- Email: [email protected]
Multidimensional coherent spectroscopy made easy
Available online at www.sciencedirect.com
Chemical Physics 341 (2007) 89–94 www.elsevier.com/locate/chemphys
Multidimensional coherent spectroscopy made easy Kenan Gundogdu, Katherine W. Stone, Daniel B. Turner, Keith A. Nelson
*
Department of Chemistry, Massachusetts Institute of Technology, 77 Mass Ave. 6-026 Cambridge, MA 02139, United States Received 13 March 2007; accepted 7 June 2007 Available online 27 June 2007
Abstract We have demonstrated a highly efficient fully coherent 2D spectrometer based on 2D pulse shaping and Fourier beam shaping. The versatility of the design allows one to measure different 2D spectral surfaces consecutively. Easy alignment, inherent phase stability, rotating wave frame detection, and arbitrary waveform generation in all of the beams are important features of this design. We have demonstrated the functionality of the 2D spectrometer by measuring a 2D spectral surface of a GaAs quantum well. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Multidimensional spectroscopy; Four-wave mixing; Coherent; Ultrafast spectroscopy; Pulse shaping
1. Introduction Two-dimensional Fourier transform (2D FT) spectroscopy is a very powerful tool for probing electronic and vibrational dynamics in molecules and complex systems. 2D FT spectroscopy in the IR regime has been used to study both intramolecular and intermolecular vibrational dynamics such as vibrational couplings, anharmonicities, dephasing, solvation dynamics and transient molecular structures of small molecules and proteins [1–6]. Application in the optical regime has been used to study exciton dynamics in light harvesting complexes and in semiconductors, revealing information regarding exciton delocalization, couplings and many-body interactions [7,8]. These dynamics are in general highly convolved and therefore, difficult or impossible to retrieve by any other spectroscopic method. 2D FT spectroscopy is an enhancement to four-wave mixing (FWM) experiments. In conventional FWM techniques the spectral and/or temporal dependence of the signal is analyzed but the phase information is ignored. The introduction of diffractive optics enabled heterodyne detec-
*
Corresponding author. Tel.: +1 617 253 1423. E-mail address: [email protected] (K.A. Nelson).
0301-0104/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.06.027
tion of phase-matched signals and complete determination of the complex signal fields, measured as a function of a single variable time delay (i.e., 1D measurements) between the two time-coincident, phase-locked excitation pulses and the time-coincident, phase-locked probe and reference pulses [9–12]. The power of 2D FT spectroscopy originates from its ability to track and correlate phase evolutions during two independent time periods. This requires the introduction of specified time delays between the non-collinear excitation pulses and the non-collinear probe and reference, without loss of control over the phase relationships between pulse pairs. Therefore, the primary challenge in constructing optical FT experiments is maintaining phase stability between the pulse pairs at about k/50 (16 nm for 800 nm pulses) while delaying pulses by steps smaller than k/2. Depending on the excitation wavelength (IR or visible), several approaches have been developed. For instance, using multiple high precision delay lines or refractive optics for accurately delaying the pulses, active interferometric feedback loops for improving the phase stability, and He–Ne tracer beams to correct both phase instabilities and inaccurate time steps are common approaches, all of which substantially increase the complexity of the setup [8,13–16]. In the visible spectral range especially, these approaches impose substantial limitations on capabilities. For example, phase stability is maintained within each
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pulse pair but not between the two pairs, i.e., the measurement is not fully phase-coherent, and in many cases two time delays are linked by a common delay stage, foregoing independent variation. Using a collinear geometry for excitation and phase cycling with an acousto-optic modulator addresses these problems, however, the signal is not background-free [17–19]. Although the strength of 2D FT spectroscopy promises important advances in many fields, the spread of this highly powerful technique beyond the group of specialized and experienced ultrafast spectroscopists who have worked actively on its development and its full realization even within this group are strongly hindered by its technical difficulty. At present, there are only a handful of research groups that are able to perform these experiments, especially in the visible spectral range. Recently, it was demonstrated that reconfigurable, automated modulation of the temporal and spatial profiles of femtosecond laser fields through 2D pulse shaping can be used to perform 2D FT spectroscopy. In contrast to conventional multi-wave mixing setups, multiple delay lines are not required. All the time delays between the non-collinear optical fields are implemented with a 2D pulse shaper [20–22]. The pulse envelope can be delayed with no shift in the optical phases and successive time delay steps can be extremely uniform; both of these are important features for Fourier transform experiments. A key element of the apparatus is its inherent phase stability, arising from common path optics for all the beams. Phase stability of k/67 among all four beams was measured recently over an 8 h period with no enclosure around the setup [22]. Finally, arbitrary waveform generation (i.e., shaping of the phase and amplitude temporal profiles) is enabled for all four fields. This novel design makes the experimental setup compact, easily aligned, robust and versatile. For instance, one
can easily perform the experiments that corresponds to socalled SI (photon echo), SII (virtual echo) and SIII diagrams [23] in a homodyne or heterodyne detected fashion consecutively without any realignment of the setup. There is also no consideration of uneven time delay steps, which is an important issue for Fourier transform experiments. The simplicity of the 2D pulse shaping-based experimental alignment combined with all these advantages suggests this approach for a turn-key, fully coherent multidimensional optical spectrometer that could be used for routine materials characterization and analysis as well as fundamental research. However, the experimental system described earlier had two significant limitations arising from the use of a spatial mask with four holes to isolate the four phase-matched beams from a spatially extended laser field [22]. Most of the light was blocked, resulting in poor throughput, and diffraction from the edges of the holes led to cross-talk between various incident beams and the outgoing signal. In this letter, we describe a new experimental design that overcomes these limitations and also greatly facilitates high-order measurements that involve more than four input beams. Our ‘‘fully coherent multidimensional Fourier transform spectrometer’’ may be easily replicated and may serve as a prototype for a manufacturable instrument. 2. Experimental design Fig. 1 illustrates the multidimensional spectrometer. It is composed of a 2D spatial beam shaper to arrange the BOXCARS geometry, and a 2D spatiotemporal pulse shaper based on a 2D liquid crystal spatial light modulator (LC SLM) to implement the relative time delays and phase shifts as well as any other temporal shaping of the pulses.
