Microscopy and Applications

Chapter 5

Coherent Optical Spectroscopy/ Microscopy and Applications Vikas Kumar1, Nicola Coluccelli1 and Dario Polli1, 2 1

IFN-CNR, Politecnico di Milano, Milano, Italy; 2CNST, Istituto Italiano di Tecnologia, Milano, Italy

Chapter Outline 1. 2. 3. 4. 5.

Introduction Coherent Optical Spectroscopy/Microscopy Importance of Lasers in Optical Spectroscopy/Microscopy Linear and Nonlinear Spectroscopy/Microscopy Linear Spectroscopy/Microscopy Techniques 5.1 Infrared (Absorption) Spectroscopy 5.2 Confocal Microscopy 5.3 Laser-Induced Fluorescence Microscopy 5.4 Spontaneous Raman Spectroscopy/Microscopy 6. Nonlinear Spectroscopy/Microscopy Techniques 6.1 Coherent Raman Spectroscopy/Microscopy 6.1.1 Coherent Anti-Stokes Raman Spectroscopy/ Microscopy 6.1.2 Stimulated Raman Spectroscopy/Microscopy

87 88 88 89 90 90 91 92 93 94 94 97 102

6.1.3 Raman-Induced Kerr Effect Spectroscopy/ Microscopy 6.1.4 Balanced-Detection Raman-Induced Kerr Effect Spectroscopy 6.2 Second Harmonic Generation Microscopy 6.2.1 A Typical Second Harmonic Generation Microscope Setup 6.3 Third Harmonic Generation Microscopy 6.3.1 Requirements of a Typical Third Harmonic Generation Microscope Setup 6.4 Two-Photon Excitation Fluorescence Microscopy 7. Conclusions References

105 107 108 110 110 111 112 113 113

1. INTRODUCTION Optical spectroscopy has always been a fascinating tool for researchers to reveal and study fundamental properties of materials by analyzing the interaction of electromagnetic radiation with matter. Measurements of absorption, emission, scattering, and rotation of light by atoms or molecules provide important structural information and their chemical identification. Furthermore these spectroscopic observables can be collected to provide a one-to-one mapping of the investigated volume of the sample to constitute a microscopic image. Fast spectroscopic imaging allows the investigation of molecular dynamics and biological mechanism. Simple linear methods such as linear absorption and photoluminescence spectroscopy were being practiced for qualitative and quantitative determination of atomic/molecular species much prior to the existence of the first laser. Ever since the advent of laser in 1960, the optical spectroscopy field has been revolutionized by the unprecedented intensity offered by lasers. Apart from enhancing the signal efficiency of the linear methods, it revealed a plethora of nonlinear optical spectroscopy techniques, which were practically impossible earlier due to very low signal efficiency provided by conventional light sources. Much improved signal efficiency and availability of high-sensitivity modern detectors have enabled many of such techniques for high-speed microscopy, few of them up to video-rate imaging. On the basis of their unique characteristics and capabilities, optical spectroscopy/microscopy techniques have got a variety of important applications in material science, biology, pharmaceutical, and medical fields. This chapter will briefly cover different optical spectroscopy/microscopy techniques based on the coherent excitation of the investigated atoms/molecules and on the scattered radiation from them either being incoherently added or being composed

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of their coherent superposition. We will be focusing on a few important coherent optical spectroscopy/microscopy techniques and discuss in detail their key features, methods, and simplified implementation schemes; parameters required for excitation source; and detection mechanism followed by their main application areas.

2. COHERENT OPTICAL SPECTROSCOPY/MICROSCOPY In optical spectroscopy experiments, a group of atoms or molecules are irradiated by light and we study their interaction with light. Optical spectroscopy techniques can be divided into two important categories based on whether the detected signal is coherent or incoherent. First category is “coherent optical spectroscopy techniques,” which are often characterized by a fixed phase relationship between individual radiations emerging from different atoms/molecules under study. The individual fields will be coherently added, and in this way, the total electric field attained by averaging over all the emitters is nonzero ( s 0). Second category is “incoherent optical spectroscopy techniques,” where phases of the individual fields emerging from different emitters are uncorrelated (random), therefore the total field attained by averaging over all the emitters is zero ( ¼ 0), but not the total intensity (), which can still be nonzero. Fig. 5.1 gives a simple example for the two situations. Molecules having intrinsic vibrational frequency U are irradiated by input coherent radiation (usually called “pump” radiation) at frequency u; if u is different from U, the molecules in the entire focal volume are agitated (Fig. 5.1A) and they start vibrating and act like electric dipoles oscillating at frequency U but with random phases. These oscillating dipoles radiate in random phases in all 4p steradian directions in a sphere, consequently the total signal field attained by averaging over all the oscillating dipoles (emitters) is zero, but the total signal intensity will still be obtained by incoherent addition of their individual intensities. Raman scattering and fluorescence are such type of incoherent signals. On the other hand, if u is in resonance with U, the molecules in the focal volume are coherently driven (Fig. 5.1B) and they act like coherently oscillating electric dipoles, consequently they radiate individual fields having fixed phase relationships among them, hence they constructively interfere in some particular directions. In this way, the total electric field attained by averaging over all the emitters is nonzero in those particular directions and it will form a coherent signal in a well-defined direction. Rayleigh scattering and coherent Raman scattering (CRS) produce such coherent signals. We will discuss later in detail the advantages of coherent techniques. It is worth to mention here that u can also be a combination of two or more fields at different frequencies, e.g., u h u1  u2. It will be seen later that such combinations are used in multiphoton nonlinear techniques to generate much enhanced coherent signal with respect to the signal levels in their incoherent linear analogs. Coherent Raman techniques are the best examples where signal enhancement is achieved to an order of 105 or more with respect to the signal in incoherent spontaneous Raman technique.

3. IMPORTANCE OF LASERS IN OPTICAL SPECTROSCOPY/MICROSCOPY Lasers have revived the classical spectroscopy world and have also made feasible several new spectroscopy techniques. Laser light is far beyond the light from conventional sources in terms of brightness, directionality, and spectral purity.

FIGURE 5.1 Laser-induced molecular vibrations: (A) incoherent and (B) coherently driven.

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These favorable properties of laser have increased the efficiency of the lightematter interaction and consequently the signal efficiency. As a result, it has increased manyfold the sensitivity and the resolution of the classical techniques such as absorption spectroscopy, fluorescence spectroscopy, Raman spectroscopy, etc. In addition, laser light can also be synthesized in extremely intense and short-duration pulses. Employing such intense short pulses has made otherwise inefficient higher-order lightematter interactions observable, which paved the path for popular nonlinear spectroscopy techniques such as coherent Raman spectroscopy, second harmonic generation (SHG) spectroscopy, third harmonic generation (THG) spectroscopy, two-photon excitation fluorescence spectroscopy, etc. Many of them are at present capable of video-rate imaging, all thanks to the laser. High monochromaticity of the laser can induce selective quantum transitions between specific atomic/molecular levels. The fixed optical frequency lasers were used to produce full Raman spectra. It is the advent of optical frequency tunable lasers that have galvanized the laser spectroscopy world. Utilizing these tunable lasers, one can sweep the entire frequency range to observe the lightematter interaction to collect the signature spectra of the matter. Furthermore, evolution of broadband laser sources has made possible to watch the entire spectra at once. The development of tunable and broadband optical parametric amplifiers (OPAs) and optical parametric oscillators (OPOs) has filled the gaps in optical frequency range, which were unreachable by conventional lasers. Lasers and their combination with OPA/OPO are now the workhorse in several widespread spectroscopy/microscopy applications carried out worldwide.

4. LINEAR AND NONLINEAR SPECTROSCOPY/MICROSCOPY Optical spectroscopy/microscopy techniques can further be classified in two categories: linear and nonlinear. This classification resides in electric properties of the material, which in turn is a relationship between the induced electric polarization density P and the externally applied electric field E. In a dielectric medium, the induced polarization density P is the macroscopic sum of dipole moments p induced by the external electric field E, i.e., P ¼ N p, N being number density. A material is called “linear” as long as it is characterized by linear relationship between P and E. This linear relationship is expressed as: P ¼ ε0 cðuÞE

(5.1)

where ε0 is the “permittivity of free space” and cðuÞ is called the “dielectric susceptibility” of the material. On the other hand, the material is said to be “nonlinear” when the relationship between P and E becomes nonlinear. The spectroscopy/ microscopy techniques that deal with the linear behavior of the targeted material are called “linear techniques,” whereas those dealing with its nonlinear behavior are named “nonlinear techniques.” Now, we will see in which conditions a material will behave linearly or nonlinearly. When an external electromagnetic field E ¼ ½A expfjðut  kzÞg þ c:c:, where A is the field amplitude and c.c. represents “complex conjugate” term, is applied on a material, the linearity of Eq. (5.1) holds correctly as A is small at normal intensities. But at high intensities, a situation easily achievable at focused laser spot, the field amplitude A may become comparable to the interatomic field strength (w105e108 V/m). When this happens, the anharmonicity incorporated in the induced polarization leads to a nonlinear material response expressed as the following nonlinear relationship between P and E [1]: P ¼ ε0 cð1Þ ðuÞ: E þ cð2Þ ð  u3 ; u1 ; u2 Þ: E E þ cð3Þ ð  u4 ; u1 ; u2 ; u3 Þ: E E E þ .

(5.2)

where c(i) is the (i þ 1)th rank tensor and c(1), c(2), and c(3) are, respectively, called linear dielectric susceptibility, secondorder dielectric susceptibility, and third-order dielectric susceptibility. They contain linear, second-order, and third-order characteristic response of the bulk material, respectively, when interacting with an electromagnetic field. Double dot (:) indicates a tensorial product between c(i) and fields E. The first term on the right-hand side of Eq. (5.2) is the linear harmonic contribution PL to polarization density, whereas remaining other terms constitute the nonlinear contribution PNL. PL ¼ ε0 cð1Þ ðuÞ: E

(5.3)

PNL ¼ cð2Þ ð  u3 ; u1 ; u2 Þ: E E þ cð3Þ ð  u4 ; u1 ; u2 ; u3 Þ: E E E þ .

(5.4)

Pð2Þ ¼ cð2Þ ð  u3 ; u1 ; u2 Þ: E E

(5.4a)

Pð3Þ ¼ cð3Þ ð  u4 ; u1 ; u2 ; u3 Þ: E E E

(5.4b)

where

and so on.

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Even if we consider the field at focused laser spot, in general, the applied field E is small in comparison to the interatomic field strength, hence the nonlinearity is usually very weak. This implies that higher-order susceptibilities (c(2), c(3), and so on) are very small quantities as compared to linear susceptibility c(1). In fact, for practical purposes the contributions beyond the third-order term are neglected. In Eqs. (5.4a) and (5.4b), the use of optical frequencies u, u1, u2, u3, and u4 in brackets emphasizes the fact that nonlinearity can be supplied not only by an input field at single optical frequency u, instead a combination of fields at different optical frequencies u1, u2, u3, and u4 will do the job as well. In this way, the second-order and third-order susceptibilities are regarded as three-wave mixing and four-wave mixing (FWM) mechanisms, respectively, being provided on the site of atoms/molecules. The sign  indicates that at a time either þ or e sign is considered, and every bracket in front of c(i) must have at least one frequency with þ sign (that means there must be at least one “input” frequency in the interaction, otherwise all frequencies would be created without any input, which is physically impossible). E is the superposition of all the interacting fields. For example, in an FWM mechanism we will deal with third-order polarization P(3), and in this particular case, E will be: E ¼ Eu1 þ Eu2 þ Eu3 þ Eu4

(5.5)

E ¼ A1 expfjðu1 t  k1 :zÞg þ A2 expfjðu2 t  k2 :zÞg þ A3 expfjðu3 t  k3 :zÞg þ A4 expfjðu4 t  k4 :zÞg þ c:c: (5.6) Here ki is the wave-vector associated with the field Eui. Introducing Eq. (5.5) in Eq. (5.4b), the cube of E generates a vast number of terms. Keeping in mind the degeneracy among the frequencies, the terms can be sorted out in several groups, each one responsible for a particular third-order process that includes THG, third-order sum-frequency generation (SFG), coherent anti-Stokes Raman scattering (CARS), stimulated Raman scattering (SRS), Ramaninduced Kerr effect (RIKE), etc. Furthermore, in association with each third-order process, we get a “wave-vector mismatch” term as: Dk ¼ k4 Hk1 Hk2 Hk3

(5.7)

For a particular process to be dominant, the corresponding phase-matching condition must be satisfied, which is incorporated in: Dk ¼ 0

(5.8)

In this way, acting on the phase matching, one can select a desired process. Similar is true for the second-order polarization term P(2), which is responsible for several important second-order processes such as SHG, optical rectification, SFG, and difference-frequency generation (DFG). These second-order and third-order nonlinear processes are utilized in several nonlinear spectroscopy/microscopy techniques because they can probe different characteristic signatures of the atoms/molecules. Now we take on few important linear and nonlinear spectroscopy/microscopy techniques and discuss their schematics and applications.

