the CARS signals can be observed if the bandwidths of all lasers involved are very small when compared with the investigated Raman line. The CARS signal shows a saturation effect through the stimulated Raman scatter process (SRS), despite of increasing laser power. 2.3.1.1. Interference effect. Due to the coherent nature of the laser sources, interference arises from the background non-resonant susceptibility and neighboring resonance’s lines. This leads to an

8

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

asymmetry of the CARS signal line profiles and it slightly shifts the CARS signal peaks from the exact frequency positions of the corresponding Raman transitions. As shown from Eq. (37), (3) is a complex quantity comprises (3) (3) real, Re j , and imaginary parts, Im j . The physical CARS spectrum is proportional to |(3) |2 , which can be written in the following form:

 2        (3) (3) (3)  (3) 2 (3) 2  Re j + i Im j  = (Re j ) | | = NR +   j j j +



(3) 2

(3)

+ 2NR +



coll =



(3)

Re j

+



(3)

(3)

(Re j )(Re k )

(p, T, j)∼

j= / k

j (3)

(3)

(Im j )(Im k )

(38)

j= / k

The indices “j” and “k” are for the Raman transitions with angular frequencies ωj and ωk , respectively. The first term (1) contains a component for (3) corresponding to Raman transition ωj , term (2) corresponds to the presentation of isolated Raman lines, term (3) has no frequency dependence and it is related to the non-resonant background of that spectrum, term (4) is a mixing term for Raman (3) transitions ωj and ωk with NR and it corresponds to the interference of the individual Raman lines ωj and ωk with the non-resonant (3)

background. The non-resonant susceptibility NR is frequency independent, its spectral behavior is determined from term (4) through the real part of (3) . According to Eq. (38), for a single Raman line ωj , the real part of (3) is ωj − (ωp − ωs )

(3)

Re j ∼ −

[ωj − (ωp − ωs )]2 + j2

(39)

while the corresponding imaginary part of (3) is (3) Im j ∼ −

j [ωj − (ωp − ωs )]2 + j2

(3) j

(3)

(42)

p

(43)

(T )1/2

which follows Lorentz profile for the corresponding transition. If

0 is the Lorentz width of a particular Raman line at a given pressure (p0 ) and temperature (T0 ), so the Lorentz width at another temperature T and pressure p is given by

(p, T ) = (p0 , T0 )

(T0 )1/2 p p0 (T )1/2

(40)

(41)

i.e. the CARS intensity for a single line is proportional to the imaginary part of susceptibility which delivers a Lorentzian profile. The interference of a Raman line with the non-resonant background is represented in Fig. 4. Beside shifting the maximum to the lower frequency side, an asymmetry for the line profile arises with a characteristic minimum on the higher frequency side. Therefore, (3) (3) the ratio of NR /|R | limits the applicability of the CARS measurements and influences the signal to noise ratio. 2.3.1.2. Broadening mechanisms of CARS spectral lines. The broadening effects influencing the CARS profiles have been taken into account considering the exact line shapes of particular transitions. Stark, pressure and Doppler broadening are three different broadening mechanisms. The first one appears for vibrational–rotational transitions with j = / 0, and with values for the CARS-laser intensities in the range of 1014 –1015 W m−2 . In many experiment, the laser intensities are seven orders of magnitude less, including measurements of the Q-branch with j = 0. Therefore the Stark broadening can be neglected, considering only the characteristics of pressureand Doppler-broadening.

(44)

For many cases the classical model of pressure broadening is note suitable. For diatomic molecules, the realized models for collision broadening are the semi-classical theory of Robert and Bonany [20] and the method of Rahn et al. [21]. The first model represents a short-range interaction potential as a sum of atom–atom Lennard–Jones potentials, introducing a parabolic trajectory for close collisions instead of straight path. The quasi-classical model represented by Rahn is based on atom–atom pair wise additive short-range potential and a Monte Carlo averaging over the collision parameters. Utilizing the real intermolecular potential and taking into account the j-dependence of the linewidth gives the following expression [22],

(p, T, j) = (AT −a − BJT −b )p cm−1 (HWHM)

where |R |2 ∼Im j

1 coll N v¯

where  coll is the molecular collision cross section, “N” is the molecular density and v¯ is the average thermal velocity. By Maxwell’s distribution, using the ideal gas law, one can write the following relation:

(3) 2

(Im j ) + (NR )

j

2.3.1.2.1. Pressure broadening. The pressure broadened Raman line width for an isolated transition is represented by the damping constant in Eq. (37). It is coupled with inelastic life timelimiting collisions and by the elastic collisions which dephase the vibrational or rotational motions. For the vibrational Q-branch transitions of interest, the rotational inelastic collisions are the dominant contribution to the line width [10]. From the kinetic gas theory, the time interval between two collisions is [19]:

(45)

which could be applied to linear molecules. For T ≥ 900 K, the values of the parameters for gaseous nitrogen are A = 4 × 10−3 , B = 9.3 × 10−3 , a = 0.71 and b = 1.45 with p in mbar. Now it is clear that the Q-branch line widths do not have an appreciable dependence on the vibrational band, which means that the Raman line widths are assumed to be due to only rotationally inelastic collisions. This means that the vibrational relaxation and all elastic defacing processes are assumed not to have a contribution to the line-shape [21,22]. Thus the collision line widths j are given by

(p, T, j) = j =



ij (HWHM)

(46)

i= / j

where  ij is the first-order rate constant of the transition probabilities from rotational level “j” to rotational level “i” within a vibrational state. The summation is only for transitions having equal nuclear spin symmetries: |j − 1| = 2n, n ∈ N. The transition rates  ij can be calculated using the Modified-Exponential EnergyGap (MEG) model [23–26]. If the life time-limiting rotationally inelastic collisions are predominant, then the line widths of pure rotational Raman, microwave, infrared and vibrational Raman, all should be roughly the same. Therefore, a good approximation to the unknown Q-branch Raman line widths might be provided by the microwave line width data [10].

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

2.3.1.2.2. Doppler broadening. The thermal motion of molecules causes broadening of spectral lines due to Doppler effect. Therefore, Doppler broadening belongs to non homogeneous broadening mechanisms. The broadening for a resonant frequency ωj of a molecule of mass, mm , moving in z-direction is ωj (z ) = ωj



z 1+ c



(47)

Considering the integration of the velocity distribution function f(z ) over all the possible velocities z of the molecules and assuming a thermal equilibrium, i.e. Maxwell–Boltzmann’s distribution, so f (z ) =

 m 1/2 m 2kB T



exp

mm z2 − 2kB T



ε0 n 42h ¯

(3)

×

×

mz2 2kB T

 dz

 dj  d˝

 2c 4  m ωs

 j

j

1/2 

2kB T

i() W ωD



dj d˝



∞  j

j

exp −∞

ωD = ωi

mc 2

(53)

The CARS intensity is obtained by inserting the fact (53) in the CARS polarization expression and integrates it over all spectral profiles of the three laser beams. Besides, no statistical correlation between the individual beams must exist. This is valid for the Stokes-beam against the pump-beams but not for the pump-beams mutually, especially when they originate from the same laser. Farrow et al. [31] indicated that, to get uncorrelated pump beams, it is required to introduce a delay in one pump-beam path equal to or more than the coherent length:

ωp − ωs − ωj + i j

(54)

I(ωAs ) =

2 L2 ωAs



|(3) (ωp1 − ωs ) + (3) (ωp2 − ωs )|2 Ip

16ε20 c 4

×(ωp1 )Ip (ωp2 )Is (ωs )ı(ωp1 + ωp2 − ωs − ωAs )dωp1 dωp2 dωs

ωs

(55)



(49)

ωD

= 1.753 × 10−20 (T [K])1/2

2c ωp

According to [30–33], the CARS intensity at frequency ωAs is given by:

 2c 4

where ωD is the Doppler width of a forward scattering Raman transition [27] which can be expressed as

 2k T 1/2 B

(3) (ωp − ωs ) → (3) (ωp1 − ωs ) + (3) (ωp2 − ωs )

Lc =

1 ε0 n = ωj (1 + (z /c)) − (ωp − ωs ) − i j 42h ¯ 1/2

Therefore, the CARS susceptibility must symmetrically be divided relatively between both pump laser beams,

(48)

By substituting of f(z ) into Eq. (35), the resonant part of the CARS susceptibility is given by R (ωp − ωs ) =

9

The integration of all collected signals by the photomultiplier (scanning CARS), follows that Eq. (55) is integrated over all anti-Stokes frequencies where: IAs =

ωi (m [kg])1/2

2 L2 ωAs





Ip (ωp1 )

16ε20 c 4



× (ωp2 )dωp2 +

(50)



Is (ωs )|(3) (ωp1 − ωs )|2 dωp1 dωs

Ip



(3)

Is (ωs )

Ip (ωp1 )|

2

(ωp1 − ωs )dωp1 | dωs (56)

moreover, i W (z) = 

∞

exp(−t 2 ) dt, z−t

Im(z) > 0

(51)

−∞

is the complex error function [28,29]. The real part of the complex error function (imaginary part of (3) ) is equivalent to a normal Voigt profile (convolution on a Lorentzian of any Gaussian). 2.3.2. Influence of laser characteristics on CARS spectra Because of the nonlinear and coherent characters of the CARS process, the spectral profile is influenced in a complicated manner by the optical and statistical properties of the laser beams employed to drive the process. So it is essential for accurate CARS temperature measurements to incorporate those factors properly into the simulation procedure [30]. The cross coherence effect and the saturation of CARS-signal through the stimulated Raman scattering (SRS) will be discussed next. 2.3.2.1. Cross coherence-effect. The effect of laser line width and its statistical characteristics on the recorded CARS profile is very important especially when the profile is composed of more than a single Raman line, their individual line widths and separations being of the same order or less than the laser widths. The exchange of two pump photons lying within the laser line width with frequencies ωp1 and ωp2 , respectively, (four colors CARS) generates – due to the symmetry of CARS process – CARS photons which have the same frequency and phase, because in both cases: (ωp1 − ωs ) + ωp2 = ωAs = (ωp2 − ωs ) + ωp1

(52)

Eq. (56) contains two terms, the first one is given by Yuratich [32], for this term the CARS process includes statistically independent pump photons. In contrast, Kotaoka [30] and Teets [33] showed that the second term, which is called cross coherence, is a pure statistical element. It is obtained from all coherent superimposed contributions of CARS polarization, produced by fixing the Stokes frequency and exchange both pump photons. In case of CARS with laser spectral lines having Gaussian profiles with half widths ωp , ωs , the CARS intensity in Eq. (56) could be rewritten as: IAs =

2 L2 ωAs

16ε20 c 4

((ωp2 + ωs2 ))

× |(3) (ω)2 |dω +

1 ωs ()1/2





1 1/2

exp

exp

−

(ω − (ωp − ωs ))2



ωp2 + ωs2

   ω − ωs 2 −

ωs

⎤  1/2 

2    ω − ωp 1   × exp − (3) (ω − ω) dω dω⎦ ωp  ωp ()1/2  (57)

2.3.2.2. Saturation of CARS spectra. In case of low susceptibility values, as often present in plasma, increasing the laser power could be a solution to increase the CARS signal, and hence its detection limit. But there are factors which define the used laser power. The most crucial factor is the stimulated Raman scatter process (SRS), where

10

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

the resonance condition of this process is ωp = ωs + ωj

(58)

which is identical to the CARS resonance condition. SRS reduces the difference of population densities,  j , of the participating rotational levels. Thus the CARS signal shows saturation despite increasing laser power, whereas the CARS intensity is proportional to  j2 . This perturbation on the population densities introduces a deviation from Boltzmann’s distribution. A detailed description of saturation through SRS can be found in [34,35]. The influence of the saturation is given by [9]: 0.1 T2

Ip Is <



h ¯ ωs2 4c

2

dj

−1

(59)

d˝

where “” is the average time between two angular momenta distributing collisions and T2 is the transversal relaxation time [9]. Furthermore, normalization of Eq. (59) by the differential scattering cross sections ˙ j includes frequency dependence as follows:



Ip Is <

0.1 ωs 2 (¯hc) 2c T2 ˙j =

4 d −1 j d˝

N2

Q,N2

(60)

where the gross ˙ j gives light saturation. Acetylene has for example ˙ j = 7.2 which is a gross normalized differential scattering cross section. Wolf et al. [36] determined T2 for methane experimentally, where T2 = 1.4 × 10−10 s at p = 50 kPa and T = 300 K, the collision time “” of acetylene is 2 × 10−10 s. This gives Ip Is < 9.7 × 1025 W2 m−4 . The intensity product is 3.1 × 1025 W2 m−4 for average focus diameter of = 200 ␮m and pump- and Stokes-beams with pulse energy of 5.0 and 1.0 mJ, respectively, with a saturation in the order of 32%. Thus the saturation may be neglected for laser power of order of 10 kW at STP. No saturation has been experimentally observed for the measured spectra of acetylene and hydrogen in the pressure range of 105 –104 Pa. 2.4. Theoretical CARS spectra for selected molecules In this section theoretical calculation of CARS spectra for a few selected molecules such as H2 and N2 are presented. The fundamentals of this calculation are drawn depending on the determination of Raman scatter cross section as a function of , j, frequency and polarization of the beam. It also depends on the population densities and the difference between population densities of the vibrational–rotational states together with the frequency positions of the Raman transitions of the spectral lines of the studied molecules. By substituting the CARS susceptibility from Eq. (49) into Eq. (57), it is possible to obtain the Q-branch spectra of acetylene, hydrogen and nitrogen under the consideration of the cross coherence, Doppler and collision broadening. The relative Raman scattering cross sections of the different gases were determined relative to that of the Q-branch of the vibrational Raman band of nitrogen. The relative normalized differential Raman scattering cross section [37] is: ˙j =

(p − 2331 cm−1 )

−4

(d/d˝) (d/d˝)Q,N2

(61)

where the absolute normalized Raman cross section of N2 is given by [37]:

 d  d˝

−48

Q,N2

= (5.05 ± 0.1) × 10



1 × p − 2331

(, j, k) =



1 E(, j, k) (2j + 1)gI exp − z kB T



(63)

where , j are the vibrational and rotational quantum numbers, respectively, and k is a rotational quantum number for nonlinear molecules, which is characterized by a (2j + 1)-fold degeneracy for the probability of the angular momentum related to the molecules configurations. The z-component of the angular momentum in space coordinates system could takes (2j + 1) possible values. As the coupling between vibrations and rotations is neglected, the partition function is represented as the following product [44]: z = zrot zvib

0.1 × 1.956 × 108 W s2 m−4 T2 ˙j

(p − j )−4

The numerical values of ˙ j and all Raman data for a few important molecular gases are summarized in Table 1 [37]. The Raman data of trimethylboran are from Ref. [38], while for diboran from Ref. [39], for acetylene from Ref. [40], for disilane from Ref. [41] and the remaining values are from Refs. [37,42,43]. The population densities of vibrational–rotational states described at thermal equilibrium by Boltzmann’s distribution by

−4

6

cm sr

−1

(62)

(64)

where zvib is the partition function of a fundamental vibratory mode of vi with a degeneracy factor gI in a harmonic oscillatory approach [44]. At thermodynamic equilibrium, Trot = Tvib = T, and zrot =



 E( = 0, j, k) 

(2j + 1)g1 exp −

and zvib =

(65)

kB Trot

j,k



(zvib (vi ))gi

(66)

v1

zvib (vi ) is satisfied as follows: zvib (vi ) =

∞ 



exp

=0



−

( + 1/2)vi kB Tvib



× 1 − exp −

vi





= exp −



vi 2kB Tvib

−1 (67)

2kB Tvib

where  is the vibrational quantum number corresponding to the fundamental mode vi . 2.4.1. Calculation of hydrogen spectra The energy of the rotational–vibrational levels of hydrogen molecule in the electronic ground state X 1 ˙g+ can be represented by [45]: 2

3

E(, j) = G + B j(j + 1) − D j2 (j + 1) + H j3 (j + 1) + I j4 (j + 1)

4

(68) 1H 2

The corresponding molecular constants of for 0 ≤  ≤ 4 are listed in Table 2. The nucleus degeneracy factors of H2 are the same as for acetylene where, gI = 1 (for even j), = 3 (for odd j)

(69)

For very light molecules as 1 H2 , the Raman cross section must be multiplied by a j-dependent factor [42], as:



1+

2

˛0 j(j + 1) 2ωe

(70)

The numerical data for ωe and ˛0 [44] are listed in Table 2. In Ref. [10], the pressure broadening was measured with

= 1.5 × 10−3 cm−1 at p = 105 Pa and T = 300 K. Applying Eq. (44) a value for A = 1.28 × 10−4 is obtained.