5. LINEAR SPECTROSCOPY/MICROSCOPY TECHNIQUES In this section, we will develop a brief understanding of the basic methods of spectroscopy and microscopy through few well-known linear techniques. These understandings will be extended in nonlinear techniques where the need of coherent excitation of the targeted molecules is more significant and that leads to the coherent signal emission from them.

5.1 Infrared (Absorption) Spectroscopy Infrared absorption spectroscopy [2] is a linear absorption technique in which intrinsic vibrational modes of the molecules are utilized to identify them [3]. In fact, each chemical functional group is associated with its own set of vibrational modes with their corresponding frequencies of vibrations. In general, whole molecular frequency range can be classified into two regions: the region 600e1600 cm1 is called fingerprint region and the region 2800e3300 cm1 is called CH-stretching region. The IR absorption spectra display absorption lines in these regions depicting vibrational transitions of molecules to register the presence of the molecules. This makes IR absorption an important phenomenon and IR absorption spectroscopy a valuable technique. The vibrational transitions correspond to fundamental vibrations of chemical bonds, and they are related to nuclear coordinates Q, the internuclear displacement from the equilibrium position. Quantum mechanically, the transition

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probability between the two vibrational states (i to f ) in Q is given by the square of the modulus of transition moment, i.e., jRj2 , where transition moment R is given as, Z R ¼ jv; f pjv;i dQ (5.9) Here, vibrational wave function P jv(Q) is a function of nuclear coordinates only. The quantity p is electric dipole moment operator given as p ¼ i qi ri ; where qi is the charge and ri is the displacement from the equilibrium position, of the ith charge particle (nucleus or electron). It is quite indicative that for homonuclear diatomic molecules (such as H2, and O2), p ¼ 0, and hence R ¼ 0, it implies that all vibrational electric dipole transitions are forbidden. On the other hand, for a heteronuclear diatomic (polar) molecule, situation is favorable, p s 0, and can be expanded in Taylor series around Q as:    2 dp 1 d2 p p ¼ peq þ Qþ Q2 þ . (5.10) dQ eq 2! dQ2 eq Here “eq” stands for “at equilibrium.” Substituting Eq. (5.10) in Eq. (5.9):   Z Z dp  jv; f Qjv; i dQ þ . R ¼ peq jv; f jv;i dQ þ dQ eq

(5.11)

The first term in aboveRequation vanishes, because jv,i and jv, f being eigenfunctions of the same Hamiltonian are orthogonal, i.e., for i s f, jv; f jv;i dQ ¼ 0. Neglecting the higher-order terms, we get Eq. (5.12) that gives transition moment governing the vibrational transitions.   Z dp jv; f Qjv;i dQ (5.12) R ¼ dQ eq It suggests that the necessary condition for a vibrational transition to be allowed is R s 0, which implies that  dp  s0, i.e., a change in electric dipole moment must occur. Furthermore, because Q is an odd function, in order the dQ eq

integral to be nonzero, the selection rule Dn ¼ 1 must be satisfied for vibrational quantum number n, which guarantees that parity of the wave function j must change during transition. In a nutshell, only such transitions in (polar) molecules can be probed by IR absorption spectroscopy. An advantage of infrared absorption spectroscopy is that the use of an infrared laser overcomes the problem of fluorescence, which usually occurs following the absorption of a visible or ultraviolet photon by atom/molecule. Generally, in a dispersive (grating-based) IR spectrometer, the sensitivity is very low. It is the intensity advantage of Fourier transform infrared (FTIR) spectrometers, which opened up the door for routine use of infrared lasers for spectroscopy. With modern infrared sources such as Globar source (silicon carbide rod) and more sensitive infrared sensors such as Ge and InGaAs detectors, nowadays it is possible to obtain FTIR spectra in few seconds. IR absorption spectroscopy finds key applications in industry as well as in research. By the help of characteristic spectra and their strength, it is used in qualitative identification and quantitative analysis of the substances. It is employed in the study of progress of chemical reaction by observing the rate of disappearance of absorption bands of reactants and the rate of appearance of absorption bands of products [4]. It is used in detection of impurities by comparing spectra of the substance with the reference spectra of pure substance [5]. It also finds applications in forensic science [6] and in analysis of lipids in biomedical fields.

5.2 Confocal Microscopy In a conventional microscope, under wide-field illumination (Kohler illumination), whole depth of the sample is illuminated. Consequently, both the out-of-focus scattered signal and desired signal from the focal plane are detected. It generates the unwanted background and blurring of the desired image. This problem is simply removed in confocal microscope through “optical sectioning,” a process based on rejection of out-of-focus signals just by applying a confocal pinhole at the confocal plane in front of the detector, to produce clear images of focal planes. Confocal pinhole not only improves the image quality but also inherently provides a way to select a section of the sample to image. The technique of confocal microscopy was invented by Marvin Minsky, a postdoctoral fellow at Harvard University in 1957 as a stage-scanning confocal microscope [7]. Ever since, several types of confocal microscopes have been developed [8] and almost every

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FIGURE 5.2 Schematics of (A) confocal laser scanning optical microscope, (B) laser scanning nonlinear optical microscope, and (C) simplified Jablonski energy level diagram for laser-induced fluorescence process.

biology lab has at least one of them. A schematic of a popular confocal laser scanning optical microscope is shown in Fig. 5.2A. At present, one of the significant applications of confocal microscopy is in the study of corneal diseases [8]. This is done by performing in vivo quantitative response analysis of cornea cells to understand the difference between cellular microstructures in the normal and infected human cornea. Later, we will see that confocal geometry assists many other microscopy modalities, which do not incorporate themselves any 3D sectioning capability. However, it is worth to mention that microscopes based on nonlinear optical techniques (Fig. 5.2B) have got inherent optical sectioning and do not require any confocal pinhole.

5.3 Laser-Induced Fluorescence Microscopy Laser-induced fluorescence (LIF) microscopy [9] is the most popular linear microscopy technique among biologists. Its principle lies in the fact that the fluorescent molecules (endogenous or foreign markers) can be selectively excited by an appropriate optical frequency (typically in visible or ultraviolet) laser beam, and then emitted fluorescence signal, which is slightly redshifted in frequency, can be visualized just by spectral filtering. A simplified Jablonski energy level diagram for the process is shown in Fig. 5.2C, where absorption of a laser photon at optical frequency u excites a fluorophore molecule to its first electronic excited state. From there after rapid relaxation to the lowest vibrational level of the same electronic state, transition to ground-state lowest vibrational level radiates a redshifted fluorescence signal. LIF microscopy offers very high sensitivity. Even a single fluorophore molecule can be identified in the presence of 1011 ordinary molecules. Despite all its virtues, LIF microscopy lacks optical sectioning, it is like wide-field illumination. Therefore, it is carried out in a confocal microscope where confocal plane sets the image plane and the spatial resolution. Because the fluorescence signal photons generate almost from all the trajectory of the excited beam inside the sample volume, only the photons originating from the confocal plane set by the external confocal pinhole provide the useful signal for the image contrast. However, this works well for thin slices of the sample. Dealing with thick sample can still pass the extra photons coming from rest of the regions through the pinhole and can add a background to the image. Furthermore, because of the involvement of first electronic excited state, a visible light is required in one-photon fluorescence microscopy; hence penetration depth is poor in tissues due to high scattering and absorption. Later we will see that this problem can be easily removed in its nonlinear version called “two-photon excitation fluorescence (TPEF) microscopy,” where the use of nearinfrared excitation light allows deeper penetration depths. LIF microscopy can be immediately employed for imaging of inherent fluorescent pigments and their distribution in otherwise translucent/opaque tissues. For the microscopy of translucent samples where ordinary bright-field microscopy becomes incapable, LIF microscopy can be applied fruitfully after treating the translucent samples with suitable fluorophores. LIF has been applied to intravital microscopy [10], a technique used to investigate the mechanism in living organisms those have already been treated with appropriate fluorophores.

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5.4 Spontaneous Raman Spectroscopy/Microscopy Spontaneous Raman spectroscopy is a popular noninvasive technique based on Raman effect. It utilizes intrinsic Ramanactive vibrational, rotational, or other low-frequency modes of a sample for species identification. However, we will confine our discussion to the involvement of vibrational modes only. In practice, the sample is irradiated by visible or nearinfrared laser, and the Stokes or the anti-Stokes shifted intensities, containing vibrational signature of the molecules, are recorded. Being spectrally shifted from the incident field, the Stokes/anti-Stokes Raman signals can be readily isolated by proper optical filters. Raman signals are naturally very weak, a typical order of 103 times the Rayleigh scattering signal. Hence, dispersive (grating-based) spectrometer is not feasible for Raman spectroscopy. Instead, Fourier transform configuration called FT-Raman spectrometer is employed where usually a single-frequency IR laser (Nd:YAG, 1064 nm) source irradiates the sample. A classical explanation of “Raman effect” portrays features of Raman spectroscopy. The molecular deformation induced by an optical field [E ¼ A exp( jut) þ c.c.] is determined by molecular polarizability a and gives rise to the induced dipole moment p given as: p ¼ aE

(5.13)

Furthermore, the nuclear vibrational modes of the molecule can be approximated to harmonic motion in internuclear displacement Q with phase f as: QðtÞ ¼ Q0 ½expð jUt þ fÞ þ expðjUt  fÞ

(5.14)

The nuclei possess a random phase f, because being much heavier than the electrons, they cannot follow exactly the adiabatic motion of electrons at the exciting frequency u. The quantity a contains the information of the nuclear modes, because even though the visible or near-infrared photons cannot induce directly the nuclear modes, but their field sets in motion the electrons bound to nuclei and in response, the motion of bound electrons interacts with the intrinsic nuclear modes. With the help of Taylor series expansion of a in Q and in analogy to Eqs. (5.12) and (5.13), we get:     da da p ¼ aeq A expð jutÞ þ Q0 A exp½ jðu þ UÞt þ f þ Q0 A exp½ jðu  UÞt  f þ c:c: (5.15) dQ eq dQ eq  da  is a measure of coupling strength between nuclear mode and the electronic motion. Eq. (5.15) indicates that Here dQ induced dipole moment oscillates at three distinct frequency components u, (u  U) and (u þ U), giving rise to radiations at frequencies u, (u  U), and (u þ U), which account for “Rayleigh scattering,” “Stokes Raman scattering,” and “antiStokes Raman scattering,” respectively.  da Moreover, the dipole moment terms responsible for Stokes/anti-Stokes Raman scattering are linearly proportional to dQ , and this indicates the necessary condition that the polarizability must change for Raman scattering to take place. Inserting Eq. (5.15) in Eq. (5.9) provides selection rule for Raman transition as Dn ¼ 1, which is same as for vibrational transition. However, Raman spectroscopy has an advantage over IR spectroscopy that it is possible with homonuclear molecules (such as H2 and O2), because polarizability can be altered in them, even if they lack change in dipole moment. Raman spectroscopy has widespread applications in various fields. The most general application is the quick nondestructive quantitative characterization of the chemical composition and the structure of materials in any physical state such as solid, liquid, gas, powder, or gel. The key areas where Raman spectroscopy has been well established are life science, cosmetics and pharmaceuticals, mineralogy [11], and study of carbon materials and semiconductors. For example, it has been applied for the analysis of food and pharmaceutical nanomaterials [12] and design and analysis of pharmaceutical products [13] and for characterizing graphene layers, graphite, and single-walled carbon nanotubes (SWNTs) [14]. Combining confocal microscope design and Raman spectroscopy leads to a powerful instrumentation enhancement called “micro-Raman,” which enables the chemical analysis of a very small sample area or volume down to the micron scale. Micro-Raman imaging has been applied to biomedical research. For example, Raman line-scan imaging of about 60-mm length of a polytene chromosome from the salivary gland of the insect Chironomus thummi thummi is obtained in a measurement time of 1800 s using a laser power of 48 mW [15]. The requirement of long integration time due to very low cross section of spontaneous Raman process indicates that spontaneous Raman is not suitable for real-time imaging. Furthermore, spontaneous Raman spectroscopy usually suffers by the presence of fluorescence signal. Even a nanomolar concentration of fluorophores is sufficient to suppress a great amount of the Raman signal. These flaws are removed in coherent Raman techniques.