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

11

Table 1 Raman data for some gas molecules. Column 3: vibrational frequency (cm−1 ) of the ground state. Column 4: cross section relative to the Q-branch of nitrogen, column 5: degree of depolarization in case of non-polarized light, and column 6: degree of depolarization in case of polarized light, where s and As are valid for p = 532 nm. Molecule N2 1 H2 12 C2 H35 Cl 11 B2 H6

Vibrational mode

Frequency (cm−1 )

˙j 1.00 4.0 3.2

16

2330 4155 1612 2886 2527

4 2 /45˛2

s (nm)

As (nm)

0.18 0.07

0.152 0.051

0.4

0.50

607.3 683.0 581.9 628.5 614.6

473.3 435.7 490.0 461.2 469.0

628.8 571.2 552.0

461.0 497.8 513.4

648.3 594.4 549.9

451.1 481.5 512.2

n

p

11

B(11 CH3 )3

s CH3 (a1 ) ıs CH3 (a1 ) s BC3(a1 )

2893 1290 680

12

C2 H2

1 (g+ ) 2 (g+ ) 4 (g )

3372 1974 612

12

CH3

1 (a1 )

3005

633.2

458.7

12

C2 H6

1 (a1g ) 3 (a1g ) 10 (e.g.) 11 (e.g.)

2954 993 2969 1468

631.2 561.7 631.8 577.1

459.7 505.3 459.4 493.5

12

CH4

1 (a1 ) 3 (f2 )

2917 3020

8.56 4.82

629.7 633.8

460.5 458.4

12

C2 H4

1 (ag ) 2 (ag ) 3 (ag )

3022 1623 1342

6.9 1.5 2.8

633.9 582.3 572.9

458.3 489.7 496.5

14

NH3

1 (a1 )

3334

6.4

646.7

451.9

28

SiH4

1 (a1 )

2187

602.0

476.6

28

Si2 H6

1

2163

601.2

477.1

2.1 7.2 0.87

2.4.2. Calculation of nitrogen CARS spectra The energy of the rotational–vibrational levels of 14 N2 in its electronic ground state X 1 ˙g+ can be written as a power series in +1/2 and j(j + 1) [46] as:



E(, j) = ωe  + + ωe Ze



1 2





− ωe e  +

1 + 2

4

1 2

2



+ ωe Ye  +





+ · · · + Be − ˛e  + 2

+· · ·] × j(j + 1) − [De + · · ·]j (j + 1)

2

1 2



1 2

2 

+ e  +

1 2

2

0.215 0.059 3/4

6/7

0 6/7

0 3/4

0.402 0.0854

0

Table 3 Molecular constants of 14 N2 . ωe (cm−1 ) ωe xe (cm−1 ) ωe ye (cm−1 ) ωe ze (cm−1 ) Be (cm−1 ) ˛e (cm−1 )  e (cm−1 ) De (cm−1 )

ω0 (cm−1 ) ˛0 (cm−1 ) ˇ0 (cm−1 ) 0 (cm−1 ) ω1 (cm−1 ) ˛1 (cm−1 ) ˇ1 (cm−1 ) 1 (cm−1 )

2358.5849 14.23245 −2.106 × 10−3 −2.583 × 10−4 1.998241 0.0172978 −4.15 × 10−5 −5.76 × 10−6

m (14 N2 ) (kg)

2329.92 −0.0173808 −9.16 × 10−9 −2.58 × 10−13 2301.2551 −0.0174638 −1.00 × 10−8 −2.58 × 10−13

4.651765 × 10−26

(71)

where the first term on the right hand side of Eq. (71) is the vibrational energy of a harmonic oscillator, while the next three terms are related to the anharmonicity of 14 N4 -molecule’s vibrational potential. These four terms represent pure vibrational energy of nitrogen molecules. The remaining terms of the formula describe the rotational structure of a given vibrational state. The contribution ∼j(j + 1) corresponds to the energy of rigid rotor. The corrective terms −˛e ( + (1/2)) and  e ( + (1/2))2 arise from a rotational–vibrational coupling, which change the average distances between the two nuclei with increasing the vibrational quantum number. The contribution ∼j2 (j + 1)2 accounts for the centrifugal distortion of the molecule. Both vibration and rotation energies change the mean

value of the molecule’s bond length and consequently influence its rotational energy via the momentum of inertia. The molecular constants of 14 N2 which appear in Eq. (71) are listed in Table 3 [42]. An expression for calculating the line positions of the Q-branch ( = 1, j = 0) CARS spectra of the first two vibrational bands can be written as [42], 2

ωj = ω + ˛ j(j + 1) + ˇ j2 (j + 1) +  j3 (j + 1)

3

(72)

The nucleus spin degeneracy factor gI for 14 N2 follows the rule: gI = 6 (for even j), = 3 (for odd j)

(73)

Table 2 Molecular constants of 1 H2 . 

G (cm−1 )

B (cm−1 )

0 1 2 3 4

0.00 4161.14 8086.93 11782.36 15250.31

59.3301 56.3672 53.4726 50.6167 47.7858

m (4 H2 ) (kg)

0.33470876 × 10−26

ωe (cm−1 )

D (cm−1 ) 0.04544 0.04377 0.04233 0.04088 0.03956 4402.93

H (cm−1 ) −5

4.48 × 10 4.23 × 10−5 4.14 × 10−5 3.97 × 10−5 3.79 × 10−5 ˛e (cm−1 )

L (cm−1 ) −3.49 × 10−8 −3.13 × 10−8 −3.15 × 10−8 −3.01 × 10−8 −2.85 × 10−8 3.0525

12

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

Fig. 6. Pulse sequence for time-resolved femtosecond CARS. A first pulse with sufficient bandwidth to contain ωp and ωs excites vibrational coherence, which is proposed by a second pulse after a delay , Ref. [58].

sured I as (0)

Fig. 5. Comparison between a measured N2 CARS spectrum and its theoretical fitted spectrum at room pressure and temperature.

The constants for calculating Lorentzian line width (HWHM) of nitrogen according to Eq. (45) are [18,22]: A = 4 × 10−3 , B = 9.3 × 10−3 , a = 0.685, b = 1.443 at T ≤ 850 K. A = 4 × 10−3 , B = 9.3 × 10−3 , a = 0.710, b = 1.450 at T > 850 K. where the pressure p is measured in mbar. Evaluation of the experimental CARS spectra means reading out information concerning the molecular number density N and the excitation rotational temperature Trot , which via Doppler-broadening is the transitional temperature of the considered gas. Therefore, the measured CARS spectrum has to fit a theoretical spectrum, minimizing the squares of differences. Fig. 5 illustrates comparison between a measured N2 CARS spectrum and its theoretical fitted spectrum at room temperature and pressure, where the error in measuring the temperature is less than 7%. 3. Advances in CARS spectroscopy 3.1. Advances in CARS experiments 3.1.1. Determination of inhomogeneous broadening In addition to methods such as the spectral hole burning, singlemolecule spectroscopy, fluorescence line narrowing and photon echo, an alternative method for distinguishing the inhomogeneous broadening from the homogeneous width of the vibronic spectra was reported [47]. This method depends on that the excitation profiles of CARS and coherent Stokes Raman scattering (CSRS) of identical molecules are having same shape, while only the excitation spectrum of CSRS is shifted in wavenumber (the frequency of Raman mode) to the high frequency side. Furthermore, for molecules in solvents or impurity centers in crystals the excitation profiles of CARS and CSRS obtain different shapes due to the ever-existing inhomogeneous profiles. Thus the comparison of the intensities of CARS and CSRS could provide the estimation of homogeneous and the inhomogeneous broadening using the half-width of the absorption band and the Raman frequency ωj of a Raman mode j. For this, it needs to measure only two points/intensities: (1) the CARS signal ICARS (˝ = ω0 + ωj ) at pump frequency ωp = ω0 (e.g., at the absorption maximum) and the Stokes frequency ωs = ω0 − ωj ; (2) shifting the pump frequency to ωp = ω0 + ωj , and the Stokes frequency to ωs = ω0 , register the CSRS signal ICSRS (˝ = ω0 − ωj ). Consider the case of moderate Gaussian distribution of pure electronic frequencies and I(ωp ) = I (0) (ωp ) + 2G I (1) (ωp ), so the inhomogeneous broadening, G , is determined through the mea-

2G =

ICARS (ωp ) (1)

D(ωp )/I − ICARS (ωp )

(74)

where the difference in the intensities, I = (ICSRS − ICARS )/ICARS ,

(75)

and (1)

(1)

D(ωp ) = ICSRS (ωp + ωj ) − ICARS

(76)

The proposed method has an advantage that it may be used for examining inhomogeneous broadening in biological molecules at room temperature. 3.1.2. Time-resolved two color single-beam CARS Quantum coherent control first developed as a theoretical field [48]. Recently, due to the advance of femtosecond laser technology and pulse-shaping techniques, it has been successfully applied to various systems such as atoms, crystals, molecules in gas or liquid phase, or biological compounds. Coherent control is selectively manipulating quantum states through the interaction with laser light [49,50] and it has applications in nonlinear optics [51,52], and nonlinear spectroscopy as a single-beam coherent anti-Stokes Raman scattering [53]. Since CARS is typically performed with laser pulses of different color, therefore, when ultrafast lasers are used all these frequencies can be obtained in one broadband femtoseconds pulse. If a delay is established between the pump and the Stokes pulses and the separate probe pulse, the molecular vibrations can be directly observed in time-domain [54]. For any experimental realization of single-beam CARS, a broadband laser source and a femtosecond pulse shaper [55,56] are needed. Such optical bandwidth can be obtained from compressed supercontinuum output of microstructured fiber, which is pumped by a standard 100-fs oscillator [57]. Based on coherent control, time-resolved single-beam CARS is proposed [58]. From a broadband supercontinuum source two delayed pulses for time-resolved experiments of the pump-probe type are derived. The pulses have sufficient bandwidth to coherently excite molecular vibration, see Fig. 6. The experimental setup is shown in Fig. 7. The two-color double pulses are generated in the shaper by applying a linear phase function to shift the red part of the excitation spectrum, which is to function as pump and Stokes pulse (E1 ). For the blue part of the excitation spectrum, which is destined to be the probe pulse (E2 ), a constant zero phase is written on the SLM (spatial light modulator). The reason for not using a triangular phase (linear spectral phases of opposite slopes) to generate the double pulses is to avoid any artifact oscillations. The discontinuity in the applied spectral phase leads to some minor pre- and after-pulses in the time domain. The intensity contained in these

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

13

Fig. 7. Experimental setup, where supercontinuum from a standard 100-fs oscillator is generated and shaped for single-beam CARS spectroscopy. FI: Faraday isolator, SLM: spatial light modulator, KE: knife-edge in the Fourier plane to cut off the blue wing of the excitation spectrum, MO1-2: microscope objectives, IF: interference shortpass-filter, Ref. [58].

pulses is almost negligible and did not show to be destructive for the nonlinear CARS measurement. Furthermore, additional amplitude shaping designed as spectral apodization would allow completely justifying this effect. 3.1.3. High spectral resolution multiplex CARS spectroscopy The CARS microscopy for chemically selective imaging of complex (e.g., biological) systems may include low signal levels and heating of the samples. These two limiting factors suggest utilizing femtosecond lasers due to their low average powers. However, a femtosecond pulse width implies low spectral resolution (e.g., ∼200 cm−1 relative to sample line widths of 15 cm−1 ), which reduces the resonant to non-resonant CARS signal, and consequently, the chemical selectivity. Multiplex CARS have all employed broadband (femtosecond) light sources to simultaneously excite several vibrational modes in the sample, followed by a probe pulse that is of narrow bandwidth. This is accomplished using a synchronized femtosecond/picosecond laser combination, wherein the picosecond laser defines the spectral resolution [59,60]. Dispersing bandwidth of a femtosecond pulse (e.g., with prisms or gratings) and then introducing a slit in the dispersed beam decreases bandwidth and converting the femtosecond pulse into a picosecond pulse [61]. Through the use of chirped laser pulses, the spectral resolution is defined by the temporal overlap of the 90 fs pulse with a temporally chirped pulse stretched to several picoseconds. The advantages of this technique are that the spectral resolution can be easily adjusted via the grating separation to match the natural line widths of the sample transitions, thereby increasing the ratio of resonant to nonresonant CARS signal. Since all of the pulses originate from the same laser, this technique also obviates the need for synchronizing two separate laser systems. Cheng et al. [59] in their multiplex CARS setup observed a decrease of overall spectral bandwidth of the CARS signal against the increase of chirp rate of Stokes pulse. They noted that the overall spectral bandwidth of their CARS signal decreased for increased chirp rate of the Stokes pulse. They [59] attributed this behavior to the decreased overlap of the spectral components of the chirped pulse. However, interesting effects occur when the probe pulse is chirped, namely increased spectral resolution and enhanced resonant signal to background [62].

An effective ‘temporal slit’ is introduced into the optical path since the 90 fs pulse temporally overlaps with only a small portion of the much longer ωp pulse. Due to the temporal chirp, this overlap also corresponds to only a small fraction of the ωp frequency bandwidth, as shown in Fig. 8 [62]. The effective spectral resolution of the CARS output in the case that the chirped (ωp ) pulse is much longer than the ωs pulse and is described as: ts × ωp = ωspec tp

(77)

where ts is the pulse width of the unchirped ωs pulse, tp is the pulse width of the chirped (ωp ) pulse, ωp is the spectral bandwidth of the chirped (ωp ) pulse and ωspec is the resulting effective spectral resolution of the CARS signal. The drawback with this technique is to remain CARS a picosecond rather than a femtosecond technique. The pulse-shaping techniques could overcome this drawback [63]. These techniques avoid undesired nonlinear effects by reducing the pulse peak-power and to target a specific mode or a group of selected modes. 3.1.4. Non-resonant wavepacket using a single ultrashort pulse Since CARS is sensitive to rovibrational resonances, thus, the application of femtosecond pulse-shaping adds a versatile mode selective excitation of rovibrational levels and a sharp probing of the excited modes. The picosecond CARS technique has several applications particularly in microscopy, as it will be seen later.

Fig. 8. A temporal slit where only a fraction of the ωp bandwidth generates CARS signals, Ref. [62].