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6. NONLINEAR SPECTROSCOPY/MICROSCOPY TECHNIQUES The nonlinear spectroscopy/microscopy techniques, as we have discussed in Section 4, are based on multiphoton nonlinear processes. Their signal strengths have quadratic or cubic dependence on the total input field intensity (will be discussed later), consequently efficient signal generation takes place in a very small volume at input laser focus. Hence, they all possess inherent optical sectioning capability without the need of any confocal pinhole, which makes them preferred candidates for microscopy. Furthermore, they all associated with them a unique phase-matching condition contained in Eq. (5.8), which gives us facility to choose one of them at a time to target particular property of the sample molecules and to perform both spectroscopy and microscopy together. We will see in subsequent sections that the interplay between the optical property of the sample and the phase-matching condition may give rise to forward as well as backward scattered signals, both of which can be collected in forward detection and epi-detection configurations. A typical multiphoton microspectrometer is shown in Fig. 5.3 with forward detection and epi-detection schemes. Now we will discuss few important nonlinear spectroscopy/microscopy techniques and their important applications.

6.1 Coherent Raman Spectroscopy/Microscopy CRS spectroscopy/microscopy techniques [16] are extremely popular noninvasive nonlinear techniques. Same as spontaneous Raman technique, they also utilize the Raman-active vibrational modes of the investigated molecules. The popular CRS spectroscopy/microscopy techniques are CARS, SRS, RIKE, and balanced-detection Raman-induced Kerr effect (BD-RIKE) spectroscopy/microscopy. They can be regarded as the coherent version of the spontaneous Raman spectroscopy technique. As we have discussed in Section 5.4, that spontaneous Raman scattering yields very weak incoherent signal, which makes it not suitable for high-speed imaging. The sensitivity of Raman signal can be boosted by many orders of magnitude in CRS processes. This high-yield signal makes all of the CRS techniques suitable for high-speed imaging up to video rate. In CRS techniques, two synchronized narrowband laser beams, namely, “pump” at optical frequency up and “Stokes” at optical frequency uS, are focused on sample molecules. The frequency difference between the pump and the Stokes beams is tuned to a Raman-active vibrational mode U of the targeted molecules such that U ¼ up  uS (Fig. 5.4). The situation is same as we have discussed in Section 2 and depicted in Fig. 5.1B, the only difference is that the driving field at u is now the combination of the two fields, i.e., (up  uS) and it is in resonance with U. The molecules in the focal volume are coherently driven by this field, and they act like coherently oscillating Raman scattering dipoles. Consequently, they radiate individual fields having definite phase relationships among them, which constructively add up and determine the total amplitude of the scattered signal in CRS. Spatial coherence and the fixed polarization of the incident beams set the coherent emitters in definite orientations. This provides spatial coherence in CRS signal leading to a directional beam. Hence, in contrast to the spontaneous Raman, entire CRS signal can be detected experimentally with proper

FIGURE 5.3 A typical multiphoton microscope and spectrometer in forward detection and epi-detection configurations.

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(A)

(B)

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Energy

Input fields

ωp

ωs

Ω ωs

ωp

v

V′′=1 V′′=0

Ω

FIGURE 5.4 Excitation for a coherent Raman scattering process: (A) spectral scheme and (B) energy level diagram.

implementation of the collecting optics. Coherent nature of the CRS signal is the fundamental difference, which establishes CRS techniques superior in many aspects to its incoherent counterpart spontaneous Raman spectroscopy. All CRS techniques are the third-order nonlinear processes, and the sample response to the incident fields is governed by third-order nonlinear susceptibility cð3Þ ð  u4 ; u1 ; u2 ; u3 Þ as an FWM process. The basic mechanism of signal generation in each CRS technique can be understood as a two-step phenomenon. In the first step, when synchronized pump and Stokes laser pulses irradiate the targeted molecules with their optical frequency difference tuned to U ¼ up  uS (Fig. 5.4A), a vibrational coherence state is generated in the molecules. They start vibrating coherently and become ready for the second step. Then in the second step, a third laser pulse called “probe” at optical frequency upr interacts with coherently vibrating molecules prepared in the first step, to produce the CRS signal (the fourth) pulse. Different modalities of the second step differentiate various CRS techniques. The energy level scheme for the first step (Fig. 5.4B) suggests that one photon of pump up and one photon of Stokes uS are mediated by a virtual level of the system to connect the actual vibration level of the molecule. As we have seen in Section 5.4 for spontaneous Raman case that an off-resonance laser beam at u can change the molecular polarizability of the molecules to indirectly induce the molecular vibrational (nuclear) modes at U vibrating with random phases. Here in CRS process, because both the input field frequencies up and uS are much higher than the molecular mode frequency U, the fundamental frequencies cannot drive efficiently the nuclear modes. However, the bound electrons can follow the fundamental fields adiabatically. Under the influence of sufficiently high input fields, the motion of bound electrons becomes nonlinear. Their nonlinear motion most likely may contain the combination of the input field frequencies including (up  uS). The heavier nuclei also follow the oscillations but with some lag. This makes   molecule to behave like driven harmonic oscillator by the input field component E ¼ Ap As expfjðup  uS Þtg þ c:c: . Again the coupling between the  da  nuclear mode and the electronic mode is given by dQ . Therefore the classical equation of motion for driven harmonic i h  da  Ap As expfjðup  uS Þtg þ c.c. can be written as: oscillator for nuclear mode Q under driving force FðtÞ ¼ dQ d2 Q dQ FðtÞ ¼ þ U2 Q þ g dt 2 dt m

(5.16)

where g is the damping constant and m is the reduced mass of the nuclear oscillator. The stationary harmonic solution of Eq. (5.16) is given as:  da=dQ 1 Qðup  uS Þ ¼  2 (5.17) Ap As expfjðup  uS Þtg þ c.c. 2 m U  ðup  uS Þ  jUg Eq. (5.16), with the help of Taylor series expansion of a in Q and the total input electric field, will become: "   #   da Q Ap expð jup tÞ þ As expð juS tÞ þ c:c: (5.18) p ¼ aeq þ dQ eq

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  Using Eq. (5.17) in Eq. (5.18) and collecting the terms containing Ap Ap As , we get nonlinear polarization terms for a particular CRS process called CARS as:  2 da=dQ 1 ð3Þ pNL ðuas Þ ¼  2 Ap Ap As exp½ jð2up  uS Þt (5.19)  2 m U  ðup  uS Þ  jUg Multiplying Eq. (5.19) by molecular number density N (we get “polarization density” for CARS), and comparing it with Eq. (5.4b), we can rewrite Eq. (5.19) as: Pð3Þ ¼ 6ε0 cð3Þ ð uas ; 2up  us ÞAp Ap As exp½ jð2up  uS Þt where 6 is the number of permutations for the frequencies, and c is written as: 2 3  2 N da 1 4 5 cð3Þ ð uas ; 2up  us Þ ¼  6ε0 m dQ U2  ðup  uS Þ2  jUg

(5.20)

(3)

(5.21)

Three more equations, similar to Eq. (5.20), will be obtained if we collect terms containing As As Ap , Ap Ap As , and As As Ap separately as: Pð3Þ ¼ Kε0 cð3Þ ð ucsrs ; 2us up ÞAs As Ap exp½ jð2us  up Þt

(5.22)

Pð3Þ ¼ Kε0 cð3Þ ð us ; up  up þ us ÞAp Ap As exp½ jð uS Þt

(5.23a)

Pð3Þ ¼ Kε0 cð3Þ ðup ; up þ us  us ÞAs As Ap exp½ jðup Þt

(5.23b)

Here K is a number representing the permutation for the frequencies. Eqs. (5.20), (5.22), (5.23a), and (5.23b) are responsible for four different CRS processes, namely, CARS, coherent Stokes Raman scattering (CSRS), stimulated Raman gain (SRG), and stimulated Raman loss (SRL), respectively. Under semiclassical approach, starting from Maxwell’s equations, the equation for field propagation for P(3) ¼ p(3) exp [ j(u)t] can be obtained as: vA m u0 c ð3Þ ¼ j 0 p expðjDkzÞ vz 2n

(5.24)

Birefringent Properties of c(3): The third-order susceptibility c(3) is mathematically a fourth-rank tensor. It encompasses 34 ¼ 81 elements in total obtained by permuting four indices (i, j, k, l) over three Cartesian coordinates (1, 2, 3) ð3Þ corresponding to X-, Y-, and Z-axes. Each element can be represented in general as cijkl . The symmetry within material ð3Þ environment decides the tensor properties of the material and hence the number of independent elements cijkl . In an (3) isotropic media with inversion symmetry, there are only four independent elements of c , which hold the following relationships: ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

c1111 ¼ c2222 ¼ c3333 ¼ c1122 þ c1212 þ c1221 ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

c1122 ¼ c1133 ¼ c2211 ¼ c2233 ¼ c3311 ¼ c3322 ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

ð3Þ

c1212 ¼ c1313 ¼ c2121 ¼ c2323 þ c3232 þ c3131 c1221 ¼ c1331 ¼ c2112 ¼ c2312 þ c3113 þ c3223

(5.25a) (5.25b) (5.25c) (5.25d)

ð3Þ cijkl

For generic term in a CRS process, it is customary to assign indices i, j, k, and l to the four interacting beams in the order ucrs, up, us, and upr, respectively, to represent polarization state of their electric fields. In this type of componentwise representation, a generic third-order polarization for CRS processes can be expressed as: 3Þ ¼ Kε0 Pðcrs

X jkl

   ð3Þ  cijkl ucrs ; up ; us ; upr Ap As Apr exp j up þ upr  us

(5.26)

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ð3Þ

In a CARS or SRS process, we probe c1111 component only, because input pump and Stokes beams are linearly polarized in the same plane, hence the generated CARS beam is also polarized in the same plane. Unless not strictly needed, we omit the subscript (1111). CRS spectroscopy/microscopy requires typically tunable few picosecond duration pump and Stokes pulses at MHz repetition rates within optimal wavelength range from 760 to 1300 nm. Upper wavelength limit is to avoid water absorption in biological samples, whereas the lower wavelength limit is mainly to avoid multiphoton absorption through ultraviolet electronic resonances. Such synchronized pump and the Stokes pulses are generally synthesized either by electronically locking two laser oscillators, where one provides pump pulses while the other derives Stokes pulses, or by one laser oscillator pumping an OPA/OPO [17]. Alternatively both pump and Stokes, inherently synchronized, pulses are derived from a single fiber-format oscillator through highly nonlinear fiber or frequency doubling crystals [18,19]. Now in subsequent sections, we will elaborate few CRS techniques and utilize the formalism developed in this section.

6.1.1 Coherent Anti-Stokes Raman Spectroscopy/Microscopy

(A)

(B)

ωs

ωp

Ω ωs

(C) V′′=1 V′′=0

CARS signal

CARS

ωp

ωas=2ωp–ωs

virtual states

Intensity

CARS spectroscopy [20] is a popular well-established noninvasive label-free nonlinear spectroscopy technique. CARS has been developed since the availability of reliable pulsed laser sources, and now it is rapidly gaining recognition for noninvasive biomedical imaging of cells and living tissues. In 1963, R.W. Terhune [21] reported the first CARS as a by-product of stimulated Raman emission. Later in the same year, Maker and Terhune demonstrated CARS from several samples, by using a 0.1 J pump pulses from Ruby laser and the “Stokes” pulses synthesized from stimulated Raman emission from benzene. The name “Stokes” for the second input beam in Coherent Raman terminology has been adopted from the derivation of that Stokes-generated second beam in their historic CARS experiment. In comparison with spontaneous Raman spectroscopy, CARS offers many order of magnitude higher signal levels, which makes it suitable for video-rate imaging even with moderate excitation intensities. As in all CRS processes, CARS requires two synchronized narrowband pump (up) and Stokes (us) pulses with the facility to tune their difference frequency (up  uS) to a Raman-active molecular mode. When this happens, a strong laserlike beam called CARS signal is generated at anti-Stokes frequency (uas ¼ 2up  uS), which carries the chemical signature of the investigated molecules. The corresponding energy level diagram for CARS process is shown in Fig. 5.5. In the first step, one pump photon and one Stokes photon mediated by a virtual level induce a real vibrational level of the molecule. This step generates a vibrational coherence in the molecules in the laser focus volume. Then in the second step, the generated vibrational coherence interacts with another pump photon (sometimes termed as “probe” photon) per molecule to generate an anti-Stokes (CARS) photon. The probe photon may differ in optical frequency from the pump photon, i.e., upr s up, in that case, it is called “nondegenerate CARS” and consequently the anti-Stokes signal is shifted to uas ¼ up þ upr  uS. In normal situation, when upr ¼ up, it is called “degenerate CARS.” In nondegenerate CARS, a third synchronized laser beam at frequency upr is needed to be shined on the same sample volume. This increases the complexity of the nondegenerate CARS setup.

Ω

ks

Ω ωp

ωas

v

kas kp

kp

FIGURE 5.5 (A) Energy level diagram for coherent anti-Stokes Raman scattering (CARS), (B) relative spectral position of CARS signal with respect to input beams, and (C) schematic diagram of phase matching for CARS process.

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Molecular and Laser Spectroscopy

Under the assumption of negligible pump and Stokes intensity depletion, i.e., Ap y constant and As yconstant, which is usually the case in a CARS process, the integration of Eq. (5.24) over the sample length L gives: ZL dAas

m u0 c ¼ j 0 2n

0

ZL

pð3Þ expð jDkzÞdz

0

(3)

Substituting P responsible for CARS from Eq. (5.20) in the above equation and taking initial condition as Aas(z ¼ 0) ¼ 0, provide total anti-Stokes field at length L as: Aas ðz ¼ LÞ ¼ j

m 0 u0 c 6ε0 cð3Þ Ap Ap As 2n

ZL expð jDkzÞdz 0

    jDkL DkL 0Aas ðz ¼ LÞ ¼ j aas cð3Þ Ap Ap As L exp  sinc 2 2

(5.27)

0 where aas ¼ 6u 2nc is a constant and Dk h kas  2kp þ ks is the “phase-matching term” for the CARS process. In practice, instead of fields we detect optical intensity given as:

Ias ðz ¼ LÞ f jAas j

2

 

2 DkL 0Ias ðz ¼ LÞ ¼ a2as cð3Þ I2p Is L2 sinc2 2

(5.28)

Eq. (5.28) highlights the main features of the CARS process. It shows that CARS intensity is linearly proportional to the Stokes intensity while it scales quadratically to the pump intensity and to the interaction length L within the focal volume in the sample, provided the phase matching condition is satisfied, i.e., Dk h kas  2kp þ ks ¼ 0 (Fig. 5.5C). In practice, Dk is hard to manage exactly to be zero, then the limit on interaction length L is being set by the condition   to be significant. Because of this phase-matching condition, in a transparent medium, (Dk.L  p) for factor sinc2 DkL 2 CARS signal propagates coherently in a defined direction, as reported in wave-vector diagram of Fig. 5.5C. Furthermore,

2 CARS intensity is proportional to cð3Þ . Eq. (5.21) suggests that the c(3) depends linearly on number density N and  4  da  da . We will see quadratically on coupling strength dQ . Consequently the CARS intensity is proportional to N2 and dQ later that this squared dependence of c(3) strongly affects the spectral response of the CARS signal. The dependency on  da  indicates that CARS probes Raman-like signature. polarizability change dQ In a CARS spectroscopy experiment, typically the pumpeStokes optical frequency detuning (up  uS) is varied to sweep over a molecular vibrational resonance, and the generated anti-Stokes intensity is registered as a function of (up  uS). This intensity spectrum is called “CARS spectrum.” On the other hand, in a CARS microscopy experiment, (up  uS) is kept fixed at a particular molecular vibrational resonance, the beams at focus are scanned over the desired sample area, and the corresponding CARS signal is collected from each point. This point-by-point intensity map is called “CARS image” of the sample at that molecular resonance frequency. The scanning for imaging can be achieved either by raster scanning of the sample stage over the fixed focus of beams with the help of a piezoelectric translator (it is called sample scanning) or by scanning beams over the fixed sample stage through a set of galvanometric mirrors (it is called beam scanning). For fast imaging speeds, beam scanning is preferred. For beam-scanning flat-field microscope objectives are required to have flat field for the moving input beams in the sample. 6.1.1.1 Phase Matching at Tight Focusing Condition To satisfy phase-matching condition in CARS process in practical implementation, several phase-matching geometries for the input beams have been proposed. Among them, collinear CARS, BOXCARS, and folded BOXCARS have been usually exercised. In normal focusing conditions, the folded BOXCARS has been the most favorite geometry shown in Fig. 5.6A. In this geometry, the Stokes beam and the CARS beam are in one plane perpendicular to another plane consisting of the two pump beams. This arrangement provides optimal separation of the CARS signal from the input beams, achieving greatly improved signal-to-noise ratio. However, aligning a folded BOXCARS geometry is a tedious job. The availability of modern tight-focusing high numerical aperture objectives has relaxed the strict requirement of

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FIGURE 5.6 Phase-matching geometries for coherent anti-Stokes Raman scattering (CARS): (A) folded BOXCARS and (B) under tight focusing.

phase-matching geometries. In a much simpler collinear CARS geometry where pump and Stokes beams are collinear, under tight focusing conditions, the large angular dispersions of the wave-vectors of pump and Stokes readily satisfy phase-matching condition in a well-defined cone of wave-vectors and that makes the CARS signal to be generated in a cone as well (Fig. 5.6B) [22]. This greatly simplifies the CARS microscope/spectrometer setup. All modern CARS spectrometers/microscopes employ this simple collinear CARS geometry. 6.1.1.2 Spectral Advantage of Coherent Anti-Stokes Raman Scattering Process The most favored advantage of the CARS signal lies in its anti-Stokes character. It falls on the high frequency side of the input fields (Fig. 5.5B) and can be easily spectrally isolated from the input beams and also from parasitic linear fluorescence background, which is typically present at lower frequency side of the excitation fields. Therefore CARS signal is in principle free from linear optical background. A typical CARS spectroscopy/microscopy setup is shown in Fig. 5.3 where multiphoton microscope is fed by synchronized pumpeStokes pulses, and the forward CARS and epi-CARS are collected by two photomultiplier tubes. Fig. 5.7A and B shows CARS images of a blend of 6-mm polymethyl methacrylate (PMMA) beads and 3-mm polystyrene (PS) beads at pumpeStokes frequency detunings 2953 and 3060 cm1, respectively, acquired in forward direction by such a homemade setup of CARS microscope/spectroscope. Fig. 5.7C presents the acquired CARS spectra of PMMA (in blue)

FIGURE 5.7 Coherent anti-Stokes Raman scattering (CARS) images of a blend of 6-mm polymethyl methacrylate (PMMA) beads and 3-mm polystyrene (PS) beads at pumpeStokes frequency detunings: (A) 2953 cm1 and (B) 3060 cm1, respectively, acquired by CARS setup at Dipartimento di Fisica, Politecnico di Milano, Italy. (C) CARS spectra of PMMA (in blue (gray in print versions)) and PS (in red (dark gray in print versions)) in CH-region, (D) CARS images at different axial position of the objective showing 3D sectioning capability, (E) 3D reconstruction of the beads on the basis of CARS images taken for 3D sectioning.

100 Molecular and Laser Spectroscopy

and PS (in red) in CH region. 3D sectioning capability of the CARS microscope is represented in Fig. 5.7D. A 3D reconstruction of the beads can be done by rendering the data of 3D sectioning (Fig. 5.7E).

2 However, CARS signal has a serious problem that it suffers from a nonlinear background hidden in its cð3Þ dependence. 6.1.1.3 Presence of Nonlinear Background in Coherent Anti-Stokes Raman Scattering The c(3) involved in CARS process in practice has a resonant and a nonresonant components, i.e., cð3Þ ¼ cð3ÞR þ cð3ÞNR The resonant component c(3)R is coming from the combination of incident frequencies, which are in resonance with vibrational frequencies of the targeted molecules (Fig. 5.8A). Another combination of the same input frequencies is also possible. This new combination leads to another FWM phenomenon (Fig. 5.8B), which is coming purely from the electronic contribution and does not involve the real vibrational levels of the investigated molecules. This nonresonant process constitutes the nonresonant contribution c(3)NR. In addition, the background molecules (the molecules other than the targeted ones), which are not in resonance with the input frequency combination, may also contribute to nonresonant part c(3)NR through their electronic response. In short, nonresonant contribution c(3)NR is coming from pure electronic response away from the resonance. Electronic response is instantaneous because electrons being lighter in mass can follow the fields adiabatically. Hence c(3)NR is spectrally flat and can be treated as constant in a small frequency range (Fig. 5.9A). Furthermore, according to Eq. (5.21), c(3)R is a complex quantity and can be separated into its real and imaginary parts. Thus, the total c(3) can be expressed as:  ð3ÞR ð3ÞR ð3ÞNR þ jcim þ cre (5.29) cð3Þ ¼ cre where 

ð3ÞR ¼ cre

ð3ÞR

cim

N da=dQ 6ε0 m 

¼

N da=dQ 6ε0 m

2

2

2 6 4

3 U  ðup  uS Þ 7 5; 2 U  ðup  uS Þ2 þ U2 g2 2

2

2

2 6 4

(5.30a)

3 Ug U  ðup  uS Þ 2

2 2

þ

U2 g2

7 5;

(5.30b)

and cð3ÞNR yConstt. re

(5.30c)

FIGURE 5.8 (A) Resonant contribution to coherent anti-Stokes Raman scattering (CARS) process by targeted molecules, (B) another four-wave mixing process providing electronic nonresonant contribution to CARS signal, and (C) electronic nonresonant contribution to CARS signal from background molecules.

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2 FIGURE 5.9 Spectral shapes of (A) different components of c(3), (B) the individual squared components, (C and D) full cð3Þ at different ratios of resonant and nonresonant contributions. ð3ÞR

Far from any possible electronic transitions in the system, the imaginary resonant component cim is the contribution coming from the nuclear modes of the targeted molecules and it represents the actual “third-order Raman response.” It has the typical “Lorentzian spectral lineshape” of spontaneous Raman response centered at resonance frequency of the molecule as represented by Eq. (5.30b) and shown in Fig. 5.9A. On the other hand, the real resonant component cð3ÞR re is the electronic contribution, which oscillates around the resonance frequency. It involves electrons of the targeted molecules. It has a dispersive shape around the resonance frequency of the targeted molecules as represented by Eq. (5.30a) and shown in Fig. 5.9A. Not to mention, cð3ÞNR is also real, originating from pure electronic involvement of the background molecules. re

2 Since CARS intensity is proportional to cð3Þ , both resonant and nonresonant contributions being coherent in nature interfere with each other. This can be understood by writing c(3) dependence of CARS intensity with the help of Eq. (5.29) as:

2 ICARS f cð3Þ



2

ð3ÞR ð3ÞR ð3ÞNR

0ICARS f cre þ jcim þ cre





2 ð3ÞR 2 ð3ÞNR 2



þ cim þ c

þ 2 cð3ÞR

cð3ÞNR

0ICARS f cð3ÞR re re re re

(5.31)



2 ð3ÞR 2

2

, c , and cð3ÞNR are plotted in Fig. 5.9B, whereas the spectral The spectral shapes of individual terms cð3ÞR im re re

2





2

ð3ÞNR

c

is plotted in Fig. 5.9C and D. The terms

cð3ÞNR

shape of total cð3Þ that includes the interfering term 2 cð3ÞR re re re





ð3ÞR

ð3ÞNR

and 2 cre

cre constitute the “nonresonant background (NRB)” in CARS. By observing the plots in Fig. 5.9, one can draw following important conclusions regarding CARS signal: The spectral shape of the CARS signal is asymmetric and it has a nonzero base line. The presence of the interfering term distorts it



ð3ÞR 2 from its Lorentzian shaped pure Raman response governed by the term cim . The peak of the CARS signal is redshifted with respect to Raman resonance frequency U.