14

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

Its most stringent technical requirement is the synchronization of pulses of different color. This is circumvented by the singlepulse CARS technique [53] that derives the three photons involved in the process from a single femtosecond pulse. Elimination of non-resonant third-order competing processes (usually referred to as non-resonant background due to their spectrally broad character) with also spectral selectivity is recovered by femtosecond shaping techniques that take advantage of the coherence and tensorial properties of the third-order emission. Since the control of the mode excitation only dealt with amplitude issues, using single-pulse CARS the group of Silberberg [63] reported the control in amplitude and phase over a vibrational wavepacket in liquid Toluene. The excited wavepacket is detected in a manner sensitive to the induced modes relative phases with improved probing technique for non-resonant background rejection. Shaping of a single femtosecond pulse generates phase-locked femtosecond pulse sequences sufficient for performing phase-sensitive twodimensional vibrational spectroscopy. This in principle can be applied not only to ground-state dynamics but also to probe excited state dynamics through either direct or multi-photonic absorption. 3.1.5. Generation of blue coherent radiation by SRS In 1962, Armstrong and Bloembergen [64] suggested the quasiphase matched interaction in media with periodic variations in the second-order nonlinearity (2) along longitudinal coordinate for efficient second harmonic generation and a blue coherent radiation production. The conversion efficiency from pump into anti-Stokes component does not exceed 3–6% [65,66], while for four-wave phase-matching systems the experimental anti-Stokes conversion efficiency does not exceed 15% [67]. A new four-wave mixing method of anti-Stokes generation by stimulated Raman scattering in media with variations of third-order nonlinearity (3) along longitudinal coordinate was presented [68]. As a result of numerical simulation of steady-state and transient stimulated Raman scattering, SRS, the quasi-phase matching condition in different media is determined and the conditions of high anti-Stokes conversion efficiency is obtained. The dependence of energy conversion from pump into anti-Stokes on the ratio of pump to Stokes input intensities is calculated, providing an efficiency of anti-Stokes generation exceeded 35%. Furthermore, it is found that the conversion efficiency depends on the ratio of dephasing time to pulse duration and essentially decreases with its increasing. The results can be used for the development of new effective Raman nonlinear-optical devices. 3.1.6. Time-resolved femtosecond CARS The interference between the resonant and the nonresonant signals in the four-wave-mixing technique (FWM) occurs due to the nonlinear interaction of the laser beams in ns-CARS, where the nonresonant signal limits the accuracy and degrades the sensitivity of that technique [69]. Because of the unavailability of high-repetition-rate and high-power ns lasers, the measurements are generally performed at low repetition rates (10–20 Hz), which lack the temporal resolution. Therefore, the study of unsteady phenomena in reacting flows is complicated. However, the use of femtosecond (fs) laser systems for CARS spectroscopy has three important possible advantages [70]: • Reduction or elimination of the nonresonant contribution to the CARS signal when the probe beam is delayed with respect to the pump beam. • Reduction or elimination of the effects of collisions on the CARS signal, thereby reducing modeling uncertainty and increasing signal-to-noise ratio. • Capability of generating signals at rates of 1 kHz or greater. The reductionor elimination of the nonresonant background and col-

lisional effects will greatly simplify the modeling of CARS spectra and improve accuracy by eliminating the need for information concerning Raman linewidths. Although the use of femtosecond laser pulses allows for an interaction with molecules on the time-scale of elementary selective chemical processes like bond breaking and formation, but the use of femtosecond lasers limits the spectral resolution considerably due to the inherently broad spectral bandwidth [71,72]. Several modes falling within the broad spectrum of femtosecond pulses are coherently excited [73,74]. However, it was demonstrated that [75] by shaping the femtosecond pulses a selective excitation of specific vibrational modes is possible. Selective excitation of CARS from the benzene solution is experimentally confirmed by shaping femtosecond laser pulses. Second harmonic generation frequency-resolved optical gating (SHGFROG) technique is adopted to characterize the original and optimal laser pulses. The results show that two-pulse CARS technique has good signal-tobackground ratio accompanied high sensitivity [76]. In time-resolved N2 CARS experiment [70], even with the large frequency bandwidths of the pump and Stokes beams, fs-CARS multiple pump-Stokes pairs contribute to the excitation of the same molecular transition creating a significant Raman coherence in the medium, as shown in Fig. 9. Many Raman transitions are excited with the same phase when both the pump and the Stokes beams are nearly Fourier transform-limited. Time-resolved fs-CARS has been used for the first time by Leonhardt et al. [77,78] to study the molecular beat phenomena in liquid phase benzene, cyclohexane, and pyridine. Hayden and Chandler [79] used fs-CARS for investigating the molecular vibrational dynamics of ground-state gas-phase benzene and 1,3,5-hexatriene. Schmitt et al. [80] used fs-CARS to study the ground- and excited-electronic state dynamics of iodine vapor. These studies demonstrated the potential for applying broad-bandwidth fs-lasers for gas-phase spectroscopic studies. Scherer et al. [81] used fs lasers for investigating the ultrafast dynamics of isolated molecule, while Dantus et al. [82] observed the molecular vibration and rotational dynamics. Similar to the fs-CARS technique, Zewail’s group [81,82] prepared an excited state with a pump beam and detected the laser-induced fluorescence signal when excited by a delayed probed beam. The molecular coherence is prepared by the overlapping pump and Stokes beam and is then probed by a delayed probe beam. Dantus [83] provided a comprehensive discussion of the coherent nonlinear spectroscopy based on ultrafast lasers. Lang et al. [84] used fs-CARS of the H2 molecule for determining molecular parameters and gas-phase temperature from the time-resolved oscillatory pattern of the Raman coherence following pump-Stokes excitation. Also fs-CARS has been used to investigate rotational energy-transfer processes [85] in a dense medium, for determining the concentration of ortho- and paradeuterium [86], and for measuring single-shot temperature by probing the hydrogen molecule using a chirped probe pulse [87]. More recently, fs-CARS has been used for the detection of bacterial spores in the presence of other molecules [88], the characterization of polymer thin films [89], studying a mixture of benzene and chloroform [75], background-free analysis of analytes trapped in aerogel [90], and temperature measurements in hightemperature flames, based on the frequency-spread dephasing rate after the initial impulsive excitation of the Raman coherence in the N2 molecule by fs pump and Stokes beams [70]. Temperature from the time-resolved N2 CARS signal is extracted by means of a simple theoretical model by concentrating on the signal decay during the first few ps after the pump-Stokes excitation. These decay results from the slight frequency mismatches between the neighboring Q-branch transitions and it is completely insensitive to collisions [91].

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

15

Fig. 9. Coherent excitation process in ns- and fs-laser-based CARS spectroscopy, Ref. [70].

3.1.7. Time- and frequency-resolved fs-CARS for quantum computing Feynman [92] suggested that controlled manipulation of quantum coherences can be used for quantum computation or information transfer. The concept is developed by the formal arguments presented by Deutsch [93]. Fs-CARS technique [94] combines the elements of preparation, manipulation, and interrogation of molecular coherences that are the key ingredients of quantum control applied in quantum chemistry and quantum computing. Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. Studies are implemented in iodine vapor, with its thermally occupied statistical rovibrational density serving as initial state. The evolution of the massive rovibronic superpositions, consisting of 103 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated frequency-resolved CARS. The third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single rovibronic transitions, whereas time-gated detection permits the projection of arbitrary rovibronic superpositions from the coherent third-order polarization. The images of the rovibrational coherences can be explained in terms of phase evolution in rotation–vibration–electronic Hilbert space, using time-circuit diagrams. Control and imaging of chemistry and the controlled manipulation of massive quantum coherences suggest the possibility of quantum computing. So the universal logic gates necessary for arbitrary quantum computing – all single qubit operations and the two-qubit controlled-NOT (CNOT) gate – are available in timeresolved four-wave mixing in a molecule. The molecular rotational manifold is naturally “wired” for carrying out all single qubit operations efficiently. Therefore, vibronic coherence is taken as an example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit. 3.1.8. CARS with frequency-shifted and shaped pulses from a photonic-crystal fiber The advent of photonic-crystal fiber (PCF) [95] – which has a silica–air or glass–air microstructure cladding – allows the creation of new light sources, based on nonlinear-optical spectral transformations of ultrashort pulses in strongly confined guided modes. Dispersion and spatial field profiles in PCF can be controlled by modifying the design of the fiber structure [96], offering new solutions for the enhancement of nonlinear-optical interactions of ultrashort laser pulses [97]. Efficient frequency conversion and

supercontinuum generation in PCFs have been shown to enhance the capabilities of chirped-pulse coherent anti-Stokes Raman scattering (CARS) [98] and coherent inverse Raman spectroscopy [99]. Novel light sources based on frequency shifting in PCFs provide a useful tool for the measurement of second-order optical nonlinearities in organic materials [100] and offer interesting new options in CARS microscopy [101]. Ivanov et al. [102] demonstrate that PCFs can provide frequency-shifted and temporally shaped pulses ideally suited for CARS spectroscopy. In their experiments, a delay of chirped pulses produced by the photonic crystal fiber with a specially designed dispersion profile are combined with the second-harmonic output of the Cr:forsterite laser (centered at 618 nm) to coherently probe a doublet of Raman resonances in the nonlinear response of a polyvinyl pyrrolidone (PVP) film which is used as a test object. Frequency-upconversion of fundamental-wavelength Cr:forsterite-laser pulses is performed through the nonlinearoptical spectral transformation of these pulses in PCFs [103]. The cross section view of the PCF structure is shown in Fig. 10. Dispersion of the PCFs is managed by scaling the geometric sizes of the PCF structure, as well as by varying the ratio of the core diameter to the period of the cladding and the air-filling fraction of the cladding. For the PCFs the core diameter is varied from 1.0 to 3.9 ␮m, with the ratio of the hole diameter to the period of the structure in the outer, 11-ring part of the cladding ranging from 0.55 to 0.85. The central wavelength of the fundamentalfrequency, 1.25-␮m Cr:forsterite laser output falls within the range of anomalous dispersion of the PCFs. Such pulses can form solitons as they propagate through the fiber.

Fig. 10. Spectrum of the blue-shifted PCF output pumped by 100-fs Cr:forsterite laser pulses with an energy of 50 nJ. The inset shows an SEM image of the photoniccrystal fiber, Ref. [103].

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frequency difference ω1 –ω2 of such a bi-harmonic pump should be chosen in such a way to resonantly excite Raman modes of the studied molecules. The PCF output represents a chirped pulse, where the instantaneous frequency changes from the leading edge of the pulse to its trailing edge. With the pulse width of the PCF output being much larger than the duration of the second-harmonic pulse; thus the effective frequency difference ω1 − ω2 can be tuned and scanned through a Raman resonance by varying the delay time between the pump pulses. The third, probe pulse is then scattered off the coherence prepared by the pump pulses and generates the CARS signal at the frequency ωa = 2ω1 − ω2 (Fig. 11b). So PCF has the capability to provide efficiently short light pulses with a tunable frequency shift and controlled chirp for time- and frequency-resolved measurements in coherent nonlinear spectroscopy. 3.2. CARS for gases, flames and combustion diagnostics CARS spectroscopy is successfully employed in the past four decades for gas-phase temperature, particle-producing diffusion flames, thermometry in supersonic combustion, and species concentration measurements in turbulent hot flows with temperature errors typically less than 50 K [107,108–112]. In addition CARS as a nonlinear-optical technique has been extensively used for plasma, flame, and combustion diagnostics and investigations of energy relaxation pathways in molecular systems. Therefore, the progress which has been achieved in using CARS for gas-phase, combustion diagnostics, i.e., temperature and species concentration measurements will be presented in the following section.

Fig. 11. Beam diagrams (a) and sequence of pulses (b) in chirped-pulse noncollinear CARS, Ref. [106].

Solitons generated by the input field undergo a continuous frequency down shift due to the Raman effect [104] and experience instabilities related to the third and higher order dispersion [105]. These perturbations force solitons to emit radiation energy in the form of dispersive waves in the anti-Stokes region. The central wavelength of this blue-shifted emission is controlled by the soliton-dispersive wave. The frequency of the frequency-shifted signal can thus be tuned by modifying the dispersion profile of the fiber. The spectrum of the frequency-shifted output of the PCF that is best suited for the purposes of this work is presented in Fig. 10. The spectrum features intense peaks are centered around 640 nm, which in combination with the 618-nm second-harmonic output of the Cr:forsterite laser, give an access, through the CARS process, to Raman resonances in the nonlinear response of polyvinyl pyrrolidone films. The blue-shifted PCF output is employed as a wavelengthsweeping field for chirped-pulse coherent nonlinear spectroscopy using the XFROG CARS technique [106]. The 618-nm secondharmonic output of the Cr:forsterite laser (with a frequency ω1 ) and the blue shifted PCF output (with a frequency ω2 ) are focused into a Raman-active medium in a non-collinear geometry (Fig. 11a). The

3.2.1. Nano-optical method of background suppression in CARS Limitations, due to the coherent background, arise whenever CARS is applied for the detection of low-density gas impurities, i.e., in a situation typical of ecological monitoring and detection of atmospheric pollution in a gas sample. As discussed before, the most efficient methods for the suppression of coherent background in CARS spectra are based on polarization, time-resolved techniques, and on coherence-control. All these approaches can suppress coherent background only at the sacrifice of the resonant signal amplitude. In addition, CARS measurements become more complicated because they need polarization elements, delay lines, and pulse shapers. Only polarization methods of coherent background suppression are well adapted to stationary CARS spectroscopy, time-resolved and coherence-control techniques which are essentially non-stationary. Accordingly, Zheltikov [113] proposed a nano-optical solution to overcome the problem of background suppression in CARS. Using the arguments of effective medium theory for weakly nonlinear nanocomposites a special design of a nanocomposite optimized for CARS gas-phase sensing is developed, where the pump field is predominantly concentrated in the areas of low refractive index. This spatially nonuniform pump-field distribution allows the coherent background in CARS spectra, related to the nonresonant cubic nonlinearity of the solid-phase host material, to be substantially reduced with respect to a standard CARS gas cell. The nanocomposite is consisting of a solid-phase host and voids filled with a Raman active gas (e.g., pores in a porous material). Such solid–gas nanocomposite design may provide a high level of nonresonant CARS signal from the solid host. But, however, the coherent nonresonant CARS background can be substantially reduced by tailoring the nanostructure, e.g., the network of pores in a porous material. The class of nanocomposites includes, in particular, nano- and mesoporous materials as well as silica aerogels. Assuming that the nanocomposite material consists of two components with dielectric constants ε1 and ε2 and whereas the CARS (3) (3) nonlinear-optical susceptibilities are 1 and 2 . Applying the

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

17

generic mixing rule for nonlinear susceptibilities in a weakly nonlinear isotropic nanocomposite, derived by Zeng et al. [114], it leads to: (3)

(3)

(3)

eff = A1 1 + A2 2 where





1  ∂εeff  A1 = f1  ∂ε1 

∂εeff ∂ε1

1  ∂εeff  A2 = f2  ∂ε2 

∂εeff ∂ε2





(78)

 (79)

 (80)

The weighting coefficients A1 and A2 include local-field effects allow the CARS contributions of the gas-phase components and the solid host to be controlled by varying the refractive indices and volume filling fractions. Assume that the pores of nanostructure are filled with a Raman(3) active medium, providing a resonant contribution, r , the mixing rule is (3)

(3)

1 = r

= ¯ (3) g( ),

(81)

where = (ω1 − ω2 − ˝)/ is the frequency detuning of the biharmonic pump from the Raman resonance normalized to the linewidth . Whereas g( ) is a complex function describes the line profile and the phase of the resonant part of  ¯ (3) in the bulk of the Raman-active material. The second material which has a nanocomposite structure provides a nonresonant contribution to (3) (3) the mixing rule, 2 = NR , thus deforming the resonant CARS line profile which has a Lorentzian shape of g( ) = − (i + )−1 . The intensity of the CARS signal from an isotropic nanocomposite material is written as

 

I ∝ A1

2



2

  ¯ (3)   ¯ (3) (3)  − A2 2  + A1 2 1+ 1 + 2 

(82)

The interference of resonant and nonresonant parts of the effective nonlinear-optical susceptibility of a nanocomposite system gives rise to characteristic features in CARS line profiles. The standard CARS line profiles is controlled by many factors such as the ratio of volume-averaged nonresonant and resonant CARS susceptibilities. The spatially nonuniform pump field distribution in a nanostructure makes CARS spectral profiles highly sensitive to the morphology of the structure, as well as to the refractive indices and volume filling fractions of constituent materials. A parameter controlling the CARS line profile in nanocomposite system with a Bruggeman-type is given as [113]: (3)

=

f1 |∂εeff /∂ε2 |(∂εeff /∂ε2 ) |2 | f2 |∂εeff /∂ε1 |(∂εeff /∂ε1 ) | ¯ (3) |

(83)

However, the interference of resonant and nonresonant contributions in CARS spectra can be controlled through spatially nonuniform field distribution in a nanostructure by varying the dielectric constants of constituent materials. (3) With the term A2 2 being less than the volume-averaged (3)

resonant nonlinear susceptibility, f2 2 , for the nanocomposite systems, the growth in the nonresonant background and the related distortions in CARS spectra can be made much less spectacular than in the case of a standard CARS cell (Fig. 12). Nanocomposites consisting of materials with a high ratio of dielectric constants, such as nano- and mesoporous silicon or gallium phosphide structures, allow a radical reduction of the coherent pedestal in CARS spectra related to the solid host (Fig. 12a and b) which is considered as a way to improve the sensitivity of CARS as a method of gas-phase analysis.

Fig. 12. CARS spectra from a nanocomposite system with (a) ε2 /ε1 = 12, (3) | ¯ (3) |/|2 | = 0.1; f2 = 0 (1), 0.10 (2), 0.30 (3), 0.50 (4), 0.60 (5); (b) ε2 /ε1 = 12, (3)

| ¯ (3) |/|2 | = 0.3; f2 = 0 (1), 0.10 (2), 0.20 (3), 0.40 (4), 0.70 (5); (c) ε2 /ε1 = 2.25, (3)

| ¯ (3) |/|2 | = 0.3; f2 = 0 (1), 0.05 (2), 0.10 (3), 0.15 (4)m Ref. [113].