102 Molecular and Laser Spectroscopy

Above effects become more significant as the NRB contribution increases. This situation is shown in Fig. 5.9C and D where NRB is dominating over the CARS signal. It is a well-established fact that CARS faces inherent NRB problem. This NRB problem becomes more serious while probing a very small concentration of target molecules in presence of huge amount of background molecules. Best example is probing small amount of lipids in an animal cell that contains 90% of water molecules within it. In this case, NRB may overwhelm the output signal, and CARS features will be buried in the NRB. Second problem may arise in distinguishing the two closely spaced Raman lines, because the amount of redshift and the distortion depend on the amount of NRB. Therefore, CARS technique has strong requirement for NRB suppression. In fact, several attempts have been made to circumvent this NRB problem. Many labs have developed algorithms for postdata processing to remove the NRB contribution from the acquired CARS raw data. On the other hand, several new experimental NRB suppression techniques have been proposed and successfully applied to retrieve the resonant CARS contribution. Polarization-sensitive CARS (P-CARS) [23], frequency modulation CARS (FM-CARS), time-resolved CARS (TR-CARS) [19], interferometric CARS (I-CARS) [24] are the few well-established NRB suppression techniques associated with CARS. We will not go in detail of these techniques. In the next section, we will discuss another popular CRS technique called “stimulated Raman scattering” spectroscopy/microscopy, which is inherently free from NRB and mimics the spontaneous Raman signature. CARS has two main branches of applications: chemically sensitive microscopy and combustion diagnostics. In the first one, it utilizes vibrational selectivity of CARS signal, whereas in the second, it utilizes temperature dependency of the CARS signal, which resides in the fact that CARS signal scales with population difference between the ground state and the vibrationally excited state. These populations are governed by temperature-dependent Boltzmann distribution. Hence CARS signal can measure and monitor intrinsically the temperature of flames, vapors, and hot gases. For example, local temperature fluctuation caused by turbulent diffusion combustion of decaneeair mixture in a burner flame has been measured by CARS process [25]. Similarly, it has been used to investigate the cryogenic liquid oxygen/ gaseous methane spray flames of a test facility of medium size [26]. Capability of CARS has been shown for a nondestructive highly sensitive method of stand-off detection and imaging of particles of explosives and other hazardous materials in the real world in concentration down to 2 mg/cm2 [27,28]. The first use of CARS in cell biology has been reported in 1982 by Duncan et al. [29] for onion-skin cells soaked in D2O using a noncollinearly overlapped pump and Stokes beams. Then, in 1999, Zumbusch et al. [20] were able to implement CARS microscopy in a collinear beam geometry using tightly focused femtosecond laser source for biological imaging. Since then, CARS has entered the field of biology and medicine [22] and has been successfully applied for single-cell analysis, for imaging lipids and proteins at submicron resolution, for monitoring lipid droplet dynamics in differentiation in cells, for studying early embryo development, and in several other studies. Single-frequency CARS image acquisition speed has been reported up to video rate [30]. On the other hand, broadband CARS covering spectral range of 3000 cm1 is recently shown with 3.5 ms acquisition time per pixel [31].

6.1.2 Stimulated Raman Spectroscopy/Microscopy SRS spectroscopy is an important noninvasive CRS spectroscopy/microscopy technique, which has now got widespread applications in biomedical and pharmaceutical fields. Similar to CARS, SRS also utilizes the inherent Raman-active vibrational modes of the molecules to uniquely identify them. However, it has unprecedented advantage over CARS that it is inherently free from NRB. Another fundamental difference is that in CARS, we probe the induced vibrational coherence, whereas in SRS, the excited vibrational population is probed. As common to all CRS techniques, SRS too requires two narrowband synchronized “pump” and “Stokes” beams with the facility to tune their optical frequency difference to a molecular vibrational mode frequency such that U ¼ up  uS. When this happens, the simultaneous presence of both pump and Stokes beams stimulates the excitation of the probed vibrational state of the molecules, and consequently it accelerates the rate of population transfer to the excited vibrational state. The excitation rate Rst. in such stimulated Raman process depends on the number of photons ns present in the Stokes beam by the following relation: Rst: fðns þ 1ÞRsp: where Rsp. is the corresponding excitation rate in spontaneous Raman process. Only a laser beam can provide sufficient number of Stokes photons ns to increase sufficiently the excitation rate Rst. to be significant over spontaneous Raman process. Each excited-state vibrational photon created in the process is accompanied by simultaneous absorption of one pump photon and creation of one Stokes photon all to conserve energy and momentum during the whole process. Consequently, depletion of pump beam takes place, which is called Stimulated Raman Loss (SRL), and simultaneously amplification of Stokes beam takes place, which is called Stimulated Raman Gain (SRG) (Fig. 5.10). In an SRS experiment, we measure either SRL or SRG to detect the presence of the molecule. The expression for SRG or SRL can be obtained by substituting Eq. (5.23a)

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FIGURE 5.10 (A) Energy level presentation for stimulated Raman scattering (SRS) process, (B) spectral positions of input fields and the generated output fields, and (C) a representation showing phase matching automatically satisfied in SRS. CARS, coherent anti-Stokes Raman scattering; CSRS, coherent Stokes Raman scattering; SRG, stimulated Raman gain; SRL, stimulated Raman loss.

or (5.23b), respectively, in Eq. (5.24), and integrating it for Stokes or pump field propagation for sample interaction length L. For example, for SRG we get: ZL ZL m 0 u0 c dAS ¼ j pð3Þ expð jDkzÞdz 2n 0

0

0AS ðz ¼ LÞ ¼ j aS c

ð3Þ

Ap Ap L

ZL As dz 0

 2  0AS ðz ¼ LÞ ¼ AS ðz ¼ 0Þexp  j aS cð3Þ jAp j L 0 Here small depletion assumption is made for the pump beam, i.e., Ap y constant, and aS ¼ 6u 2nc is a constant. The phase-matching condition (Dk h kS þ kp  kp  kS ¼ 0) is automatically satisfied for the forward direction. Expanding the exponential term in Taylor series and then neglecting the higher-order terms, above equation takes the form:   0AS ðz ¼ LÞ ¼ AS ðz ¼ 0Þ 1  j aS cð3Þ jAp j2 L

0DAS hAS ðz ¼ LÞ  AS ðz ¼ 0Þ ¼ jAS ðz ¼ 0ÞaS cð3Þ jAp j2 L

(5.32)

Here, DAS is the change in Stokes field due to stimulated Raman process. DAS interferes constructively to the incident Stokes field to produce the intensity at the photodiode, given as: Itotal ¼ jAS þ DAS j

2

  2 2 0Itotal ¼ jAS j þ jDAS j þ 2Re AS $DAS   0Itotal ¼ IS þ DIS þ 2Re AS $DAS

(5.33)

In right-hand side of Eq. (5.33), the first term IS is the incident Stokes intensity, second term DIS is the change in the Stokes intensity due to stimulated Raman process, and the third term gives the homodyne amplification of DAS by the incident Stokes field AS . The second term DIS is negligibly small as compared to the third term, hence it can be neglected, although its magnitude is comparable to the CARS signal intensity. The third amplified term, which contains the SRS information, is usually extracted by modulating the pump beam and probing the modulation transfer to Stokes beam due to SRS process by phase-sensitive detection employing lock-in amplifier detection technique. In this way, the first term IS in Eq. (5.33) is also rejected and SRG signal is retrieved as:   2Re AS $DAS SRG ¼ IS

104 Molecular and Laser Spectroscopy

Substituting the value of DAS from Eq. (5.32), we get:   2  SRG ¼ 2Re AS :  jAS aS cð3Þ jAp j L IS   0SRG ¼ 2Re  jaS cð3Þ Ip L Now substituting expression for c(3) from Eq. (5.29) in the above equation: h  i ð3ÞR ð3ÞNR SRG ¼ 2Re  jaS cð3ÞR Ip L re þ jcim þ cre ð3ÞR

0SRG ¼ 2aS cim Ip L

(5.34a)

Similarly, the expression for SRL can be obtained as: ð3ÞR

SRL ¼ 2aS cim IS L

(5.34b)

Eq. (5.34a) exhibits the remarkable properties of the SRS process. SRG/SRL is linearly proportional to the pump/ Stokes intensity and to the interaction length L in the sample. Phase-matching condition is automatically satisfied in SRS. This provides SRS, unlike the CARS, a well-defined point-spread function, which can be directly utilized for image deconvolution. On the other hand, in CARS, the point-spread function depends on to which extent phase matching is ð3ÞR achieved. A remarkable property is that SRS signal is linearly proportional to the imaginary component cim , therefore it is inherently free from NRB. The spectral shape of SRS signal is symmetric and has Lorentzian profile (Eq. 5.30b). In other words, it mimics the spontaneous Raman signal. Huge rich database of spontaneous Raman can be directly utilized to interpret SRS spectra or images. Furthermore, SRS is linear to the number density N of the targeted molecules, irrespective of the presence of the background molecules. Hence, quantitative analysis is straightforward. Because of linear dependency on N, SRS is more sensitive at low concentration as compared to CARS, which has quadratic dependence on N. In addition, SRS is immune to two-photon fluorescence contamination, unlike CARS that is easily affected by it. However, these several advantages of SRS technique come at the expense of challenges in practical implementation. Because the SRS signal is not spectrally isolated from input fields and it is a tiny signal (for example, a typical SRG signal is 104 to 105 of the Stokes itself) sitting on a huge background of the input field itself, it strictly requires high-sensitive detection schemes. This is the reason why SRS is limited to few advanced laboratories. Fig. 5.11 represents scheme of a typical SRS setup. Excitation scheme is the same for any CRS technique except the additional modulating element, such as acoustooptic modulator or electrooptic modulator, which is needed for modulation transfer technique, whereas detection is done by a high-sensitivity photodiode followed by a lock-in amplifier. Few representative SRG images are shown in Fig. 5.12 [17]. SRG images (400  400 pixels) of a cross section of a leafestem (plant cells) of Abutilon pictum acquired at Raman shifts for cellulose (2890 cm1), lignin (2945 cm1), and water (3250 cm1) molecules, respectively, with 300 ms pixel dwell time are shown in Fig. 5.12AeC. These images show the ability of SRS to perform high-speed chemically selective microscopy.

FIGURE 5.11 Schematics of a typical stimulated Raman scattering setup. AOM, acoustooptic modualtor; DM, dichroic mirror.

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FIGURE 5.12 Stimulated Raman gain (SRG) images of a cross section of a leafestem (plant cells) acquired at Raman shifts for (A) cellulose, (B) lignin, and (C) water molecules.

First stimulated Raman microscopy, which was very close to the current configuration but without any lock-in detection, was implemented in 2007 by Ploetz et al. [32]. The detection sensitivity was poor. It was in 2008 that the demonstration by Freudiger et al. [33] of monitoring of human lung cancer cells with SRL microscopy using lock-in detection reaching detection sensitivity up to 107 at 300 ms integration time paved the way for current popularity of high-speed SRS microscopy in biology and medical fields. Recently, in vivo SRS imaging of tissue at 30 frames/second with frame-by-frame wavelength tenability is reported [34].

6.1.3 Raman-Induced Kerr Effect Spectroscopy/Microscopy RIKE [35] spectroscopy/microscopy is a kind of CRS technique. It utilizes the third-order material response based on optical Kerr effect induced by a vibrational Raman mode activated by the incident light fields while interacting with targeted molecules. In other words, in RIKE, the polarization of one of the excitation beams changes due to presence of Raman-induced birefringence in the sample. We probe this change in polarization to uniquely identify the molecule. Being a CRS technique, RIKE requires two synchronized pumpeStokes laser beams at optical frequencies up and uS, respectively, with the facility to tune their difference to match a Raman vibrational mode U such that U ¼ up  uS. Depending on the incident beam polarization geometry, the traditional RIKE has two forms of excitation schemes: (1) Linear RIKE: Pump beam is linearly polarized and its polarization plane is oriented at 45 degrees with respect to polarization plane of linearly polarized Stokes beam (Fig. 5.13C). (2) Circular RIKE: Pump beam is circularly polarized, whereas the Stokes beam is linearly polarized (Fig. 5.13D). In both the cases, when frequency detuning (up  uS) matches to Raman mode U, polarization rotation of linearly polarized Stokes beam takes place. Recalling the birefringent properties of c(3), in an isotropic media with inversion ð3Þ ð3Þ ð3Þ ð3Þ ð3Þ symmetry, only c1111 ; c1221 ; c1212 ; c1122 , and their permutations are the nonvanishing elements. Among them, only c1212 ð3Þ and c1122 are excited in the linear and the circular RIKE polarization geometries. Because RIKE (both linear and circular schemes) is an FWM process, the associated third-order induced polarization can be derived from Eq. (5.26) as:    ð3Þy ð3Þ ð3Þ PlinearRIKE ðuS Þ ¼ 3ε0 c1212 þ c1122 Axp Ayp Axs exp½ jðus Þ (5.35a) h i   ð3Þy ð3Þ ð3Þ PcircularRIKE ðuS Þ ¼ 3ε0 j c1122  c1212 Axp Ayp Axs exp½ jðus Þ ð3Þ

(5.35b)

ð3Þ

Keeping in mind that both c1212 and c1122 have the resonant and nonresonant components as shown in Eq. (5.29), the effective c(3) involved in linear and circular RIKE can be written as:   ð3Þeff ð3Þ ð3Þ ð3ÞR;re ð3ÞR;re ð3ÞNR;re ð3ÞNR;re ð3ÞR;im ð3ÞR;im clinear h c1212 þ c1122 ¼ c1212 þ c1122 þ c1212 þ c1122 þ j c1212 þ c1122 (5.36a)    ð3Þeff ð3Þ ð3Þ ð3ÞR;im ð3ÞR;im ð3ÞR;re ð3ÞR;re þ j c1122  c1212 ccircular hj c1122  c1212 ¼ c1122  c1212 ð3ÞNR;re

ð3ÞNR;re

(5.36b) ð3Þeff

¼ c1212 is used. Noticeable point is that ccircular is free from any kind of In deriving above, the property c1122 NRB. Because Eqs. (5.36a) and (5.36b) are similar to Eq. (5.23a) for SRG, just by following the similar derivation that we

106 Molecular and Laser Spectroscopy

FIGURE 5.13 (A) Schematic of Raman-induced Kerr effect (RIKE) excitation and detection setup. A half-wave plate or a quarter-wave plate is used in pump branch for linear and circular RIKE, respectively; (B) Stokes beam polarization without the action of pump beam; polarization schemes of linear (C) and circular (D) RIKE, respectively. Dashed lines represent rotation of Stokes beam by RIKE.

did to obtain Eq. (5.3) for SRG, we can readily obtain the component of the RIKE field, perpendicular to Stokes initial polarization directions, written as:    ð3Þeff x y DAS hAy;linear ¼ ja Axs L (5.37a) c S linear Ap Ap s    ð3Þeff x y ¼ ja Axs L DAS hAy;circular c S circular Ap Ap s

(5.37b)

6.1.3.1 Detection Scheme for Raman-Induced Kerr Effect In a traditional detection scheme of RIKE, after the sample, the pump beam is spectrally rejected by appropriate filter, and then in path of the remaining Stokes beam, a crossed polarizer with respect to incident Stokes polarization plane is used as an analyzer, so that RIKE (rotated Stokes) component Ay;linear or Ay;circular is allowed to pass through it to reach the detector s s 2 (Fig. 5.13A). The measured RIKE intensity IfjDAS j , on the detector will be:



ð3Þeff 2 Islinear f a2s clinear Ip2 Is L (5.38a)



ð3Þeff 2 Iscircular f a2s ccircular Ip2 Is L

(5.38b)

2

ð3Þeff

ð3Þeff Because of clinear dependency in Eq. (5.38a) where clinear is given by Eq. (5.36a), the detected linear RIKE intensity ð3Þeff is a complicated mixture of resonant and nonresonant intensity terms. On the other hand, although ccircular given by Eq.