3.2.2. Combination of CARS and photo-acoustic spectroscopy for gas detection Measurements of trace greenhouse gases such as CO2 and CH4 are highly important to avoid environmental pollution problems. Continuous monitoring of the leak of inflammable gases, such as H2 , CH4 and H2 S, is also important in chemical plants and along gas pipelines for safety precautions. A new technique for photo-acoustic Raman spectroscopy (PARS) and CARS is proposed and demonstrated for the detection of H2 and CH4 at atmospheric pressure [115]. In the proposed scheme of this technique, only a pulsed Nd:YAG laser is used as a pumping source while the tunable laser is replaced by a Raman shifter that is filled with the same gas to be detected as shown in Fig. 13. This allows automatic generation of the Raman-shifted radiation. In the case of CH4 , the measurement with the optimized scheme shows that detection limits up to 1 ppm for PARS and 15 ppm for CARS are achieved. The proposed PARS technique allows the measurement of the CH4 concentration in the natural air. Although the sensitivity of CARS is lower than that of PARS, the signal to noise ratio for higher concentrations is improved. 3.2.3. Flame thermometry by femtosecond CARS The fs-CARS technique for thermometry in the hot environment of a flame is demonstrated using the isotropic Q-branch of nitrogen [116]. Because the non-resonant term of the molecular polarizabil-

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Fig. 13. Scheme of PARS and CARS without tunable laser, Ref. [115].

ity interferes with the CARS signal in a small time window only as long as the pulses temporally overlap, it can be separated from the main CARS transient in the time domain [117]. The high repetition rate and superior stability of fs-laser system make the fs-CARS transients are very sensitive to temperature and pressure, and hence it will be suitable for turbulent combustion. The signal amplitude decreases rapidly in time due to collision-induced dephasing. Fitting the flame transients yields the collisional dephasing rate of the induced ground-state coherence and the flame temperature. Figure 14 illustrates room temperature fs-CARS transient measured in a cell filled with 200 mbar N2 . The contribution of the nonresonant polarizability to the CARS signal at time zero is visible in the inset on an extended timescale.

Fig. 14. Room temperature fs-CARS transient measured in a cell filled with 200 mbar N2 , Ref. [116]. The contribution of the non-resonant polarizability to the CARS signal at time zero is in the inset on an extended timescale.

3.2.4. Errors of spatial averaging in CARS temperature measurements In non-intrusive in situ temperature measurements of reacting flows the temperature varies over the length of the CARS probe volume which is defined by the overlap region of the three CARS input beams. However, the measured temperature is biased toward the cold side rather than reflecting the mean temperature or the temperature at the center of the volume. Such situation provides an error in temperature measurements due to the spatial averaging, particularly when eddies of hot pockets of gas are adjacent to cooler eddies. Spatial averaging is important in laminar systems at flame fronts and near boundaries where temperature gradients are steep. The cold gas in the CARS probe volume contributes more to the signal than the hot gas due to primarily density effects. Spatial averaging errors are often overlooked, especially in turbulent systems where instantaneous temperature gradients are hard to quantify. A study on scanning CARS measurements made on a Wolfhard–Parker slot burner to quantify these spatial averaging errors in nominally two-dimensional nonpremixed combustion flames using a very stable laminar diffusion flame with a known temperature gradient is reported [118]. Results are compared to the calculated average temperatures using both analytical and experimental inputs to a CARS spectral fitting program. While spatial averaging has significant errors caused by the domination of the signal by colder and denser gases, the results assess how accurately errors in CARS thermometry can be predicted. During the fitting of CARS temperature measurements, spectra from the center of the flame showed large nonresonant contributions. These large nonresonant contributions are resulted from the lack of nitrogen available for resonant signal generation in the methane flow and the relatively large nonresonant nonlinear susceptibility of methane. Any nitrogen present in the methane flow must diffuse across the flame front from the co-flowing air. This implies that the spatially averaged CARS temperature measurements are not only weighted by the changes in density due to temperature, as would be the case in a premixed flame, but also by the changes in mole fraction of nitrogen. The contributions to the spatially averaged measurements are especially weak in the center of the burner where the mole fraction of nitrogen is low. The study [118] concluded that information about the effects of spatial averaging is essential when interrogating systems with high temperature gradients using CARS and other crossed beam techniques for thermometry. In the same trend of predicting temperature profiles in hot gas flames, the structure of two-dimensional, axisymmetric, unconfined laminar hydrogen–air flames (in which a cylindrical fuel stream is surrounded by co-flowing air) is investigated using laserdiagnostic and computational techniques [119]. Stimulated Raman scattering SRS and CARS are used to measure the distributions of major species and temperature. Computationally, the governing conservation equations for mass, momentum, energy, and species, using detailed chemistry and transport are solved [119]. The fuel is diluted with nitrogen (1:1) to reduce heat transfer to the burner and to match the zero temperature gradient at the fuel exit. Comparisons of the measured and computed results are performed for radial profiles at a number of axial positions, and along the axial centerline. Peak major species mole fractions and temperatures are quantitatively predicted by the computations, and the axial species profiles are predicted to within the experimental uncertainty. In the radial profiles studied, base-case computations excluding thermal diffusion of light species were in excellent agreement with the measurements. While the addition of thermal diffusion led to some discrepancy with the measured results, the magnitude of the differences was no more than 25%. The computations predicted the axial centerline profiles from the burner exit to the maximum

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temperature, declaring that the experimental temperatures in the downstream mixing region are decreased somewhat faster than the computed profiles. Radiative losses are seen to be negligible in these flames, and changes in transport properties and variations in initial flow velocities generally led to only modest changes in the axial profiles. The results showed quantitatively the detailed axial profiles of major species and temperature at different fuel jet velocities. 3.2.5. Dephasing kinetics of molecular hydrogen rotational transitions The main dephasing mechanisms of hydrogen molecules are the following [120]: • Doppler dephasing, caused by thermal motion of the particles in gas. • Velocity changing collisions, which limit the free motion of molecules in gas, and which suppress the Doppler dephasing (Dicke effect). • Elastic collisions, which change phases of elementary oscillators. • Inelastic collisions, including exact resonance, quasi-resonance and inelastic nonresonance collisions. If excited transition is isolated as pure rotational transitions in hydrogen, all the three types of collisions result in homogeneous character of dephasing. Velocity changing collisions slow down dephasing while elastic and inelastic collisions speed it up. So the contributions of velocity changing and dephasing collisions can be separated quite easily. For the dephasing of rovibrational transitions of hydrogen, systematic measurements of pure rotational transitions were made by means of SRS. High-resolution coherent Raman spectroscopy has been used for measurements of broadening and the shift of rovibrational lines of H2 and its isotopes with pressure and temperature. Due to the relatively broad Doppler linewidth the narrowest spectral line was observed at pressures of several atmospheric pressures. To diminish the Doppler broadening it is more preferable to use forward scattering time-domain CARS on pure rotational transitions [120]. This technique gives the opportunity to observe dephasing processes, directly, in real time scale. Furthermore it possesses all advantages of coherent method. In this case the Doppler linewidth is only 0.003 cm−1 and to observe Dicke-effect one should be able to measure linewidths of the order of 0.001 cm−1 . 3.2.6. Triple-pump and dual-pump CARS for combustion diagnostics Measurement of temperature using N2 CARS in practical combustors has the advantage that N2 is present almost everywhere at high concentrations. However, applying CARS technique to the temperature measurement in practical combustors is always challenging, mainly due to the following factors: 1. Interference from highly luminous environments. 2. Steering of the laser beams due to density gradients. 3. Absorption of the CARS signal by the strong C2 Swan bands [107,121]. Interference from flame luminosity can be minimized using either a mechanical shutter in front of the spectrometer [122] or an interline-transfer charge-coupled-device (CCD) camera or data acquisition [123]. In practical combustors with highly sooting environments, the effect of beam steering can be greatly reduced by arranging the CARS beams in a collinear fashion rather than in folded BOXCARS geometry [107]. The absorption of CARS signal by

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the strong C2 Swan band can be voided by shifting the CARS signal generation to a different wavelength region. Recently, CARS techniques have been demonstrated for the simultaneous measurement of multiple species concentrations [107,124,125]. Roy et al. [126] presented two types of triple-pump CARS systems for the simultaneous measurement of temperature and multiple-species concentrations in reacting flows. In the first system, the ro-vibrational transitions of N2 , O2 , and H2 are probed using three narrowband pump beams and a broadband Stokes beam. The system is a combination of two dual-pump CARS systems using four laser beams to generate CARS signals near two distinct wavelengths. Both wavelength regions exhibit an N2 CARS signal along with the CARS signal from another target molecule. Each pair of CARS signals is generated over a relatively narrow wavelength region and can be captured with fixed wavelength detection. In the second system, pure rotational transitions of N2 /O2 and the ro-vibrational transitions of N2 /CO2 are probed using two narrowband pump beams, a broadband pump beam, and a broadband Stokes beam. A dual-broadband rotational CARS system is combined with a dual-pump CARS system, and four laser beams are used to generate CARS signals near two distinct wavelengths. The use of a broadband pump source in the second CARS system allows rotational and ro-vibrational transitions of different molecules to be probed simultaneously, unlike the first triple-pump CARS system which employs either single-longitudinal-mode or narrowband pump beams. For both CARS systems the signals appear at two distinct wavelengths. The CARS signals at the two wavelengths are separated by dichroic mirrors before being detected by two spectrometer-CCD detection systems. For proof-of-concept demonstrations, single-shot and averaged measurements are performed in an atmospheric-pressure hydrogen–air diffusion flame and in a carbon dioxide-seeded, near-adiabatic hydrogen–air flame stabilized over a Hencken burner. One of the main advantages of this technique is that very accurate temperature measurements can be acquired at both low and high temperatures. In the combustion zone or the exhaust of a real combustor, there is a wide spatial and temporal variation of temperature due to the inherent turbulent nature of the flow field. Thus, the rotational spectra of N2 /O2 will provide better temperature accuracy at lower temperatures, generally below 1500 K [127]; whereas the ro-vibrational spectra of N2 /CO2 will provide improved temperature accuracy at higher temperatures as population is transferred to higher energy levels. Triple-pump CARS offers the possibility of monitoring the local temperature and concentrations of two target species with respect to a reference species (generally nitrogen) using a single hardware platform with high spatial and temporal resolution. The technique minimizes also the test-cell operation time without the need for correlation of highorder time-varying statistics. Several other CARS techniques such as dual-broadband rotational CARS [128], simultaneous vibrational and rotational CARS [129], and dual-pump CARS [130] have also been used for temperature and multiple-species concentration measurements. Dual-pump CARS, first proposed by Lucht [124], allows one to shift the N2 CARS signal output away from 473 nm by shifting one of the pump frequencies away from 532 nm. This technique also allows simultaneous concentration measurements of a second species, such as O2 , CO2 , H2 , or CO, in addition to the temperature measurements. The wavelength of the second pump beam is selected so that the CARS spectra for the two species under study are observed at nearly the same frequency, enabling detection with a single spectrometer and CCD camera and eliminating systematic errors due to the wavelength dependence of the detection-system efficiency. The dual pump CARS technique has been applied to the simultaneous measurement of N2 –O2 [124,131], N2 –H2 , N2 –CH4 [132], and N2 –CO2 [133]. It is also applied in the exhaust stream of

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a practical combustor to measure temperature and CO2 concentration from a single laser shot [130]. Single-shot, dual-pump CARS measurements of N2 and CO2 are performed in the exhaust stream of a swirl-stabilized JP-8-fueled combustor under sooting conditions [134]. The dual-pump allows pursuing future CARS measurements in the reaction zone of the combustor under sooting conditions along with laser-induced incandescence (LII) and planar laser-induced fluorescence (PLIF) measurements to quantify soot formation and to study unsteady flame characteristics. 3.2.7. Resonant CARS for measuring species concentration and temperature profiles Resonant CARS (RECARS) is a much more suitable technique rather than normal CARS for diagnose of the radiative properties and the energy transport of the discharge plasma. RECARS signals are produced by parametric four-wave mixing. During the inelastic scatter process the photon gains a rovibrational quantum. In contrast to ordinary CARS, for electronic resonant CARS at least three of the four energy levels involved are in resonance, which results in a resonant amplification of the scattered signal [135,136]. The phase matching condition is fulfilled with a folded BOXCARS arrangement, to reach a good spatial resolution, to avoid nonresonant CARS signal generated through the presence of chamber windows, and to separate the anti-Stokes signal from pump and Stokes beams. Notice that the CARS scatter process results from a coherent oscillating ensemble of particles, which means a strict proportionality of the scatter signal to particle density squared. Instead of using one frequency-fixed pump laser and one tunable Stokes laser as in the case of degenerate CARS, two frequency-tunable lasers are needed for RECARS. By proper choice of the pump and Stokes frequencies the rovibrational Raman spectrum of the molecular species under investigation is detectable in the visible or near-UV regime of the spectrum with high sensitivity and spectral resolution. The calculation of CARS intensities utilizes the nonlinear polarization of matter by the incident pump beam and the Stokes beam. Group of Uhlenbusch performed RECARS experiments for measuring concentration and temperature profiles of CH radical produced in a microwave (2.45 GHz) excited Ar/CH4 plasma [136] and for metal halide indium iodide (InI) in commercially available metal halide lamps [137]. In these experiments a combination of a Nd:YAG and two dye-laser systems with a high-beam pointing stability, a comparatively low bandwidth of 0.07 cm−1 at 411 nm, and the possibility of attenuating the laser beams over two decades is utilized for the RECARS experiments. The Bordé diagram technique allows the calculation of the third-order susceptibility valid for RECARS processes. Important entries for numerical evaluation of these formulas are the frequency positions of Raman transitions and dipole transition moments. The investigations pay particular attention to frequency transition combinations generating triple resonances. These resonances are very specific for a molecule; they are like fingerprints, and the appropriate RECARS process can be performed by applying laser systems with low-pulse energy (1.0 mJ). The temperature of InI molecules is determined with an accuracy of 7% in the range of 850–1200 K. Experiments are performed on commercially available lamps with an internal pressure of 1 MPa. These experiments did not result in RECARS spectra appropriate for temperature and density evaluation because of the large broadening effect. Investigations with lamps at lower pressure (30 kPa) are also failed because of instantaneous wall blackening due to sputtering. 3.2.8. CARS for non-equilibrium pulsed ns discharge investigation at atmospheric pressure Control of ignition and combustion processes in aircraft jet engines is important for their performance and reliability. Some of

the technical issues which required to be controlled are; reduction of ignition delay, flame-holding and flame stability improvement, flame blow-off prevention, and extension of flammability limits [138]. These processes are generally investigated by methods based on conventional thermal ignition systems (arc discharge) with limited success. Modifying the chemical reaction kinetics by generating and sustaining large electron number densities, which results in a non-equilibrium excitation of the gas mixture, is another choice. Better efficiency of population transfer within electronic and vibrational states can be obtained using pulsed nanosecond discharges which handle a reduced electric field [139]. Information concerning energy transfer between the plasma and the gas medium are not fully available. Thus, experimental values of the population distributions of neutral molecules are important quantities that can be used as input parameters for the simulation of this interaction. Because of limited spatial dimensions and short duration in the pulsed discharge, only laser-based methods such as CARS have the potential to provide information about the kinetics of vibrational and rotational populations energy transfer in discharge-excited molecular gases without disturbing the plasma configuration. The thermodynamics and kinetic properties of a streamer nonequilibrium nanosecond discharge produced between two needles at atmospheric pressure were investigated [138]. Time-resolved ns-CARS is used to measure, within the plasma produced in pure air and in different methane/air mixtures, the population distribution of N2 in its ground electronic state. Temporal evolution of these populations is recorded by delaying the probe lasers relative to the discharge pulse (from 10 ns to 1 ms). For a discharge in air, N2 exhibits a strong vibrational non-equilibrium with a peak vibrational temperature of 2000 K whereas rotational temperature does not exceed 900 K. Experiments were also carried out in premixed CH4 /air flames to study the effect of a nanosecond pulse discharge on flame ignition and stabilization at atmospheric pressure. Energy transfer, which is induced by collisions between N2 and CH4 , yields noticeable increase of the thermal heating of the gas (up to 2500 K). The results were used to assess the feasibility of temperature single-shot measurements with CARS in order to get an insight into the thermodynamics and kinetic properties of discharges in hydrocarbon/air mixtures. 3.2.9. CARS and laser-induced fluorescence in flame measurements Since the pioneering work of Hottel and Hawthorne [140], jet diffusion flames have become one of the most extensively investigated flame systems. Over the past two decades significant amount of data on statistical parameters such as fluctuations in velocity, temperature, and concentration in turbulent combustion processes have been obtained through the use of single-point and planar-imaging techniques [141]. Detailed studies of flame–vortex interactions and the effects of preferential diffusion on the flame’s structure in turbulent combustion are carried out [142]. A combined experimental and numerical study is conducted on a low-speed, buoyant, jet diffusion flame of hydrogen in air. A timedependent, axis-symmetric mathematical model with detailed transport processes and a chemical-kinetics mechanism is used to simulate the dynamics of the flame. Single-shot measurements of temperature and the concentrations of molecular hydrogen H2 , the pollutant nitric oxide NO, atomic oxygen O, atomic hydrogen H, and the hydroxyl radical OH are made using optical BOXCARS and planar laser-induced fluorescence. Flame temperatures are derived from the observed Q branch of the CARS spectrum of N2 . For the measurements of H2 the Q branches of the Raman emission are probed. Planar laser-induced fluorescence is used to probe OH. Temperature and mole fractions of different species are presented in two-dimensional contour maps

F. El-Diasty / Vibrational Spectroscopy 55 (2011) 1–37

Fig. 15. Structure of low-speed, buoyant, jet diffusion flame. Instantaneous image obtained using reactive-Mie-scattering technique shown on left half; instantaneous temperature distribution obtained using UNICORN model shown on right half, Ref. [142].

and compared with the numerical predictions. Measured and computed instantaneous images of the flame are shown in Fig. 15 [142]. Both left and right halves, respectively, are illustrating the dynamic flame structure. A comparison of computed and measured images suggests that the model captured the important features of this low speed flame. The bright region in this image (left half of Fig. 15) is the luminous flame surface, as captured simultaneously with Mie-scattered light. Fig. 16 compares the measured and computed values for temperature and concentrations of H2 , OH, H, NO, and O. The measurements captured the depletion of radicals, such as H, O, and OH, where the flame is compressed. The buildup of these species is occurred, as predicted by the model, which predicted the behavior of the experimentally observed dynamic flame, including variations in temperature and molar concentrations of fuel and tracer species such as H, OH, and NO. 3.2.10. VCRS and DBB-RCARS for diagnosis of fuel-rich sooting flames The capability of the spontaneous Raman technique that is applied to fuel-rich stronger sooting flames was investigated by Kohse-Höinghaus [143]. Polarization scheme and averaging over a large number of laser pulses are used. It was found that background levels were too high for temperature determination by the use of the Stokes and anti-Stokes signals. Another approach using spontaneous Raman scattering in a sooting flame was performed by Rabenstein and Leipertz [144]. A new approach for the simultaneous determination of temperature and concentration in the same flame by using CARS is applied [145]. Accordingly, single-pulse

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simultaneous measurements of temperature and relative concentration of O2 /N2 and CH4 /N2 using a combined vibrational coherent CARS (VCARS) and dual broadband rotational CARS (DBB-RCARS) technique are developed. Because of the choice of the dye wavelength only one dye laser must be employed. In contrast to the most used approaches of multi-color CARS, a normalization of the different CARS signals is not necessary because the smeared VCARS and the DBB-RCARS signal are generated by the same lasers. For VCARS, the exciting laser frequencies are selected to stimulate the transition between rotational–vibrational energy states of the molecules of interest. Because of its molecular symmetry, methane can only be observed by VCARS. The temperature is determined from the population difference between these energy levels. For the most relevant molecules in combustion processes, the vibrational energy levels depart from the exciting frequency in a range approximately between 500 and 4200 cm−1 . Thus, with a typical broadband dye laser (FWHM < 150–350 cm−1 ) only a few molecules can be probed with the same laser source. For the simultaneous detection of several molecules using VCARS, an experimental setup with several dye lasers is often necessary [107]. Usually the temperature measurements of the Q-branch of nitrogen are probed using VCARS because of its high concentration in the premixed unburned gas as well as in the exhaust gas. For the interest in the concentration of fuel, e.g. methane, and oxygen, a complex multi-color CARS setup has to be employed [131,132,146]. Using pure rotational CARS (RCARS), only the transitions between the rotational energy levels within the vibrational states of the molecules are probed. For temperatures approximately up to 2000 K, the relevant pure rotational transitions of nearly all molecules, except of H2 , are within a range of about 400 cm−1 . Over a wide temperature range, the stimulation of the pure rotational transitions is possible for nearly all molecules of interest with only one single dye laser [144]. For combustion diagnostics two different experimental approaches for RCARS have been used; the conventional [147] and DBB-RCARS techniques [148,149]. Due to advantages of the DBB-RCARS approach, the conventional RCARS technique is quite rarely used. For sooting flames, RCARS has a significant advantage to VCARS when a frequency-doubled Nd:YAG laser at 532 nm is used. In this case, parts of the N2 -vibrational-CARS spectrum near 473 nm are strongly influenced by a C2 interference [150]. The RCARS spectrum and DBB-RCARS are free of interference even for stronger sooting flames [151]. 3.3. CARS for liquid diagnostics Despite of many liquids/solutions appear to be transparent macroscopically, they are not necessarily homogeneous at the molecular level. Depending on the kind of intermolecular interactions among the component molecules, a variety of microscopic structures are thought to be formed in liquids/solutions. They are often referred to as local structures. Information on such local structures is crucial for elucidating the nature of liquids/solutions. It also enables us to discuss macroscopic properties of liquids/solutions, such as density, dielectric constant and solvent effects in terms of microscopic structures. Local structures in liquids/solutions have been studied with various experimental and theoretical approaches [152] such as X-ray, neutron scattering, NMR, computer simulation, and vibrational spectroscopy. Among these methods, X-ray scattering has been the most extensively employed. However, it inherently lacks in molecular specificity, because X-rays are scattered by electrons in atoms. If different kinds of molecular species coexist in a sample, it is not possible to distinguish which species is responsible for the structure derived from the radial distribution function of Xray scattering. In contrast, vibrational spectroscopy has a definite

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Fig. 16. Contour plots of measured (left) and computed (right) flow-field parameters in space (radius) and time at 135 mm downstream of jet exit: (a) temperature, (b) H2 concentration, (c) OH concentration, (d) H concentration, (e) NO concentration, and (f) O concentration. Experimental O concentration is multiplied by a factor of 3m Ref. [142].

advantage with respect to molecular specificity, since vibrational spectra are highly molecular specific (molecular fingerprint). In addition to conventional infrared and spontaneous Raman spectroscopy, various nonlinear vibrational spectroscopic techniques including CARS have been used and developed [153–156]. 3.3.1. Nonlinear Raman probe for local structures in liquids and solutions The cascading third-order Raman process in the benzene/nhexane binary mixture was investigated [157]. It found an unexpected behavior that suggests the presence of local structures in this mixture. It came to an assumption that the spatial distribution of nonlinear Raman signals, such as the CARS signal, around the phase-matching direction should vary and reflect the size of local structures. To elucidate the relation between the spatial distribu-

tion of a CARS signal and possible local structures, a simple model describing the generation of the CARS electric field from the thirdorder polarization that is induced in an optically inhomogeneous medium is considered [152]. Such an inhomogeneous environment can be modeled by considering the coordinate dependence of the third-order susceptibility. Local structures in liquids and solutions can be quantitatively probed with molecular specificity by measuring the spatial distribution of a CARS signal. These spatial distributions of the breathing mode of benzene in neat benzene, benzene/ cyclohexane, benzene/carbon tetrachloride, benzene/ethanol, and benzene/acetonitrile were measured [152]. No appreciable change in the spatial distribution pattern is observed for neat benzene and benzene/cyclohexane, whereas the other binary mixtures evidently showed broadened patterns. These broadened patterns are

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explained by assuming that the CARS phase matching is somewhat relaxed due to the local structure formation in the binary mixtures. Aqueous suspensions of polystyrene micro-particles having different diameters are measured [152] and found that the distribution pattern is broader for polystyrene particles having smaller diameters. This means that the broadening is size dependent and carries quantitative information on the size of the local structure. The phase factor which determines the spatial distribution pattern is closely related to the refractive index contrast between the constituent solvents of the binary mixtures. Such a difference in the refractive indices may be affected by dominant intermolecular interaction in the mixture. For instance, the so-called aromatic interaction will act among benzene molecules, while ethanol molecules tend to link together through hydrogen bonding. It is also suggested that [158,159] acetonitrile molecules interact with each other via the dipole–dipole interaction of the C≡N group. Further investigation such as vibrational mode dependence and time-resolved measurements of spatial distribution patterns provide more insights into the microscopic nature of the optical inhomogeneity in the binary mixtures.

characterized by an exponential decay. This decay constant is called the intermolecular dephasing constant. For the latter mechanism, the time profile has a Gaussian form. The structure of intermolecular dephasing constant is derived from Markov approximation. The ultrafast, sub-picosecond dephasings observed in CARS profiles of neat benzene liquid in terms of the rovibrational interference mechanism were analyzed. In the same approach, noisy light based interferometric coherent anti-Stokes Raman scattering (I2 )CARS has been used [162] to recover with high precision, vibrational dephasing rate constants, vibrational frequencies and the relative contributions of the resonant and nonresonant third order hyperpolarizabilities using a Brownian oscillator lineshaping model [163]. Three low frequency modes of benzene are investigated for their possible role in the vibrational dephasing process. Unlike CW CARS, it is found that (I2 )CARS can strongly discriminate between the dephasing activity of the three low frequency modes which suggests that rotation about the C6 axis is responsible for dephasing in this case. This agrees with previous findings in femtosecond CARS experiments on the liquid.

3.3.2. Dephasing in time-resolved fs-CARS from molecules in liquids Femtosecond time-resolved nonlinear CARS is a method for clarifying the origin of ultrafast dynamics associated with molecular motions in liquid [160]. Considering the molecular dephasing processes, differences in the creation of the molecular coherence between coherent and incoherent (spontaneous) Raman scattering should be noted. In the time-resolved, nonlinear, coherent scattering processes, each molecule in the liquid receives the photon wave vector transiently through spatial coherence of the photon field. As a result, a transient intermolecular coherence is created. The transient macroscopic nonlinear polarization of the molecular ensemble is therefore given as the summation of the induced nonlinear polarization on each molecule. In the absence of longrange spatial correlation between molecules, the intensity can be expressed in terms of the absolute square of the ensemble-averaged nonlinear polarization. The decay of rovibrational coherence is expressed by the ordinary intramolecular dephasing constant. This consists of the population decay constant and the pure dephasing constant. The former originates from inelastic interaction between the molecule of interest and heat bath modes. The latter constant originates from an elastic interaction between the molecule and the eat bath modes. Thus, intermolecular phase dynamics from liquids is directly reflected in time-resolved, nonlinear, coherent Raman scattering profiles through the information content in both coherent and incoherent Raman scattering experiments. Quantum beats appear in the time profile of the CARS spectrum from a molecular mixture with frequency equal to the difference between frequencies of vibrational modes of molecules in the mixture. With the creation of sets of intermolecular rovibrational coherence, it can be expected that ultrafast dephasing will result from interference between the sets of the rovibrational coherence. This phenomenon is one of the main origins of inhomogeneous Gaussian component in the time profile, which is photon polarization dependence. This polarization-dependent time profile has been observed in sub-picosecond time regime in nonresonant CARS from benzene in liquid [161]. The mechanisms of ultrafast dephasings appearing in timeprofile of coherent Raman scattering from molecules in liquids were examined [160], where two mechanisms are used. One is associated with intermolecular interactions between molecules at different sets through heat bath modes. The other is associated with the interference between rovibrational Raman transitions. In the former mechanism, the time profile of coherent Raman scattering is

3.3.3. Femtosecond CARS in liquid phase Since the work of Leonhardt et al. [77,78] to use CARS on a femtosecond time scale and femtosecond time-resolved, CARS spectroscopy became an ideal tool for the investigation of the dynamics of high frequency Raman modes in a molecular system. Ring-puckering vibration [164] involves an out of plane vibration, which causes the ring to switch between two configurations. This kind of vibration is characteristic of cyclic molecules having –CH2 –, –O– or –S– groups. The potential energy curve for the vibration shows, therefore, two identical minima corresponding to the ring being puckered upwards or downwards. This low frequency vibration yields a large amount of information on molecular structure and forces. Scaria et al. [165] reported, for the first time, on femtosecond time-resolved CARS applied to molecules exhibiting ring puckering vibrations via probing the C–H stretching region. The investigation is focused on the band progressions and hot band structures observed in the high frequency Raman region resulting from the interaction between the low frequency out of plane vibration (ring puckering vibrations) and some other suitable vibrational modes (e.g. C–H stretching vibration). In their work [165] they tried to answer a number of questions. (1) Are CARS experiments feasible also for the relatively low pressure gases of ring puckering molecules? (2) What coherence lifetime can be observed in the gas and in the liquid phase of these molecules? (3) Does the signal depend on the polarizations of the lasers and the signal detection? (4) What spectral resolution can be achieved from the Fourier transform of the CARS transients? (5) Do the beating frequencies fit the observed Raman lines? In their way to answer [165], the dynamics recorded differ considerably for both the gas and the liquid phases. While the coherence lifetime of the gas phase anti-Stokes signal is on the order of tens of picoseconds, the liquid phase transients decay after few picoseconds. The long living beating structure in the gas phase results in fast Fourier transform spectra. In addition, small frequency differences between the Raman lines could be observed with high accuracy. Comparing the results of the different molecules, besides the line positions in the Raman spectra that reflected in the beating structures of the fs-CARS transients, no distinct differences could be found, which is attributed to the different potential barrier heights. Interestingly, the CARS results did not depend on the arrangement of polarizations of the lasers and the signal (e.g. magic angle). Orientational variations due to the rotational motion of the molecules obviously do not reflect in the CARS transients for these molecules above a detectable limit.