2

ð3Þeff

(5.36b) is free from nonresonant terms, yet ccircular dependency in Eq. (5.48b) yields a circular RIKE intensity as a mixture of intensities involving resonant real and resonant imaginary components. In the next section, we will discuss another kind of detection scheme called “balanced-detection RIKE,” which is able to detect separately the real and imaginary components of c(3). Multiplex microscopy based on RIKE has already been tested for polystyrene beads in toluene [36]. As a proof of applicability in biomedical field, optically heterodyne-detected RIKE microscopy of a sebaceous gland in the epidermis of mouse skin at CH2-stretching vibrational frequency of lipids (2845 cm1) has been successfully demonstrated [37].

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6.1.4 Balanced-Detection Raman-Induced Kerr Effect Spectroscopy BD-RIKE [38] is a new CRS technique. Same as normal RIKE discussed in previous section, it also relies on the Ramaninduced birefringence induced by the pumpeStokes frequency detuning (up  uS) in resonance with a vibrational mode of the molecule, which leads to a polarization rotation of the Stokes field. BD-RIKE shares the advantages of SRS; the additional advantage is that in BD-RIKE, the linear background signal of input field itself (which is present in SRS) is completely suppressed and this allows for an easier shot-noise limited detection. The suppression is done by applying a proper polarization splitter accompanied by a balanced detection configuration similar to that applied for electrooptic sampling in the terahertz domain. The balanced detection kills the Stokes linear background, and surplus advantage is that it effectively cancels the laser intensity noise. This allows to achieve readily a shot-noise limited detection and permits to efficiently measure the tiny rotated signal. In a nutshell, BD-RIKE combines the background-free detection a typical of CARS, with the absence of NRB and the linear concentration dependency typical of SRS. It can be regarded as an important addition to the arsenal of CRS techniques. 6.1.4.1 Scheme of Balanced-Detection Raman-Induced Kerr Effect An easy understanding can be developed for BD-RIKE scheme by presenting its experimental arrangement (Fig. 5.14A). BD-RIKE shares with normal RIKE the same linear or circular RIKE excitation geometries by employing a half-wave plate (HWP) or a quarter-wave plate (QWP), respectively, in pump branch. In detection, after the sample, the pump is spectrally discarded, and the remaining Stokes beam, which contains the signal, is followed by another wave plate (for simplicity let us call it “wave plate-in-detection,” it can be HWP or QWP) and a Wollaston prism. The combination of the wave plate in detection and Wollaston prism projects the Stokes field polarization in two orthogonal axes propagating in two different directions. These two separated beams are sent to a balanced detector. The current difference (IBD) of the two channels of the balanced detector is made zero (i.e., IBD ¼ 0) in absence of any pump field on the sample. It is done by just adjusting the orientations of the wave plate-in-detection and the Wollaston prism to make sure the two channels of the balanced photodiode see the same Stokes intensities but with orthogonal polarizations. Now when pump field is on, a rotation in Stokes field polarization due to RIKE generates unbalancing on the two channels of the balanced detector. The corresponding nonzero current (IBD) is our BD-RIKE signal. The small BD-RIKE signal IBD is probed by using the modulation transfer scheme by employing an acoustooptically modulator in the pump beam and then assisted by lock-in detection. The response of BD-RIKE signal depends on the configuration of the wave plate-in-detection. It can be easily  shown by simple calculations that the combination “HWP in detection plus Wollaston prism” gives IBD f2Re Axs $DAs , whereas

FIGURE 5.14 (A) Schematic of balanced-detection Raman-induced Kerr effect (BD-RIKE) spectroscopy/microscopy setup. BD-RIKE (B) and stimulated Raman scattering (SRS) (C) images of a blend of 6-mm polymethyl methacrylate beads and 3-mm polystyrene beads acquired at frequency detuning 3060 cm1 under the same experimental conditions. These images were acquired at Coherent Raman Laboratory, Department of Physics, Politecnico di Milano, Italy.

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   the combination “QWP in detection plus Wollaston prism” gives IBD f2Im Axs $DAs . Here DAs is again given by Eqs. (5.37a) and (5.37b) for linear and circular RIKE excitations, respectively. Therefore, there are two possible detection geometries (HWP or QWP in detection) for both linear and circular RIKE excitations. In other words, there are four configurations of the BD-RIKE technique, and for each of them, the signal IBD can be calculated, summarized as below. 6.1.4.1.1 Linear RIKE

h i ð3ÞR;im ð3ÞR;im HWP in detection : IBD ¼ 2aS c1212 þ c1122 Ip Is L

(5.39a)

h i ð3ÞR;re ð3ÞR;re ð3ÞNR;re ð3ÞNR;re QWP in detection : IBD ¼ 2aS c1212 þ c1122 þ c1212 þ c1122 Ip Is L

(5.39b)

6.1.4.1.2 Circular RIKE

h i ð3ÞR;re ð3ÞR;re HWP in detection: IBD ¼ 2aS c1122  c1212 Ip Is L

(5.40a)

h i ð3ÞR;im ð3ÞR;im QWP in detection : IBD ¼ 2aS c1122  c1212 Ip Is L

(5.40b)

Observing above equations, one can conclude that three configurations governed by Eqs. (5.39a), (5.40a), and (5.40b) are free from any NRB. Moreover, configurations (5.39a) and (5.40b) provide pure imaginary components, whereas configuration (5.40a) provides pure real components. This gives extremely powerful mechanism with added freedom to probe as per choice the different kinds of molecular responses and their properties just by switching among different BDRIKE configurations. The BD-RIKE spectra acquired for acetone solution in the four configurations (5.39a), (5.39b), (5.40a), and (5.40b) are reported in the literature [38], which are in good agreement with these theoretical calculations. BD-RIKE microscopy in principle can be applied as a substitute for CARS or SRS microscopy. For example, Fig. 5.14B and C shows vibrational phase-sensitive balanced-detection RIKE image and SRS image, respectively, of the same sample area of a blend of 6-mm PMMA beads and 3-mm PS beads acquired at pumpeStokes frequency detuning 3060 cm1 (a Raman resonance of PS) under the same experimental conditions. It has been successfully demonstrated [39] and can also be seen in Fig. 5.14B and C that although in comparison to SRS, BD-RIKE gives slightly lower signal, it exhibits better signal-to-noise ratio than SRS through an inherent mechanism of effective laser intensity noise suppression and hence shows better image quality with respect to SRS. BD-RIKE spectroscopy/microscopy has much potential and has still not been fully explored. Few groups are working on it. In near future we may see further advancement in the field.

6.2 Second Harmonic Generation Microscopy SHG is an emerging contrast mechanism for biological imaging. SHG was implemented first time to biological imaging in 1986 by Freund et al. [40]. They applied SHG imaging to study the polarity of collagen fibers in rat tail tendon, but at low spatial resolution. Ever since, several technological developments have been made, which have transformed SHG mechanism to be capable of imaging collagen fibers in organs such as lung, kidney, and liver as well as in connecting tissues such as tendon, skin, bones, and blood vessels. Because of the fact that in tissue imaging, SHG microscopy relies on the inherent property of an endogenous element of the tissue, it is a noninvasive and an ideal candidate for in situ imaging. SHG is a second-order nonlinear coherent scattering process, which results from phase matching and summation of light fields that are induced by molecular arrangement possessing ordered noncentrosymmetric structures. In an SHG process, the two photons at optical frequency u of an input laser beam are mediated by two virtual states of the system and are upconverted to a single photon at optical frequency 2u (Fig. 5.15A). The SHG process originates from induced polarization rather than real absorption. This substantially reduces the probability of photobleaching and phototoxicity, which are detrimental in one-photon and multiphoton fluorescence techniques. As discussed in Section 4, the second-order induced polarization term responsible for SHG process can be derived from the general expression of P(2) given by Eq. (5.4a) and is written as: ð2Þ

PSHG ¼ 2ε0 cð2Þ ð2u; u; uÞ:Au Au expð j2utÞ

(5.41)

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FIGURE 5.15 Second harmonic generation (SHG) process: (A) energy level diagram, (B) spectral positions of input and output fields, (C) perfect phase matching, and (D) usual wave-vector mismatch in tissue environment, which is compensated by randomness and dispersion.

where c(2) is an element of second-order susceptibility tensor responsible for SHG. The full c(2) tensor has 33 ¼ 27 matrix elements, and it shares the same kind of birefringent properties as c(3) possesses. In analogy to Eq. (5.24), under semiclassical approach, starting from Maxwell’s equations, the equation for field propagation for P(2) ¼ p(2)exp[ j(2u)t] can be obtained as: vA2u m u0 c ð2Þ p expð jDkzÞ ¼ j 0 2n vz where Dk h k2u  2ku is the “phase-matching term” for SHG process. Under the assumption of negligible input intensity depletion, i.e., Au y constant which is usually the case in SHG microscopy, the integration of above equation over the sample length L, assuming initial condition as A2u(z ¼ 0) ¼ 0, will have the form:   DkL A2u ðz ¼ LÞ ¼ j a2u cð2Þ $Au Au L expðjDkL=2Þsinc 2 u0 Here a2u ¼ is a constant. As in practice, instead of fields, we measure intensity on photodetectors, the measured nc SHG intensity is given by:  

2 DkL 2 ISHG hjA2u j ¼ a22u cð2Þ I2u L2 sinc2 (5.42) 2 Eq. (5.42) readily interprets few important facts regarding SHG process. SHG intensity is proportional to the square of the input intensity Iu. c(2) is nonzero only for ordered noncentrosymmetric structures. This property is used in SHG microscopy for selective imaging of ordered molecules having noncentrosymmetric structures. SHG intensity has quadratic dependence on susceptibility c(2), i.e., it has N2 dependence where N is the number density. Furthermore, SHG intensity is proportional to the square of the interaction length L, provided that the phase matching is exactly satisfied (Dk ¼ 0). When   term. Dk s 0, dependency is governed by sinc2 DkL 2 Same as in more familiar environments of uniaxial SHG crystals and interfaces, the repetitive noncentrosymmetric units are present in large scale in biological materials, for example, polymeric proteins, fibrillar collagens, strained muscles. They facilitate SHG signal to probe them. However, in uniaxial crystals and interfaces, the SHG is perfectly phasematched, i.e., Dk ¼ 0, which gives whole SHG signal in forward direction. On the other hand, because of inherent randomness and dispersion in the biological tissues, the SHG from them never completely satisfies the phase matching (Fig. 5.15D). This results in random distribution of Dk values within an anisotropic domain, which consists either of single fibril or an ensemble of small fibrils. Consequently, the emission has a distribution in forward and in backward directions. Within the distribution of Dk, there exists a Dk value for which the coherence length Lc ¼ 2p/Dk of the generated SHG is on the order of interspacing of fibrils, which satisfies the condition for possible quasiephase-matching (QPM) mechanism. The additional phase mismatch is provided by dispersion and randomness. Thus, QPM supports the partially coherent SHG intensity between anisotropic domains both in forward and in backward directions in tissue environment. It is obvious that the SHG conversion efficiency and its emission direction are governed not only by fibril length, but the fibril thickness, the interfibril spacing, and randomness in their packing must also be taken into account.

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The SHG signal polarizations are related in a well-defined manner to incident beam polarization and the targeted fibril orientation. This fact is utilized in determining the absolute orientation of the fibrils as well as their distribution in orientation and organization inside the tissue [41]. This information resides in nonzero elements of tensor c(2).

6.2.1 A Typical Second Harmonic Generation Microscope Setup SHG microscopes are, in general, a laser scanning microscope (Fig. 5.3). In most cases, they contain a tunable titanium sapphire (Ti:S) oscillator pumped by a Nd:YAG laser as an SHG excitation source. Tunable wavelength range (700e1000 nm) of Ti:S provides penetration depths up to few hundreds of microns in a tissue environment, making it capable of deep-tissue imaging. As we have seen that the SHG signal from tissue is quasi-coherent and emission directions depend on spatial distribution of the targeted species, it is required to have both the forward detection and the epi-detection schemes to gather the full information of the SHG mechanism. Therefore, SHG microscopes usually have the arrangements for both detections. Fig. 5.16A represents the fact that for very thin tissue, forward SHG signal is dominant over the epiSHG signal. In medium tissue thickness, the dominancy shifts toward epi-direction (Fig. 5.16), whereas in very thick tissues, it gives only epi-detection SHG signal (Fig. 5.16C). The majority of work done in SHG microscopy is focused on visualization of collagen fibers in different kinds of organs and connecting tissues. In fact, SHG microscopy is proving itself as a medically relevant technique because many types of spatially ordered structures within an organ tissue, for example, muscle myosin lattices within muscle cells, are able to generate sufficient amount of SHG without the use of any fluorescent marker. Cheng et al. have used SHG imaging in association with CARS and TPEF imaging on the same platform to study a tissue from Ossabaw swine suffering from metabolic syndromeeinduced cardiovascular plagues, the disease responsible for heart attack and stroke in human [42]. For that they compared the distribution of elastin/collagen in normal tissue to those in tissue in lesion. SHG microscopy is a natural choice for in vivo imaging and pathologies of cornea infected by collagenous stroma. Pini et al. have used SHG imaging to analyze disordered patterns of cornea collagens induced by photothermal effects [43].

6.3 Third Harmonic Generation Microscopy THG microscopy [44,45] is also a nonlinear multiphoton imaging technique, which finds contrast in local change of nonlinear refractive index or third-order susceptibility c(3). Such changes usually occur at structural interfaces [46], for example, at waterelipid and watereprotein interfaces in lipid droplets, intra- and extracellular membranes, collagen bundles or muscle fibers, and also at interfaces of inorganic structures, namely, enamel of teeth and calcified bone. In a THG process, when a laser beam falls on a material, three photons at laser optical frequency u are mediated by a virtual state of the system and upconverted into a single photon of optical frequency 3u (Fig. 5.17A). THG is an FWM coherent scattering process. Same as SHG, it also originates from induced polarization instead of any real absorption. Consequently, it possesses high threshold for photobleaching and phototoxicity. The third-order induced polarization term generating THG signal can be derived from the general expression of P(3) given by Eq. (5.4b) and can be written as: ð3Þ

PTHG ¼ 2ε0 cð3Þ ð 3u; u; u; uÞ$Au Au Au expð j3utÞ

FIGURE 5.16 Forward- and epi-detection second harmonic generation signal from different tissue thicknesses.

(5.43)

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FIGURE 5.17 Third-order harmonic generation (THG) process: (A) energy level diagram, (B) spectral positions of input and output fields, (C) perfect phase matching, and (D) usual wave-vector mismatch, which is compensated by nonlinear refractive index change at structural interfaces.

After going through the similar mathematical treatment as we did for SHG, we can retrieve the expression for the THG intensity as:  

2 DkL 2 ITHG hjA3u j ¼ a23u cð3Þ Iu3 L2 sinc2 (5.44) 2 where a3u ¼ unc0 is a constant and Dk h k3u  3ku is the “phase-matching term” for THG process. Eq. (5.44) represents noticeable properties of THG signal. The THG intensity is proportional to the third power of the input intensity Iu, and it has a quadratic dependence on susceptibility c(3), i.e., it is proportional to N2. Furthermore, THG intensity is proportional to the square of the interaction length L, provided phase matching is exactly satisfied (Dk ¼ 0). As usual, when Dk s 0,  dependency is governed by sinc2 DkL term. 2 THG seems more versatile than SHG in the sense that THG is not limited by any particular asymmetry requirement from the targeted structures, contrary to SHG that needs a noncentrosymmetric environment. On the other hand, a homogeneously dispersed medium does not produce any THG signal, because in that case c(3)(3u; u, u, u) vanishes. Instead, THG is generated by the optical inhomogeneities of sizes of the order of laser focal volume providing nonzero c(3)(3u; u, u, u). Therefore, THG signal strength depends on how much we focus the beam on a particular sample structure size. In other words, it depends on the size of the structure and the spatial resolution of the microscope. In fact, this criterion is used in THG microscopy in targeting a particular size of species. Furthermore, THG signal depends also on the polarization state of the incident laser beam.

6.3.1 Requirements of a Typical Third Harmonic Generation Microscope Setup THG microscope has an important place in biological community to map the tissue organizational morphology. The tissue scattering and water absorption put a limitation on choice of laser excitation wavelength. At higher wavelengths, tissue scattering lowers, but at wavelengths larger than 1350 nm, water molecules that are abundant in tissue start absorbing. Therefore, excitation wavelengths lower than 1350 nm are preferred for sufficient tissue penetration. On the lower wavelength side, the limit is set by strong scattering and absorption of generated THG signal in UV range by the tissue itself. Hence the best suited excitation wavelength range is in infrared (1180e1350 nm) region, which generates THG signal in blue (390e450 nm). This blue window has another advantage that in multimodal microscopes, the signal from the colored fluorophores in visible range as well as yellow-green SHG signal will not interfere with each other. A deciding factor for THG microscope configuration is the phase-matching condition. Because of the phase-matching condition, which is completely satisfied in transparent samples, i.e., Dk h k3u  3ku ¼ 0, the generated THG signal propagates in forward direction. In such case, a forward detection configuration of the laser scanning microscope is preferred. On the other hand, for less transparent samples, scattering of THG signal allows for epi-detection configuration of the laser scanning microscope. However, the epi-detection THG signal is very weak, usually detected by high-sensitivity detectors such as photomultipliers.

112 Molecular and Laser Spectroscopy

THG microscopy has been applied for interface imaging in an optical glass fiber [44], for imaging laser-induced breakdown in glass [45], in GaN semiconductors for defect distribution [47], and to visualize liquid crystal structures [48]. In biology, THG microscopy has found application in visualizing the interfaces formed between interstitial aqueous fluids (e.g., cell cytoplasm) and lipid-rich composites, mineralized or absorbing organelles in tissues [49]. Recently, THG contrast mechanism is used to image embryo morphogenesis in tiny organisms [50]. THG microscopy can detect birefringence by utilizing appropriate polarization of excitation beam, for example, it has detected microscopic anisotropy and revealed the distribution of stromal collagen lamellae in human cornea [51].

6.4 Two-Photon Excitation Fluorescence Microscopy TPEF microscopy [52] has a unique niche in biological microscopy. Although TPEF was first predicted in 1931 theoretically by Maria Goppert-Mayer in her PhD thesis at the University of Göttingen, Germany, but it was experimentally verified in 1961 [53] after the invention of laser. Then after the invention of ultrafast lasers, in 1990, TPEF was used in the microscopy [54]. TPEF microscopy can be considered as the nonlinear version of one-photon fluorescence microscopy, because it utilizes the same principle for the imaging contrast that the fluorescent molecules (endogenous or foreign markers) can be selectively excited by two photons usually from a single laser beam, and then emitted fluorescence signal can be visualized just by spectral filtering. A simplified Jablonski energy level diagram for the process is shown in Fig. 5.18B, where absorption of two laser photons at optical frequency u excites a fluorophore molecule to its first electronic excited state. From there it relaxes to the lowest vibrational level of the same electronic excited state, before radiating a red-shifted fluorescence signal while making a transition to ground-state lowest vibrational level. TPEF microscopy offers both high resolution and high sensitivity. Because the yield of fluorescence signal is naturally very high, even a single molecule detection is possible. Based on two-photon nonlinear excitation mechanism that takes place at the focal volume only, TPEF microscopy inherently possesses 3D sectioning capability. Unlike one-photon fluorescence microscopy, it does not require separately any confocal pinhole for selecting image plane. Second advantage of this microscopy over one-photon technique is that it employs higher-wavelength (in near infrared) excitation beam (Fig. 5.18C), consequently reduced scattering with the tissue environment increases penetration depth in tissues. Third advantage is that in TPEF, due to confinement of nonlinearly in focal volume, the localized excitation generates all useful signal, hence unlike one-photon technique, there is no scattered background photons contaminating the image. The fluorophores can be endogenous or can be externally supplied. Great care and engineering is done while choosing an external fluorophore or marker, because in a bad selection, the fluorophores size and their chemical properties may corrupt or even change the sample properties. In support of TPEF microscopy, over the years, several synthetic fluorophores have been invented and successfully tested. Especially, the development of genetically encoded fluorescent proteins (XFPs) has revolutionized the TPEF microscopy applications in biological field. XFPs can tag the most of the cellular proteins. Hence they can be used to study distribution and dynamics of such proteins as well as proteineprotein interaction by applying TPEF microscopy. TPEF microscopy provides an important probe for problems in neurobiology, because it has potential to resolve individual one-micron-size synapses of the brain to the neural circuits, which are in centimeter scales. Because the neurons and the intact brain tissues must be studied in their natural environment, it is quite challenging for microscopic techniques other than TPEF to implement.

FIGURE 5.18 Jablonski energy level diagram for (A) one-photon fluorescence process and (B) two-photon excitation (TPE) fluorescence process, (C) spectral positions of two-photon excitation and emission.

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One-photon or two-photon excitation fluorescence microscopy usually suffers from photobleaching and phototoxicity. Extreme effort is done in such microscopies to maximize the probability of detecting a single fluorescence photon produced per excitation event. In this way, one can minimize the excitation intensity and reduces the probability of photobleaching and phototoxicity. TPEF microscopy has found numerous applications in many fields of biology including neurology, embryology, and tissue engineering. Because of its very high sensitivity, it is even able to visualize nearly transparent thin tissues such as skin cells with detailed view [55]. Two-photon laser scanning microscope has become an invaluable tool for neuroscientists. It has been utilized for anatomical and functional imaging of neurons in brain tissue [56] and for the study of calcium dynamics in thick brain slices and brains of live animals [57,58]. In addition, TPE scanned light-sheet microscopy has been done for in vivo imaging of drosophila and zebra fish embryos [59].

7. CONCLUSIONS In this chapter, we have seen that linear microscopy techniques, such as IR absorption, one-photon fluorescence, and spontaneous Raman spectroscopy, are capable of identifying species by probing their different properties. However, they are either too weak to perform high-speed imaging or require confocal geometry to get 3D sectioning. Nonlinear techniques, such as CRS, SHG, THG, and TPEF, on the contrary, provide inherent 3D sectioning and are coherent in nature. In all of the CRS techniques, the atomic/molecular Raman response is enhanced by several orders of magnitude to go till video-rate imaging speed with chemical specificity. Because CRS, SHG, THG, and TPEF are sensitive to specific properties of the molecules or structures, they are capable of targeting different species in a complex sample without a signal overlap. Adding information obtained from multiple techniques can provide complete knowledge in a biological diagnosis and full insight in a pharmaceutical problem. A multimodal nonlinear optical microscope combining CARS, TPEF, SHG, and THG imaging has been materialized by utilizing a laser source, an OPO, and a periodically poled crystal for optical frequency doubling [60]. In fact, modern microscopes are heading toward the capability of the multimodality.