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3.3.4. Mesoscopic local structures in ionic liquids Ionic liquids are liquids that consist solely of ions. Roomtemperature ionic liquids are those who exist as liquids at or near room temperature. In contrast with ordinary molecular liquids such as acetone and CCl4 , the long range Coulomb interaction plays a dominant role in ionic liquids. Such unique environment in ionic liquids may give rise to novel physicochemical properties, functionality, reactivity, and liquid structure. Ionic liquids have unique properties such as wide liquidity temperature range, nonvolatility, amphiphilicity, high solubility of both organic and inorganic compounds, and high viscosity. For binary mixtures of benzene and several organic solvents and for aqueous suspensions of polystyrene beads, CARS was able to probe, with molecular specificity, the local structures formed in liquids/solutions [152]. As was demonstrated for aqueous suspensions of polystyrene beads [152], the spatial distribution of CARS signals carries quantitative information on the size of local structures, which is hardly obtainable from conventional vibrational spectroscopy. Therefore, the spatial distribution measurement of CARS signals is expected to provide more insight into the structure of ionic liquids. The study of 1-butyl-3-methylimidazolium chloride (bmimCl) [166] led to a hypothesis that specific local structures possessing crystal-like ordering exist, at least partially, in the liquid state. New approach to the possible local structure formation in three typical ionic liquids, 1-alkyl-3-methylimidazolium hexafluorophosphates, Cn mim[PF6 ] (n = 4, 6, 8), using the spatial distribution measurement CARS signals was reported [167]. It is found that the CARS patterns of PF6 − (which is totally symmetric stretch mode) become narrower as the alkyl-chain length, n, increases from 4 to 8. The result has been interpreted in terms of the formation of specific local structures in these ionic liquids. Therefore, the size of the local structure can be roughly estimated to be of several tens of nanometers, taking into account the fact that the method is based on the relaxation of the phase matching in the CARS process using visible pump and Stokes beams. This kind of mesoscopic structure may also be detected by small-angle X-ray scattering. The present method of CARS signal spatial distribution measurement provides unique molecular-specific information (in the present case specific to the PF6 − anion) that is not obtainable from X-ray scattering. 3.3.5. CARS and mesoporous silica aerogels host for gas- and liquid-phase sensing Nanotechnologies offer new attractive solutions for the structural design of a Raman cell for CARS spectroscopy and sensing. Silica aerogels are low-density solids, consisting of individual SiO2 particles only a few nanometers in size, which are linked into a three-dimensional network [168]. Due to their unique properties, including a high transparency in the visible, an open mesoporous structure (with a porosity of 90–99%), a high surface area (400–1000 m2 /g), an extremely low density (0.003–0.15 g/cm3 ), and low thermal conductivity, silica aerogels find wide applications as insulating materials, catalysts for chemical reactions, sound absorbers, and adsorption materials [169]. Some of the most important applications of silica aerogels include Cherenkov counters, traps for extraterrestrial grains, and low-refractive-index materials. These interesting materials also offer several important advantages for CARS spectroscopy, serving as ideal hosts for Raman-active gases and liquids and allowing a nanoscale extension of CARS methodology [170]. The synthesis of aerogels is generally based on the hydrolysis of metal alkoxide by reaction with water in the presence of alcohol and catalyst. The hydrolyzed metal alkoxide undergoes a condensation reaction, forming a metal oxide gel, from which solvents are supercritically extracted to form the aerogel. Two types of Raman-active species are studied [170]. Toluene solution is employed as an example of a liquid-phase Raman-active substance infiltrated into silica aerogel. Molecular nitrogen from

the atmospheric air filling the pores of silica aerogel samples under normal conditions served to reveal the possibility of CARS gasphase sensing in nanocomposite materials. Competent CARS signal from Raman-active modes of toluene molecules in solution and gas-phase nitrogen molecules infiltrated into the mesoporous silica aerogels is measured. Due to silica aerogels high porosity, high transparency in the visible, and weak scattering, mesoporous silica aerogels are shown to provide an ideal host for Raman-active gases and liquids, detected and analyzed by CARS. This is allowing the creation of gas- and condensed-phase sensors of chemical and biological species, including sensors of pollutants and aerosols. 3.3.6. SCARS and fifth order Raman spectroscopy Fifth order Raman spectroscopy, I(3) CARS, has been the focus of much attention [171,172]. Such spectroscopy, when applied to condensed phase studies, provides more dynamical information than do the conventional Raman techniques, such as spontaneous or coherent Raman scattering. Some examples include the ability to distinguish between homogeneously and inhomogeneously broadened lines and the probing of overtone dynamics. However, these fifth order signals may often be contaminated or even overwhelmed by sequential lower order processes. In particular, it has been previously shown [173] how a sequential event consisting of two third order CARS processes, called SCARS (overall fifth order) can dominate the direct fifth order signal. Since SCARS probes the same dynamical parameters as CARS, it is often considered as an unwanted artifact when obtaining the true fifth order signal. Nevertheless, it is absolutely imperative to fully characterize the SCARS process, both theoretically and experimentally, in order to make clear distinction between it and the more desirable direct fifth order process. The first I(3) SCARS spectrogram is presented [171] – one obtained from liquid benzene at room temperature. The 992 cm−1 ‘ring breathing’ mode of liquid benzene is examined and the signals are recorded as Raman spectrograms generated by using broadband, nontransform-limited, quasi-CW noisy laser light. The fifth order signal is entirely dominated by a sequential CARS process called I(3) SCARS. These noisy light based fifth order signals shall be referred to as I(3) SCARS and I(3) CA(2) RS1 , respectively, where the superscript (2) refers to the twice anti-Stokes shifted signal. The vibrational Raman frequency and the dephasing rate constant for this mode is extracted from combined I(3) SCARS and I(2) CARS spectrograms with high precision and potentially high accuracy. 3.4. CARS for solids diagnoses Nonlinear optical measurements – such as four-wave mixing techniques (e.g., CARS) – offer a rich source of energy structural and dynamical information of condensed matter. Therefore the most important reported works concerning the spectral, structural and dynamical properties of solid phase diagnostics will be presented in the following section. 3.4.1. CARS on carbon nanotubes and thin films excited through surface plasmons Huge optical fields could be locally generated in nanoscale metal structures during the local excitation of surface plasmons (SPs) and cause a variety of nonlinear optical processes. Metallic particles of 5–100 nm size as well as metallic films with a roughness-type structure in the range of 10–100 nm are convenient supports to confine the electromagnetic energy in subwavelength-sized regions. Using silver and gold, reproducible enhancements of the Raman signal of the order of 102 –104 on various polymeric and semiconducting materials have been demonstrated [174]. Raman scattering is widely used to characterize single-walled carbon nanotubes (SWNTs) [175].

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Baltog et al. [176] provided an interpretation for an abnormal anti-Stokes Raman emission observed on nanometric thin films of different materials and in particular carbon nanotubes. Such abnormality is characterized by an abnormal intensity, sometimes increasing with the vibrational wave number, large differences in line profiles in Stokes and anti-Stokes sides and some discrepancies between the Stokes and the anti-Stokes frequencies [177]. Under a tight-focusing of the excitation light, a CARS emission is produced, resulting from a wave mixing process between the incident laser light and the Stokes Raman light generated by a surface enhanced Raman scattering (SERS) mechanism. The results which corroborate the CARS emission can be summarized as follows: (1) a square relationship between the CARS signal intensity and the film thickness; (2) a square relationship between the CARS signal intensity and the exciting laser intensity; (3) a dependence of the CARS intensity on the numerical aperture (NA) of the microscope objective used for the detection of the anti-Stokes emission. Such effects are not specific to carbon nanotubes and have been observed with other materials accommodated in similar conditions on rough metallic surfaces acting as SERS supports. This is due to the fact that at resonance, the third-order dielectric susceptibility differs from zero, (3) = / 0, which is basically a requirement necessary in the generation of nonlinear optical processes. 3.4.2. CARS to study polymeric materials Polymeric materials are increasingly recognized as important photonic and biophotonic media due to their molecular structure tailoring ability [178]. Besides their ability to produce nano-objects as building blocks for nanotechnologies, surface functionalization, pre- and post-doping of the bulk-phase and producing inorganic/organic hybrid structures expand the function of polymers for photonics. Conjugated molecules and polymers exhibit large third-order nonlinear optical properties due to their delocalized ␲ electron backbone. In order to use synthesis to develop molecular third-order materials with sufficiently high response for device applications it is necessary to have a clear understanding of the microscopic origin of the nonlinearity and thus the structure–property relationship. CARS spectroscopy is sensitive to resonance with electronic one and two photon allowed states in the medium. Therefore by varying the electronic resonance conditions, while probing a single Raman resonance, it is possible to quantify the various contributions to the nonlinearity and isolate the intrinsic response of the material under study. This allows different chemical systems to be meaningfully compared. Coherent Raman may give complimentary information to other third-order techniques due to the different resonances probed. Because the nonresonant term of the third-order optical nonlinearity is affecting the coherent Raman line shape, so this resonance can be used to study the nonresonant nonlinearity. By studying the concentration dependence of the line shape it has been able to separate the one and two-photon molecular contributions to the third-order nonlinearity. Measurements are obtained for the molecular nonresonant third-order optical nonlinearity for trans-␤-carotene [179], which is a conjugated molecule with eleven double bonds. It has been studied not only due its relatively high third-order nonlinearity but also the interest in using a simple polyene as a molecule for theoretical modeling. Polydiacetylenes (PDAs) have many interesting physical and chemical properties due to their quasi one-dimensional electronic system. In particular, their large and ultrafast optical nonlinearities make them candidates for possible applications as nonlinear optical devices [180]. As a result of their large third order susceptibility, PDAs are well suited for an investigation by means of nonlinear spectroscopic methods, such CARS or coherent Stokes Raman scattering (CSRS). Several types of PDAs embedded in single crystals

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of their monomers have been investigated with wavenumberresolved nanosecond CARS spectroscopy [181]. Experimental results on the vibrational dynamics in the ground state of PDAs were also reported [182]. The polymers are investigated by means of the CARS technique combining both wavenumber and time resolution. The intramolecular vibrational energy redistribution (IVR) process among three vibrational modes has been studied by analyzing the wavenumber resolved antiStokes signal of a femtosecond time-resolved CARS experiment. Recently, fs-CARS has been applied to study the relaxation process in the excitonic states of PDAs [183]. It is found that the anti-Stokes signal corresponding to the phonon modes 2 (C C stretching) is stronger when the Stokes laser interacts with the sample a little later than the pump pulse. Accordingly, it is suggested that excitons are trapped in the C C bonds and the self-trapping excitons (STE) state is strongly coupled with the 2 mode of the polymer chain. Analysis of the anti-Stokes signal at a detection wavenumber of approximately 1450 cm−1 yielded the coherent dephasing time T ≈ 140 fs, which is much shorter than the dephasing time of this mode in the electronic ground state. This fast dephasing is due to the self-trapping process of the excitons. These results show that CARS spectroscopy with femtosecond time resolution and wavenumberresolved detection is a powerful tool for the characterization of dynamics in both the electronic ground and the excited states of molecules. Femtosecond time-resolved spectroscopy, as shown above, can be used to investigate the dynamics of molecular systems in electronically excited states. However, fs time-resolved CARS is capable to study vibrational relaxation processes as well as rotational dynamics in the electronic ground state of molecular systems. fs-CARS experiment has been performed on a comparably large molecular system, the magnesium octaethylporphyrin, in solution [184]. Porphyrins are of great biological relevance, because they form the active site of many important proteins. The overall decay behavior of the transient CARS signal is independent of the CARS wavenumber, and can be described by a single dephasing constant of the excited modes which occur on similar timescales. Because of the well-defined polarization directions of the CARS signal contribution from individual vibrational modes, the quantum beat structure of the detected signal is influenced by the magic angle polarization geometry of the laser beams. On the contrary to ns-CARS, where all three incident laser beams are temporally overlapped and fixed, fs-CARS is able to analyze the signal at delay times when the non-Raman resonant scattering contribution is already decayed. Therefore, when the pulse duration of the laser pulses is considerably shorter than the vibrational dephasing time, the non-Raman resonant background does not restrict the experiments, leaving the analyzer setting of the CARS signal in principle undetermined. Therefore in principle it is possible to detect vibrational modes in large molecular systems which are concealed in spectrally resolved techniques. 3.4.3. Dynamical interactions between - and -electrons in organic molecules by CARS The measurements of sharp resolved electronic energy structures of the ground and excited states of dye molecules in solutions, by the use of several frequency-domain picosecond four-wave mixing techniques such as CARS, have revealed that the absorption and emission bands are composed of dense electronic transitions [185]. The contribution of the collective behavior among the dense electronic transitions to the third-order frequency domain responses, especially in the case of CARS processes [186] was reported. It is not easy to explain these results within the framework of ␲electron approximation. Accordingly the obtained results, such as change of CARS spectra depending on the picosecond excitation pulse duration of 4–6 ps, suggest that there exist many types of

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light induced electronic coherences depending on the duration of excitation pulse. Therefore, the formation of the variety of electronic coherences in terms of the dynamical interactions between ␴- and ␲-electrons in organic molecules is investigated and discussed [187]. In case of cresyl violet in ethanol and the excitation with the shorter 4 ps pulses, the CARS spectra being composed of the multiple electronic resonances showed the specific lightinduced enhancement coupled with the dominant normal vibration (590 cm−1 , ring-breathing mode). To understand the resonant third-order nonlinear responses such as light-induced electronic coherences in organic molecules, it is necessary to consider how to treat the inhomogeneous nature of the electronic transitions without limiting the frequency domain or time domain responses [187]. The degree of inhomogeneous broadening accompanied with the electronic transitions is less than the overall system resolution around several wavenumbers. These results in cases of picosecond excitation suggest that in the weak interaction limit the guest dye molecules feel the averaged potential due to the surrounding host solvent with much faster correlation time than the pulse duration of several picoseconds used. It suggests that the ␲-electron are connected closely with the ␴-electrons constituting the conjugated chains. Also the resolved energy structures in both ground and excited states are considered to be due to the dynamical interactions between ␲- and ␴-electrons. 3.5. CARS in biological researches Advances in instrumentation are making Raman spectroscopy a powerful tool for many increasing number of bio-chemical biological applications – such as tissue diagnostics, blood analyte detection and cellular examination. This is due to several reasons including; the sensitivity to small structural changes, non-invasive sampling capability, minimal sample preparation, easily interfaced to fiberoptics for remote analysis, and high spatial resolution in the case of Raman micro-spectroscopy [188]. The most recent technical approaches employed, from the well-known surface enhanced resonance Raman spectroscopy to nonlinear Raman techniques such as CARS and related techniques will be discussed. Relevant applications of Raman spectroscopy in the fields of clinical pathology, in vivo and ex vivo imaging (i.e., giving insights into living single cells without the need for fixatives, markers or stains), classification and detection of microorganisms and chemical analysis in the recent years are also included. For detection of tissue states in vivo, it is important to understand the spectral features of pure individual components of tissues; that means cells and subcellular components. CARS has been applied to record complete spectral maps of freezedried cells as well as living cells in media without the need for any fixing technique before the mapping. The use of CARS has become possible after the development of techniques including picosecond excitation, epi-detection, phase-matching techniques, polarization-sensitive detection and the development of timeresolved CARS significantly improved the ratio of the resonant signal to the non-resonant background. Increasing the utility of Raman and CARS microscopies would facilitate their use in modern applications of high resolution molecular imaging such as pathogen/disease detection and phenotypic screening. Larger proteins such as bovine serum albumin (BSA) are able to generate Raman image contrast that is specific to the nitrile (CN) mode contained on labeled proteins. In addition, the modification of HVHP428 with 4-CN-NHS appeared to have no effect on the wild-type function of the antibody. These CN-labeled sdAb conjugates have potential applications to live cell imaging using Raman or CARS microscopy. They also may serve as novel immunochemical recognition elements if used to coat SERS-active

substrates [189]. A recombinant VH single-domain antibody recognizing staphylococcal protein A is functionalized on reactive lysine residues with N-hydroxysuccimidyl-activated 4-cyanobenzoate. Surface plasmons resonance analysis of antibody–antigen binding revealed the modified and unmodified antibodies bound protein A with similar affinities. Raman imaging of the modified antibodies has indicated that the benzonitrile group provides vibrational contrast enhancement in a region of the electromagnetic spectrum that is transparent to cellular materials. Thus, the modified single-domain antibody may be amenable for detecting protein A from samples of the human pathogen Staphylococcus aureus using vibronic detection schemes such as Raman and coherent antiStokes Raman scattering. The generality of this labeling strategy should make it applicable to modifying an array of proteins with varied structure and function. CARS microscopy is different from CARS spectroscopy in several aspects: (1) it uses tightly focused beams for which the paraxial approximation breaks down; (2) the sample composed of the objects to be imaged and of the surrounding solvent medium is heterogeneous; (3) investigate the signal generation of CARS from a three-dimensional sample which permits three-dimensional imaging. In CARS microscopy both the pump and the Stokes beams are tightly focused in a collinear geometry using an objective lens with high numerical aperture (NA). The tight focus reduces the excitation volume and permits three-dimensional CARS imaging. The reason for using collinear beam geometry in CARS microscopy is to fulfill the phase-matching condition. Collinear CARS microscopy gives a lateral resolution of better than 0.5 ␮m and a depth resolution of 0.75 ␮m with tightly focused excitation beams [190]. Comprehensive review of the theory of CARS microscopy and its experimental characterization is provided in many original publications [190–194]. 4. Advances in CARS microscopy Single molecule detection, single cell detection, and tissue imaging are currently the state of the art; the combination of Raman spectroscopy with powerful chemometric tools enables reliable quantitative analysis of target molecules, cluster classification, and identification and differentiation of cells and bacteria for clinical pathology and microorganisms studies. High resolution imaging has the potential to facilitate the detection of the molecular determinants of a disease before a diseased phenotype is present in a given tissue. Vibronic imaging modalities such as infrared and Raman microscopies provide several advantages over conventional fluorescence-based techniques. In CARS microscopy, the temporally and spatially overlapped pump and Stokes laser pulses are tightly focused into a sample to generate a signal in a small excitation volume (<1 ␮m3 ) and a depth resolution of 0.75 ␮m, thus it provides a high 3D sectioning capability. In addition, the coherence of the signal beam results in a large and directional signal, which permits low excitation powers and fast scanning rates. The signal frequency is blue-shifted from the excitation frequencies, so that as a consequence the CARS signal can be easily detected in the presence of fluorescent background. The CARS signal depends also on the object size and the microscope’s geometry for excitation and detection. For instant, forward-detected (F-CARS) microscopy with parallelpolarized pump and Stokes beams produces a large signal at low excitation power. The resonant F-CARS signal is often overwhelmed by the nonresonant background from the scatterers and the solvent. The epidetected (E-CARS) beam geometry introduces a phase mismatch, which acts as a size filter that effectively rejects the signal from the bulk solvent. E-CARS signal arises from small scatterers or from interfaces of two sizable media that have different values of (3) . The E-CARS signal could be complicated by backreflection

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of the forward CARS signal at an interface [190,194]. The imaging speed is increased by the use of a laser-scanning microscope. Developments in laser technologies including jitter reduction and the picosecond amplifier increased the imaging sensitivity even further. The description of these recent advances in CARS microscopy and its fundamental properties and applications is found in a recent review [191]. 4.1. Recent CARS microscopy investigations In 1982, Duncan et al. [195] published the first report on CARS microscopy as a vibrational imaging technique. The technique via the intrinsic molecular vibrational levels allows noninvasive characterization and imaging of chemical species and biological systems without preparation or labeling or staining with natural or artificial fluorophores that are prone to photobleaching. In 1999 CARS imaging has improved by Zumbusch et al. [196], using two tightly focused near infrared femtosecond laser beams with a collinear geometry. CARS microscopy is a powerful technique for biological imaging [197,198], chemical mapping of live cells [199,200], and in vivo imaging of biological tissues [201,202]. Since CARS is a coherent process, a large signal is produced, which makes CARS microscopy orders of magnitude (∼106 ) more sensitive than Raman microscopy [188]. The contrast mechanism in CARS microscopy is generated from the intrinsic molecular vibrational properties of the specimen, permitting three-dimensional sectioning with high sensitivity, and high spectral resolution. Epidetected CARS (E-CARS) microscopy [194] with parallelpolarized pump and Stokes beams can significantly reduce solvent background and thus improve sensitivity. Development of E-CARS detection not only allows higher sensitivity but also simplified the requirement for tissue imaging applications, as it will be seen in Section 4.1.3. Time-resolved CARS microscopy (T-CARS) [203] is used to record the Raman free induction decay (RFID) of molecular vibrations. This not only provides spectroscopic information in the time domain, but also separates the nonresonant contribution of RFID, which is instantaneous, from the resonant contribution of RFID in CARS microscopy, and thus increasing the detection sensitivity of CARS microscopy significantly. T-CARS microscopy allows threedimensional imaging based on RFID of molecular vibration with no requirement for labeling the sample with natural or artificial fluorophores. The T-CARS experiment involves three incident electric fields, that induce a third-order nonlinear polarization, at ωAS . Usually, the pair of the first pump pulse and the Stokes pulse is temporally overlapped, and impulsively polarizes the sample. The third probe pulse then interacts with the sample at a certain delay time,, with respect to the previous pulse pair, and probes the relaxation of the induced polarization. Time-domain experiments on vibrational imaging are complimentary to their analogous frequency domain experiments of chemical and biological systems. Heterodyne CARS microscopy permits separate visualization of the real and imaginary responses of samples at relatively fast imaging speeds [204]. The imaginary response is free from nonresonant background, is linear in the concentration of vibrational modes, and can be directly correlated with spontaneous Raman scattering. Moreover, heterodyne CARS imaging is useful for amplifying weak signals. With the recent improvements, the weak responses observed from certain biologically relevant molecular compounds will yield higher contrast CARS images. An attractive approach to avoid the difficulties inherent to CARS microscopy is based on the detection of stimulated Raman scattering (SRS). Quantum mechanically SRS is described as a two-photon stimulated process where one pump photon at ωp is annihilated (stimulated Raman loss: SRL) and one Stokes photon at ωS is created (stimulated Raman gain: SRG), while the Raman medium makes a

Fig. 17. F-CARS and E-CARS microscopy with co-propagating incident beams, forward and backward signal collection, respectively. Obj., objective lens; F., filter; BS., beam splitter; BC., beam combiner; L., lens; M., mirror, Ref. [208].

transition from the initial electronic ground state to the final vibrational excited state. A stimulated Raman scattering microscope with near-infrared picosecond laser pulses at high repetition rates (76 MHz) and radio-frequency lock-in detection could be used for noninvasive point-by-point vibrational mapping of chemical and biological samples with high sensitivity and without the requirement for labeling the sample with natural or artificial fluorophores [205,206]. The major benefit of this technique is the capability to respond exclusively to the linear Raman-resonance properties of the sample, thus allowing a direct quantitative interpretation of image contrast in terms of the number density of Raman-active modes. CARS microscopy has been used for selective imaging of lipid droplets in unstained living cells with a very high contrast [200,207]. In a recent study, Nan et al. [200] applied CARS microscopy to monitor the growth of triglyceride droplets during the differentiation process of 3T3-L1 cells. In addition to the traditional picture of lipid accumulation in the differentiation process, the images indicate an intermediate stage (i.e. the removal of cytoplasmic lipid droplets after addition of the induction medium). This reduction of lipid droplets is attributed to an increased activity of hormone sensitive lipase, the enzyme responsible for hydrolysing intracellular triglyceride and sterol esters. CARS microscopy has been also used for the rapid acquisition of 2-D and 3-D images at subcellular resolutions in live cells [198,199,201,208–212]. 4.1.1. CARS microscope Earlier in CARS microscopy [198,208] two synchronized pulsed lasers are used at different frequencies, one of them tunable for adjusting the desired Raman shift. These pulse trains are generated from two Ti:sapphire lasers in the near infrared (pump laser at 730 nm and Stokes laser tunable from 750 to 950 nm, repetition rate 80 MHz, pulse duration 3 ps) to prevent two-photon electronic resonances [195]. To reduce the pulse repetition rate, each beam is pulse picked with Bragg cells, thus avoiding photo-damage to the sample while maintaining high peak power. The pump and Stokes beams are temporally overlapped by an optical delay line. Expanded beams are combined in a collinear geometry, then sent into an inverted microscope, and finally focused into the sample using a water objective (40× and NA 1.2). The backscattered CARS signal is collected by the same objective lens (E-CARS for epidetection), while the forward-scattered CARS (F-CARS) is collected by a condenser lens (NA 0.5). The two signals pass through a set of band-pass filters, and are detected by two avalanche photodiodes

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Fig. 18. CARS images of live COS-7 cells: average powers incident at the sample were 80 ␮W at a laser repetition rate of 2 MHz. The Raman shift is 2845 cm−1 , in the spectral region of aliphatic C–H vibrations. One can clearly distinguish the plasma and nuclear membranes and intracellular structures such as vesicles; the acquisition time was 15 min, Ref. [208].

as shown in Fig. 17 [208]. CARS images are obtained by fast scanning the sample, using an XYZ piezo-flexure stage. Recently, the typical laser sources for CARS imaging are synchronously pumped optical parametric oscillators (OPOs) [213] and fiber lasers [214] rather than electronically synchronized oscillators. The OPO provides a continuously tunable frequency difference between the two beams over a broad range of Raman shifts (100–3700 cm−1 ) by varying the temperature of a single nonlinear crystal. The near-infrared output (900–1300 nm) allows for deep penetration into thick samples and reduced nonlinear photodamage. 4.1.2. Live cell imaging CARS microscopy permits imaging of intrinsic biomolecules without chemical labeling. Near-infrared lasers with moderate excitation powers (a few hundred of ␮W) avoid cellular photodamage [198], and permit three-dimensional sectioning with sub-micrometer resolution. CARS image formation takes advantage of the constructive coherent emission in the forward direction (F-CARS) produced by the excited molecular bonds. Examples of FCARS images of live cells are shown in Fig. 18 [208]. The signal is obtained when the frequency difference between the pump and the Stokes lasers corresponds to the Raman shift 2845 cm−1 , of aliphatic C–H stretching vibration. Aliphatic C–H bonds are abundant in the

lipid bilayer of the cell and nuclear membranes. In comparison to other microscopy techniques, CARS permits probing of different molecular bonds, in different biological systems. Examples include, imaging of C–H stretching vibration present in the lipid bilayer of the cell membranes [199,200], P–O vibration (at 1090 cm−1 ) in chromosomes [199], water in cells [215,216], proteins [217], artificial model membranes [59,208], and more recently, imaging of live tissues [201,202]. The resonant CARS signal provided by a specific excited chemical bond is not free of solvent background. The nonresonant CARS signal from the solvent is independent of the Raman shift and can be stronger than the resonant CARS signal. In such case the image contrast is considerably decreased. To enhance the contrast and differentiate specific lipids containing many different bonds such as CH, CH2 , and CH3 whose vibrational frequencies are very similar (around 3000 cm−1 ), it makes use of deuteration that changes the Raman shift but does not alter the molecular structure of the cell membrane [218]. By replacing CH2 groups by CD2 groups in lipids, their vibrational frequencies are dramatically changed (Fig. 19, left) without affecting the lipid structure [208]. The CD2 vibrational frequency is interesting because it falls in a silent region (between 2100 and 2300 cm−1 ) of other CH vibration bonds (Fig. 18, right). This rela-

Fig. 19. (Left) CARS spectrum of deuterated lipids (D54-DMPC) (right) CARS image of a Giant unilamellar vesicles (GUV), obtained by electroformation method of deuterated lipids (D54-DMPC). The Raman shift is 2105 cm−1 , corresponding to the CD2 stretching vibration, the acquisition time was 3 min, Ref. [208].

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Fig. 20. CARS images of stratum corneum. The Raman shift is set at 2845 cm−1 to address the lipid CH2 symmetric stretch vibration. Depth: (a) 0 ␮m, (b) 20 ␮m, (c) 40 ␮m, (d) 60 ␮m. The gray scale gives the E-CARS signal intensity, the acquisition time was 8 min, Ref. [208].

tively noninvasive labeling process can be used for live cell imaging [219], and investigation of the segregation of domains in model systems [220]. 4.1.3. CARS tissue imaging CARS microscopy provides chemical imaging of live skin tissues (skin: stratum corneum) [201]. The use of long excitation wavelengths (infrared lasers) enables deep penetration for thick samples, and reduces the amount of light scattering in tissues. Fig. 20 shows an example of stratum corneum (SC) imaging with the CARS technique [208]. The bright polygonal patterns outline the keratinocytes present in SC, the most superficial skin layer. The CARS images are taken at the 2845 cm−1 , C–H symmetric stretch vibration and at different depths. The signal is detected in the backward direction (E-CARS) and comes from the back-scattered strong F-CARS generated signal. This example illustrates the possibility of performing CARS microscopy in nontransparent tissues with a standard inverted microscope stand. The CARS resolution along the z-axis is 3 mm. The last remaining problem in CARS tissue imaging technique is the laser system itself which needs simplification [213,214]. 4.1.4. Focus-engineered CARS for imaging chemical interfaces Vibrational imaging is often needed to distinguish between chemically distinct microscopic objects showing up the “chemical interfaces” present in the sample under investigation. Several configurations for signal generation and detection such as polarization sensitive CARS [217], epi-CARS [194,198], heterodyne CARS [204],

frequency-modulation CARS [221] and time-gated CARS detection [203] have been developed to reduce the deleterious effects of the non-resonant background in CARS images. Among these techniques, the epi-detection method is particularly attractive because of its experimental simplicity. The inherent large phase mismatch in the epi-direction naturally suppresses the contribution from the bulk, while stressing sub-wavelength objects as a result of incomplete destructive interference. It is recently proposed that the suppression of the bulk contribution can be achieved even in the forward direction by employing CARS excitation profiles with alternative spatial phase distribution. The concept of focus engineering is proposed to enhance the sensitivity of CARS microscopy to these interfaces [222]. An engineered ␲-phase step is introduced in the excitation field so that the oscillators in one region of the focal volume are out of phase with respect to those from another region. For instance, the use of higher order Hermite–Gaussian focal Stokes fields enables the suppression of the homogeneous background while selectively highlighting “(3) -interfaces” or “chemical edges” [223]. It is also shown that the mere modification of the spatial phase of the excitation beams influences the spectral characteristics of the CARS output. Investigation of possibility of detecting longitudinal (3) interfaces – interfaces that are perpendicular to the direction of propagation of the beams – in the forward detection mode is carried out [222]. The simplest way to detect longitudinal interfaces is to suppress the bulk signal from either side of the interface by engineering a CARS excitation focal field that undergoes a ␲-phase

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Fig. 21. CARS imaging of endothelium of ex vivo carotid artery without any labeling. (a) CARS image of unstained endothelium on the lumen surface. The white bands are the innermost surface of the undulated internal elastin lamina. (b) Zoom-in image of the red rectangular area in (a) for single cell observation. (c) Spectral profile of the NLO signal from endothelium in the 450–650 nm range. A sharp CARS band generated is located around 588 nm. Little fluorescence was detected. (d) TPEF image of the plasma membrane of endothelial cells stained with FITC-IB4, Ref. [229]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

jump along the optical axis. To achieve this, a Gaussian beam is employed as the pump beam and an “optical bottle beam” as the Stokes beam for CARS signal generation. Based on numerical simulations, it has been found that [222] using a focused Stokes field with a sharp phase jump along the longitudinal direction leads to the suppression of the signal from bulk regions and improves the signal contrast from vibrational resonant interfaces oriented perpendicular to the axis of beam propagation. It is also demonstrated that [222] the CARS spectral response from chemical interfaces exhibits a clean, Raman-like band-shape with such a phase-shaped excitation. This phenomenon of interface distinction is a consequence of the coherent nature of CARS signal generation and it involves a complex interplay of the spectral phase of the sample and the spatial phase of the excitation fields. 4.1.5. Multimodal CARS microscope Two-photon excited fluorescence (TPEF) microscopy has been extensively applied to biological imaging by utilizing intrinsic fluorescence or extrinsic labeling of bio-molecular structures [224]. Being sensitive to non-centrosymmetric structures, second harmonic generation (SHG) imaging was first demonstrated in 1970s [225]. Both SHG and electronic sum-frequency generation (SFG) have been utilized for imaging biological samples such as mem-

branes [226] and protein fibrils [227]. Both TPEF and SHG are simultaneously generated by a single femtosecond laser in many tissue imaging studies [228]. A multimodal imaging system that integrates CARS, sumfrequency generation (SFG), and two-photon excitation fluorescence (TPEF) on the same platform is developed and applied to visualize single cells and extracellular matrix in fresh carotid arteries [229]. CARS signals arising from CH2 -rich membranes allow visualization of endothelial cells and smooth muscle cells of the arterial wall. It also allows vibrational imaging of elastin and collagen fibrils that are also rich in CH2 bonds. The extracellular matrix organization is further confirmed by TPEF signals arising from elastin’s autofluorescence and SFG signals arising from collagen fibrils’ non-centrosymmetric structure. Label-free imaging of significant components of arterial tissues suggests the potential application of multimodal nonlinear optical microscopy to monitor onset and progression of arterial diseases. By means of CARS imaging tuned to 2845 cm−1 , the endothelium formed by a single layer of endothelial cells could be clearly detected (Fig. 21a). The enlarged image (Fig. 21b) clearly shows single endothelial cells and cell junctions with sub-micrometric spatial resolution [229]. CARS is capable of imaging endothelial cells due to the abundant CH2 groups in cell membrane. Micro-spectrometry

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Fig. 22. Imaging and micro-spectral analysis of unstained elastin in the internal elastic lamina. The lasers were focused at ∼2 ␮m inside the lumen surface of a fresh sample. (a) F-CARS (gray) and (b) TPEF (green) image of elastin bands. (c) NLO signal spectrum of elastin. The CARS peak (red) located around 588 nm was 20 times larger than the TPEF peak around 480 nm (Green) under the same acquisition condition. (d) CARS spectrum of elastin measured by tuning the Stoke frequency from 10807 cm−1 to 11758 cm−1 . The two major peaks were located at 2870 cm−1 and 2930 cm−1 , Ref. [229]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

measurement (Fig. 21c) of cell membranes showed strong CARS signals peaked around 588 nm. Auto-fluorescence signal is undetectable in the endothelium region (Fig. 21c). To further confirm that CARS signal is indeed arisen from endothelial cells, the sample has labeled with an endothelial cell-specific marker, FITC-IB4. TPEF visualization of FITC-IB4 labeled endothelial cells (Fig. 21d) proved the capability of CARS microscopy for imaging endothelial cell membranes. At approximately 2 ␮m deep from the lumen, an undulated layer of internal elastic membrane is emerged from both CARS (Fig. 22a) and TPEF imaging (Fig. 22b) [229]. The elastin signals from these two imaging modalities perfectly overlapped with each other. Further measurements confirmed that both CARS and TPEF are generated from elastin (Fig. 22c). Spectral analysis showed strong elastin CARS signal that peaked at 588 nm and elastin TPEF emission signal that peaked around 480 nm. The distinct separation between CARS and TPEF spectra allows both signals to be collected simultaneously through bandpass filters. The intrinsic auto-fluorescence of elastin is attributed to the cross-linking structure of elastin fibers, whereas it is possible that CARS signals of elastin are attributed to the CH2 -rich amino acid side chains of lysines, which are present predominantly at the cross-linking region [230].