REFERENCES [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]

R.W. Boyd, Nonlinear Optics, third ed., Academic Press, Amsterdam; Boston, 2008 p. xix, 613 pp. D.L. Andrews, Lasers in Chemistry, third ed., Springer-Verlag, Berlin, 1997 p. xii, 188 pp. B.P. Willis, G. Zerbi, Vibrational Intensities in Infrared and Raman Spectroscopy, Elsevier Scientific Pub. Co, 1982, p. 466. J. Fagaschewski, D. Sellin, C. Wiedenhöfer, S. Bohne, H.K. Trieu, L. Hilterhaus, Spatially resolved in situ determination of reaction progress using microfluidic systems and FT-IR spectroscopy as a tool for biocatalytic process development, Bioprocess and Biosystems Engineering 38 (7) (2015) 1399e1405. I. Karamancheva, T. Staneva, Determination of possible impurities in piracetam using FTIR spectroscopy, Journal of Pharmaceutical and Biomedical Analysis 21 (6) (2000) 1161e1169. J.M. Chalmers, H.G.M. Edwards, M.D. Hargreaves, Infrared and Raman Spectroscopy in Forensic Science, John Wiley & Sons, Ltd, Chichester, UK, 2012. M. Minsky, Memoir on inventing the confocal scanning microscope, Scanning 10 (4) (1988) 128e138. J.C. Erie, J.W. McLaren, S.V. Patel, Confocal microscopy in ophthalmology, American Journal of Ophthalmology 148 (5) (2009) 639e646. J.L. Kinsey, Laser-induced fluorescence, Annual Review of Physical Chemistry 28 (1) (1977) 349e372. F.N.E. Gavins, B.E. Chatterjee, Intravital microscopy for the study of mouse microcirculation in anti-inflammatory drug research: focus on the mesentery and cremaster preparations, Journal of Pharmacological and Toxicological Methods 49 (1) (2004) 1e14. P.F. McMillan, Raman spectroscopy in mineralogy and geochemistry, Annual Review of Earth and Planetary Sciences 17 (1) (1989) 255e279. Y.-S. Li, J.S. Church, Raman spectroscopy in the analysis of food and pharmaceutical nanomaterials, Journal of Food and Drug Analysis 22 (1) (2014) 29e48. A. Paudel, D. Raijada, J. Rantanen, Raman spectroscopy in pharmaceutical product design, Advanced Drug Delivery Reviews 89 (2015) 3e20. M.S. Dresselhaus, A. Jorio, R. Saito, Characterizing graphene, graphite, and carbon nanotubes by Raman spectroscopy, Annual Review of Condensed Matter Physics 1 (1) (2010) 89e108. C. Otto, C.J. de Grauw, J.J. Duindam, N.M. Sijtsema, J. Greve, Applications of micro-Raman imaging in biomedical research, Journal of Raman Spectroscopy 28 (2e3) (1997) 143e150. G.L. Eesley, Coherent Raman spectroscopy, Journal of Quantitative Spectroscopy and Radiative Transfer 22 (6) (1979) 507e576. T. Steinle, V. Kumar, M. Floess, A. Steinmann, M. Marangoni, C. Koch, C. Wege, G. Cerullo, H. Giessen, Synchronization-free all-solid-state laser system for stimulated Raman scattering microscopy, Light: Science & Applications 5 (10) (2016) e16149. V. Kumar, M. Casella, E. Molotokaite, D. Polli, G. Cerullo, M. Marangoni, Coherent Raman spectroscopy with a fiber-format femtosecond oscillator, Journal of Raman Spectroscopy 43 (5) (2012) 662e667.

114 Molecular and Laser Spectroscopy

[19] V. Kumar, R. Osellame, R. Ramponi, G. Cerullo, M. Marangoni, Background-free broadband CARS spectroscopy from a 1-MHz ytterbium laser, Optics Express 19 (16) (2011) 15143. [20] A. Zumbusch, G.R. Holtom, X.S. Xie, Three-dimensional vibrational imaging by coherent anti-stokes Raman scattering, Physical Review Letters 82 (20) (1999) 4142e4145. [21] R.W. Terhune, Non-linear optics, Bulletin of the American Physical Society 8 (1963) 359. [22] C.L. Evans, X.S. Xie, Coherent anti-stokes Raman scattering microscopy: chemical imaging for biology and medicine, Annual Review of Analytical Chemistry 1 (1) (2008) 883e909. [23] J.-X. Cheng, L.D. Book, X.S. Xie, Polarization coherent anti-stokes Raman scattering microscopy, Optics Letters 26 (17) (2001) 1341. [24] M. Marangoni, A. Gambetta, C. Manzoni, V. Kumar, R. Ramponi, G. Cerullo, Fiber-format CARS spectroscopy by spectral compression of femtosecond pulses from a single laser oscillator, Optics Letters 34 (21) (2009) 3262. [25] V.D. Kobtsev, D.N. Kozlov, S.A. Kostritsa, V.V. Smirnov, O.M. Stel’makh, Temperature fluctuations in turbulent flame measured using coherent anti-stokes Raman scattering, Technical Physics Letters 41 (8) (2015) 756e758. [26] V.I. Fabelinsky, V.V. Smirnov, O.M. Stel’makh, K.A. Vereschagin, W. Clauss, C. Manfletti, J. Sender, M. Oschwald, CARS temperature measurement in a LOX/CH4 spray flame, Journal of Raman Spectroscopy 41 (8) (2010) 890e896. [27] M.T. Bremer, P.J. Wrzesinski, N. Butcher, V.V. Lozovoy, M. Dantus, Highly selective standoff detection and imaging of trace chemicals in a complex background using single-beam coherent anti-stokes Raman scattering, Applied Physics Letters 99 (10) (2011) 101109. [28] A. Portnov, S. Rosenwaks, I. Bar, Detection of particles of explosives via backward coherent anti-stokes Raman spectroscopy, Applied Physics Letters 93 (4) (2008) 041115. [29] M.D. Duncan, J. Reintjes, T.J. Manuccia, Scanning coherent anti-stokes Raman microscope, Optics Letters 7 (8) (1982) 350. [30] C.L. Evans, E.O. Potma, M. Puoris’haag, D. Cote, C.P. Lin, X.S. Xie, Chemical imaging of tissue in vivo with video-rate coherent anti-stokes Raman scattering microscopy, Proceedings of the National Academy of Sciences 102 (46) (2005) 16807e16812. [31] C.H. Camp Jr., Y.J. Lee, J.M. Heddleston, C.M. Hartshorn, A.R.H. Walker, J.N. Rich, J.D. Lathia, M.T. Cicerone, High-speed coherent Raman fingerprint imaging of biological tissues, Nature Photonics 8 (8) (2014) 627e634. [32] E. Ploetz, S. Laimgruber, S. Berner, W. Zinth, P. Gilch, Femtosecond stimulated Raman microscopy, Applied Physics B 87 (3) (2007) 389e393. [33] C.W. Freudiger, W. Min, B.G. Saar, S. Lu, G.R. Holtom, C. He, J.C. Tsai, J.X. Kang, X.S. Xie, Label-free biomedical imaging with high sensitivity by stimulated Raman scattering microscopy, Science 322 (5909) (2008) 1857e1861. [34] Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, K. Itoh, High-speed molecular spectral imaging of tissue with stimulated Raman scattering, Nature Photonics 6 (12) (2012) 845e851. [35] D. Heiman, R.W. Hellwarth, M.D. Levenson, G. Martin, Raman-induced Kerr effect, Physical Review Letters 36 (4) (1976) 189e192. [36] B.R. Bachler, M.E. Fermann, J.P. Ogilvie, Multiplex Raman induced Kerr effect microscopy, Optics Express 20 (2) (2012) 835. [37] C.W. Freudiger, M.B.J. Roeffaers, X. Zhang, B.G. Saar, W. Min, X.S. Xie, Optical heterodyne-detected Raman-induced Kerr effect (OHD-RIKE) microscopy, The Journal of Physical Chemistry B 115 (18) (2011) 5574e5581. [38] V. Kumar, M. Casella, E. Molotokaite, D. Gatti, P. Kukura, C. Manzoni, D. Polli, M. Marangoni, G. Cerullo, Balanced-detection Raman-induced Kerr-effect spectroscopy, Physical Review a 86 (5) (2012). [39] V. Kumar, N. Coluccelli, M. Cassinerio, M. Celebrano, A. Nunn, M. Levrero, T. Scopigno, G. Cerullo, M. Marangoni, Low-noise, vibrational phase-sensitive chemical imaging by balanced detection RIKE, Journal of Raman Spectroscopy 46 (1) (2015) 109e116. [40] I. Freund, M. Deutsch, A. Sprecher, Connective tissue polarity. Optical second-harmonic microscopy, crossed-beam summation, and small-angle scattering in rat-tail tendon, Biophysical Journal 50 (4) (1986) 693e712. [41] S.V. Plotnikov, A.C. Millard, P.J. Campagnola, W.A. Mohler, Characterization of the myosin-based source for second-harmonic generation from muscle sarcomeres, Biophysical Journal 90 (2) (2006) 693e703. [42] T.T. Le, I.M. Langohr, M.J. Locker, M. Sturek, J.-X. Cheng, Label-free molecular imaging of atherosclerotic lesions using multimodal nonlinear optical microscopy, Journal of Biomedical Optics 12 (5) (2007) 054007. [43] P. Matteini, F. Ratto, F. Rossi, R. Cicchi, C. Stringari, D. Kapsokalyvas, F.S. Pavone, R. Pini, Photothermally-induced disordered patterns of corneal collagen revealed by SHG imaging, Optics Express 17 (6) (2009) 4868. [44] Y. Barad, H. Eisenberg, M. Horowitz, Y. Silberberg, Nonlinear scanning laser microscopy by third harmonic generation, Applied Physics Letters 70 (8) (1997) 922. [45] J.A. Squier, M. Müller, G.J. Brakenhoff, K.R. Wilson, Third harmonic generation microscopy, Optics Express 3 (9) (1998) 315. [46] T.Y.F. Tsang, Optical third-harmonic generation at interfaces, Physical Review a 52 (5) (1995) 4116e4125. [47] C.-K. Sun, S.-W. Chu, S.-P. Tai, S. Keller, U.K. Mishra, S.P. DenBaars, Scanning second-harmonic/third-harmonic generation microscopy of gallium nitride, Applied Physics Letters 77 (15) (2000) 2331. [48] D. Yelin, Y. Silberberg, Y. Barad, J.S. Patel, Depth-resolved imaging of nematic liquid crystals by third-harmonic microscopy, Applied Physics Letters 74 (21) (1999) 3107. [49] D. Débarre, W. Supatto, A.-M. Pena, A. Fabre, T. Tordjmann, L. Combettes, M.-C. Schanne-Klein, E. Beaurepaire, Imaging lipid bodies in cells and tissues using third-harmonic generation microscopy, Nature Methods 3 (1) (2006) 47e53. [50] W. Supatto, D. Debarre, B. Moulia, E. Brouzes, J.L. Martin, E. Farge, E. Beaurepaire, In vivo modulation of morphogenetic movements in Drosophila embryos with femtosecond laser pulses, Proceedings of the National Academy of Sciences 102 (4) (2005) 1047e1052. [51] F. Aptel, N. Olivier, A. Deniset-Besseau, J.-M. Legeais, K. Plamann, M.-C. Schanne-Klein, E. Beaurepaire, Multimodal nonlinear imaging of the human cornea, Investigative Opthalmology & Visual Science 51 (5) (2010) 2459.

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[52] M. Oheim, D.J. Michael, M. Geisbauer, D. Madsen, R.H. Chow, Principles of two-photon excitation fluorescence microscopy and other nonlinear imaging approaches, Advanced Drug Delivery Reviews 58 (7) (2006) 788e808. [53] W. Kaiser, C.G.B. Garrett, Two-photon excitation in CaF2:Eu2þ, Physical Review Letters 7 (6) (1961) 229e231. [54] W. Denk, J. Strickler, W. Webb, Two-photon laser scanning fluorescence microscopy, Science 248 (4951) (1990) 73e76. [55] B.R. Masters, P.T. So, E. Gratton, Multiphoton excitation fluorescence microscopy and spectroscopy of in vivo human skin, Biophysical Journal 72 (6) (1997) 2405e2412. [56] W. Denk, K.R. Delaney, A. Gelperin, D. Kleinfeld, B.W. Strowbridge, D.W. Tank, R. Yuste, Anatomical and functional imaging of neurons using 2-photon laser scanning microscopy, Journal of Neuroscience Methods 54 (2) (1994) 151e162. [57] F. Helmchen, K. Svoboda, W. Denk, D.W. Tank, In vivo dendritic calcium dynamics in deep-layer cortical pyramidal neurons, Nature Neuroscience 2 (11) (1999) 989e996. [58] F. Helmchen, J. Waters, Ca2þ imaging in the mammalian brain in vivo, European Journal of Pharmacology 447 (2e3) (2002) 119e129. [59] T.V. Truong, W. Supatto, D.S. Koos, J.M. Choi, S.E. Fraser, Deep and fast live imaging with two-photon scanned light-sheet microscopy, Nature Methods 8 (9) (2011) 757e760. [60] H. Chen, H. Wang, M.N. Slipchenko, Y. Jung, Y. Shi, J. Zhu, K.K. Buhman, J.-X. Cheng, A multimodal platform for nonlinear optical microscopy and microspectroscopy, Optics Express 17 (3) (2009) 1282.