No polarization dependency in CARS intensity for elastin is observed, while polarization dependence of CARS intensity is due to ordered orientation of CH2 groups in lipid bilayer. Polarization independence of elastin is probably due to disordered orientation of CH2 -rich residues in the cross-linking region . As CARS intensity for lipid bilayer arises mainly from symmetric CH2 stretching band, CARS intensity for elastin probably arises from both symmetric and asymmetric CH2 stretching bands. Furthermore, the presence of carbonyl groups of the cross-linking residues of elastin [230] could cause a blue shift of the CH2 stretching vibration frequencies. The two peaks at 2870 cm−1 and 2930 cm−1 (Fig. 22c) assigned to the symmetric and asymmetric CH2 stretching bands of elastin, respectively. By focusing the laser beams at greater than 10 ␮m deep from the lumen, highly ordered rod-shape cells and stripes of elastin are observed with CARS imaging (Fig. 23a) [229]. Rod-shaped cells are assigned as smooth muscle cells. In addition, simultaneous SFG imaging showed strong presence of collagen fibrils around smooth muscle cells (Fig. 23b). The distribution of collagen fibrils around smooth muscle cells is in agreement with previous descriptions of tunica media structural organization [231]. To further verify the obtained assignment, doxorubicin is used, a DNA intercala-

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Fig. 23. CARS imaging of single smooth muscle cells in the tunica media layer. (a) E-CARS image of unstained smooth muscle cells at ∼10 ␮m inside luminal surface. The transverse white bands are attributed to elastin lamella. (b) Overlaid E-CARS and SFG image of the red rectangle area marked in (a). The SFG (blue) signal around the smooth muscle cells is attributed to the collagen-rich basement membrane. (c) F-CARS image and (d) TPEF image of smooth muscle cells located at ∼12 ␮m from the lumen surface. The sample was labeled with doxorubicin. The green arrow indicates a single smooth muscle cell, Ref. [229]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

tor that targets the nuclei of smooth muscle cells [232], to label a fixed artery sample. It is found that TPEF images of doxorubinlabeled nuclei are located within CARS images of smooth muscle cell membranes (Fig. 23c and d). This observation further supports assignment of smooth muscle cells to the rod-shaped cells visualized by CARS. To image arterial structures within the adventitia, the laser beams are focused onto the outer surface of an artery. Examination with CARS (Fig. 24a), TPEF (Fig. 24b), and SFG (Fig. 24c) showed that adventitia comprises mainly collagen and elastin [229]. TPEF and SFG are sensitive to elastin and collagen, respectively, while the CARS image displays both structures. Collagen fibrils (Fig. 24d) showed two signal peaks at 588 nm and 393 nm, which are attributed to CARS and SFG signals, respectively. The CARS spectrum of collagen is shown in Fig. 24e. Like elastin, CARS signals from collagen fibrils are most likely arisen from the stretching vibrations of CH2 -rich residues in the cross-linking region [233]. Because SFG signals peak at ∼393 nm, TPEF signals peak at ∼480 nm, and CARS signals peak at ∼588 nm, signals from all three imaging modalities can be collected through three distinctive bandpass filters. To get an entire view from lumen to adventitia of the carotid artery, multiple nonlinear optical image of the cross section of

an arterial with stitching them together is acquired. As shown in Fig. 25, the integrated image allowed a clear visualization of the distribution of collagen and elastin fibrils in arterial wall. CARS imaging by itself is sufficient to provide visualization of collagen fibrils and elastin (Fig. 25a), as confirmed by selective TPEF imaging of elastin (Fig. 25b) and SFG imaging of collagen fibrils (Fig. 25c) [229]. Within the adventitia, it is found that the outer layer is rich in collagen fibrils and the inner layer is rich in elastin (Fig. 25b and c). In the tunica media, it is found that collagen and elastin signals entwined with one another (Fig. 25c). Although it appears that most collagen signals are in parallel with elastin (Fig. 25c), higher resolution images showed that many collagen fibrils arranged themselves along the polarity of smooth muscle cells in the direction perpendicular to elastin (Fig. 23). Such capability should be invaluable to the evaluation of artery structural integrity or lack-there-of during the onset and progression of arterial diseases. CARS microscopy is effective in probing water dynamics in cells [215] whereas experimental doubts have been raised against probing water dynamics in membranes [234]. CARS signals are also affected not only by the experimental conditions, but also by the specimen sizes and shapes. So the conventional description of microscopy, such as point spread function (PSF), will fail to depict the imaging characteristics of CARS microscopy. Cal-

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Fig. 24. NLO imaging of adventitia. (a) CARS, (b) TPEF, (c) SFG images of adventitia in an unstained carotid artery. The lasers are focused at ∼2 ␮m from an artery outer surface. (d) NLO signal spectrum from collagen. The two peaks at 588 nm and 393 nm are contributed by CARS and SFG, respectively. (e) CARS spectrum of collagen measured by tuning the Stoke frequency from 10823 cm−1 to 11750 cm−1 . The two major peaks were located around 2875 cm−1 and 2930 cm−1 , Ref. [229].

culations for propagation of CARS signals by using the wave equation and the slowly varying envelope approximation (SVEA), the focal profile and the intensity angular distributions of CARS signals emitted by various specimens with different shapes and sizes gave quantitative-imaging characteristics of CARS microscopy [190,194,235]. Upon the nonlinear dependence of the CARS intensities on the incident intensities, the available excitation volume diminishes to about quarter of the linear excitation volume for

NA = 5.0, and the resolution power increases accordingly. To satisfy the phase-matching conditions, objective with high number aperture should be used. Because intensity angular distributions of CARS signals depend on the shapes and sizes of specimens, the shapes and sizes of specimens can in principle be estimated. In three-dimensional resolution CARS microscopy developed for vibrational imaging of chemical species, the detection of backwardCARS and forward-CARS (F-CARS) signals depends on the size

Fig. 25. Stitched cross-sectional images of a fixed carotid artery characterized by NLO (CARS, TPEF, and SFG) imaging with a 20× objective. (a) CARS (gray) image of an entire artery cross-section. Overlaid image depicts the overlapping elastin bands viewed by CARS (gray) and TPEF (green). (b) TPEF (green) image of the artery cross-section at the same region. (c) SFG (blue) image at identical place. Overlaid image shows the organization of elastin and collagen in tunica media, Ref. [229]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Fig. 26. (a) Polarization vectors of the pump and the Stokes fields, the nonresonant CARS signal, and the analyzer polarizer. (b) Nonresonant CARS signal [counts/s (CPS)] from a water–glass interface as a function of angle ϕ. The ratio of the maximum counts at ϕ ∼ 30◦ to the minimum counts at ϕ ∼ 120◦ is 600:1, Ref. [217].

and shape of the sample. The theoretical description of CARS signal generation under tight focusing conditions and its significance for F- and E-CARS detection was first developed by the Xie group [190,194,236]. Backward-CARS and F-CARS signals are measured for different polystyrene bead diameters embedded in different refractive index solvents. Refractive index mismatches between the sample and its surroundings should be maintained. The index mismatches result in a backward-reflected F-CARS signal that generally dominates the experimentally backward-detected signal [190,194,236,237]. Simulations based on geometrical and wave optics comparing forward- and backward-detected signals for polystyrene beads embedded in different index solvents confirmed that the maxima of forward- and backward-detected signals generate at different positions along the optical axis in the sample if refractive index mismatches are present between the sample and its surroundings. A miniature objective lens with a tip diameter of 1.3 mm was used for extending the penetration depth of CARS microscopy. Its axial and lateral focal widths were determined to be 11.4 and 0.86 ␮m, respectively, by two-photon excitation fluorescence imaging of 200 nm beads at a 735 nm excitation wavelength. By inserting the lens tip into a soft gel sample, CARS images of 2 ␮m polystyrene beads 5 mm deep from the surface were acquired. The miniature objective was applied to CARS imaging of rat spinal cord white matter with a minimal requirement for surgery [238]. 4.1.6. Polarization and interferometric polarization CARS microscopy CARS microcopy is not background free, and the strong nonresonant signal arising from the electronic contributions of surrounding solvent and other media in biological samples degrades the vibrational contrast and spectral selectivity in CARS imaging. In addition to time-gated CARS [203], polarization coherent anti-Stokes Raman scattering spectroscopy (P-CARS) was demonstrated in the late 1970s [239,240] to suppress the nonresonant background by making use of the polarization difference between the resonant and the nonresonant CARS fields. The theory of P-CARS has been described elsewhere [240,241]. Cheng et al. [217] demonstrated P-CARS for microscopy by considering a pump beam at frequency ωP and a Stokes beam at frequency ωS propagating along the z axis. The pump beam is linearly polarized along the x axis, and the Stokes beam is linearly polarized along a direction at an angle of  relative to the x axis, as shown in Fig. 26a [217]. Suppose that (ωP − ωS ) is resonant with a molecular vibration and the interaction of the incident beams with the sample induces a third-order polarization that contains a nonresonant part, PNR , and a vibrationally resonant part, PR . In the absence of any electronic resonance in the system, NR is a real quantity that is independent of frequency. Assuming a value of 1/3 [241] for the depolarization ratio NR of the nonresonant CARS field, PNR is therefore linearly

polarized with an angle of ˛ relative to the x axis, where the angle ˛ is related to  by tan ˛ = NR tan . The nonresonant background can be removed by the placement of an analyzer before the detector with polarization perpendicular to PNR . In practice, there exists a residual background because of the birefringence induced by the dichroic mirror in the beam path and the scrambling of polarization at the tight focus. Considering the extinction ratio r (which is defined as the ratio of the maximum to minimum signals obtained by rotation of the analyzer) and ˛ = 45◦ , then the optimal value for the angle  is then 71.6◦ , which is calculated using the relation  = tan−1 (3 tan ˛). So P-CARS microscopy can be applied to vibrational imaging by use of Raman bands with depolarization ratio of resonant CARS field R = / RN . For example, if R = 0 the contrast can be improved by r/4 times compared with the case with parallel-polarized excitation beams. The CARS signal microscopy is used to characterize director structures of anisotropic fluids giving three-dimensional images [242]. The P-CAR showed a strong dependence on alignment of chemical bonds/molecules with respect to the collinear polarizations of Stokes and pump/probe excitation beams. This dependence allows for the visualization of the bond/molecular orientations via polarized detection of the CARS signal for liquid crystal director fields, using structures in nematic, cholesteric, and smectic liquid crystals [243]. To increase the potential of the polarization technique interferometric CARS has been recently implemented to obtain resonant CARS signals without attenuation. But the introduction of an external reference CARS signal for interference usually requires a more complicated experimental system (e.g., a Mach–Zehnder interferometer) [204]. Lu et al. [244] proposed a new interferometric polarization CARS (IP-CARS) microscopy that effectively suppresses the nonresonant background while significantly amplifying the resonant signal for sensitive vibrational imaging with high contrast. They [244] used the method by imaging 4.69 ␮m polystyrene beads and unstained human epithelial cells immersed in water. To overcome the limitation of low signal levels of conventional P-CARS, they [244] introduced a second Stokes beam ES2 with polarization perpendicular to the first Stokes beam ES1 to avoid their mutual interference. Also to obtain the maximum vibrational contrast, the polarization directions of the pump and the second Stokes beams are rotated by 71.6◦ and 90◦ clockwise [217], respectively, relative to the horizontal polarization of the first Stokes beam by using half-wave plates. By modulating the phase difference between the two interference CARS signals generated from the same sample and measuring the peak-to-peak intensity of the periodically modulated interference CARS signal, the IP-CARS technique yields a 6-fold improvement in the signal-to-background ratio compared with conventional CARS while providing an approximately 20-fold amplification of the resonant CARS signal compared with conventional polarization CARS. Therefore IP-CARS technique offers the potential for detecting weak signals of various biochemical species in biological systems giving higher contrast molecular vibrational imaging. 5. Conclusion Developments and applications of ns-, ps-, and fs-laser-based CARS spectroscopy in gas-phase reacting flows are reviewed. The ns-laser-based CARS technique is used in the measurement of temperature and multiple-species concentration on a single-shot basis. On other hand, dual-pump CARS, triple-pump CARS, dualbroadband CARS, and dual-pump dual-broadband CARS are applied mainly to detect multiple species with one experimental setup. These CARS techniques are also used to increase the accuracy of the temperature measurement over a large dynamic range between 300 and 2500 K. The ns-dual-broadband CARS provides in general a better accuracy for temperatures below 1500 K, whereas the

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temperature accuracy is increased in rotational CARS for temperatures exceed 1500 K. ps- and fs-laser-based CARS spectroscopy for the diagnosis of reacting flows are developed to deal with the limitations (i.e., interference of the nonresonant background signal, NRB, with the resonant CARS signal, low data acquisition rate, and dependence of the signal on the local collisional environment) came across by ns-laser-based measurements. In ps-CARS, the probe beam is temporally delayed with respect to the pump and Stokes beams to suppress the nonresonant background. psCARS spectroscopy can also be used to measure the state-specific relaxation rates by delaying the probe beam with respect to the pump and Stokes beams. Nevertheless, ps-CARS has the same limitations relative to data acquisition and collisional dependence as ns-CARS. fs-laser-based CARS spectroscopy has the potential to overcome most of the problems associated with ns- and ps-CARS spectroscopy. Flame measurements in gas cell showed that fs lasers allow nearly collision-free measurements (i.e., for pressures less than 20 bar) at a rate of 1 kHz or greater on a time scale is shorter than the characteristic collision times. Time-resolved fs-CARS spectroscopy is able to neglect the contribution from the NRB signal and provide a high data-acquisition bandwidth, thereby capturing various instability modes and their interactions in reacting flows related to gas-turbine combustors and augmentors. Temperature and concentration measurements of diatomic and triatomic gasphase molecules can be performed using a single fs-laser beam. Development of the pulse-shaping technique would help to the application of fs-CARS spectroscopy in harsh reacting gas flows. Further experiments are required before single-beam fs-CARS can be applied to reacting flows of practical interest. CARS microscopy, as a nonlinear optical technique, is an imaging technique based on contrast derived from molecular vibrations. In CARS microscopy both the pump and the Stokes beams are tightly focused in a collinear geometry, therefore CARS signal is generated and detected under tight focusing conditions. CARS microscopy as a label-free chemical sensor is used for imaging lipids and their dynamic distribution because lipids have high density of CH2 -oscillators, thus, high CARS signals are obtained from lipid containing specimens. By tuning into characteristic vibrational resonances in samples, CARS microscopy provides chemically selective information without the use of labels or the complication of photobleaching. The stimulated coherent excitation of many vibrational oscillators provides a much stronger signal than that of conventional Raman microscopy, allowing for real-time imaging of living cells or organisms at acceptable laser powers. The CARS signal is generated at the focal spot, providing 3D sectioning of thick tissues. No pinhole is needed at the detector plane resulting in high backward-scattered signals even at substantial penetration depths into biological samples. There are many forms of CARS (F-CARS, E-CARS, P-CARS, MCARS) being developed since 1999. E-CARS or epi-directed CARS signal is generated via three different mechanisms: incomplete destructive interference by objects smaller than the wavelength of light, discontinuity of the thirdorder nonlinear susceptibility (3) at the interface of two media, and backscattering of initially forward-propagating photons in turbid specimens. The sensitivity of CARS microscopy has been improved by frequency modulation CARS detection. The most favorable light source for CARS imaging is a picosecond pulsed laser that is working above 800 nm to avoid multiphoton damage of specimens and to consent to deep penetration in thick samples. Isotope substitution by deuterium offers a well-isolated CD stretching frequency for mapping the distribution of metabolites or drugs. The much higher scanning speeds and fast image acquisition times make CARS the method of choice when dynamics on the seconds to minutes timescale are relevant to the imaging application. As a medical imaging technique, CARS is imaging at subcellular resolutions in real time.

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