Fig. 1. Schematic illustration of the fully phase-coherent spectrometer design. A single beam from an ultrafast laser source is focused onto a diffractive optic (2D Phase Mask ‘‘PM’’) designed to split it into four beams arranged at the corners of a square. This beam arrangement is sent to a 2D spatiotemporal pulse shaper consisting of a diffraction grating (G), a cylindrical lens (CL) and a 2D SLM configured for diffraction-based pulse shaping. The first-order diffracted outputs from the 2D pulse shaper are separated from the input by a beamsplitter (BS) and then focused through a spatial filter (SF) in order to reject the undesired diffraction orders. The filtered output is then focused onto the sample where the nonlinear signal is generated in the phase-matched direction and detected by a monochrometer and CCD camera (not shown).
K. Gundogdu et al. / Chemical Physics 341 (2007) 89–94
2.1. 2D Spatial beam shaper The beam shaper apparatus takes a single beam as input and generates four beams in the BOXCARs geometry to satisfy the phase-matching requirement for heterodyned FWM measurements. The critical element in the beam shaper is a 2D phase mask, PM in Fig. 1. In the present demonstration, we used two diffractive optical elements with a groove spacing of 7.5 lm, attached face to face with the grooves perpendicular to each other. When a beam is focused on the phase mask, four first-order diffracted beams diverge from the focus with equal angles of diffraction with respect to the incident beam. Weak higher-order and zero-order beams are blocked. A lens collimates the four first-order diffracted beams. The beam shaper has a power efficiency of 50%, and the output beams have the same Gaussian spatial profile as the input beam. More generally, a 2D SLM could be used to reconfigurably generate the four beams or more beams for higher-order measurements. 2.2. 2D Spatiotemporal pulse shaper We have described spatiotemporal femtosecond pulse shaping, through which an incident light field is tailored as a function of time and one spatial coordinate (vertical in the present case), in various forms through which it may be executed [21,24,25]. Our present needs are relatively simple since only four independently controlled temporal profiles are needed and the primary characteristics of the profiles that need to be controlled are the pulse delay (changing of the envelope position in time without changing the optical phase) and, when desired, the optical phase. More generally, many independent beams can be shaped and complex temporal profiles may be crafted. For control over both phase and amplitude temporal profiles, we use the spatiotemporal pulse shaper in diffraction mode [21]. The frequency components of an incident beam are dispersed in the horizontal dimension by a diffraction grating and imaged with a lens onto a 2D liquid crystal SLM. Each frequency component encounters a vertical sawtooth grating pattern of phase shifts. The phase and amplitude of the resulting first-order diffraction may be controlled by specifying the spatial phase of the grating pattern (i.e., the positions of the grating ‘‘teeth’’) and the amplitude of the pattern, respectively. The diffracted frequency components are recombined with a second lens and grating, yielding the specified shaped waveform. In this configuration, time delays (within the 12 ps window of our current pulse shaper) are introduced by applying a linear spectral phase variation as a function of frequency, executed through a linear variation of the sawtooth spatial phase as a function of horizontal position. In the current spectrometer configuration, the two orthogonal phase masks are oriented at roughly 25° angles relative to the horizontal and vertical so that the four beams form a square that is tilted at a similar angle. In
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this manner, each of the four beams arrives at a vertically distinct region of the 2D SLM so it can be temporally shaped independently of the others. See Fig. 1. The four first-order diffracted fields are selected by a spatial filter situated at the focal plane of lens L1 and collimated by a second lens, L2. The sample is located at the focal plane of lens L3. We arbitrarily choose one of the beams as the local oscillator (LO) and delay the pulse to positive times so that it transmits through the sample long after the three excitation pulses. The signal that emerges from the sample at the phase-matching direction is spatially overlapped with the local oscillator and is heterodyne detected through spectral interferometry [26]. In this experimental design, once the LO is chosen, one can determine the interaction order of three excitation pulses to perform the experiments corresponding to SI (photon echo), SII (virtual echo) and SIII diagrams without changing the experimental alignment. Flexibly alternating between heterodyne detected transient grating and SIII scans in the conventional design using optical delay lines is not possible because the partners in each pair of time-coincident pulses must be exchanged. In order to reduce spurious interferences of the signal with scattered light (mainly from the SLM or the sample), phase cycling [22] is executed by varying the phases of selected beams by p and subtracting signals, thereby suppressing signals that do not depend on each of the three excitation fields. 3. Experimental demonstration In order to demonstrate the performance of the device, we have measured 2D spectra of GaAs quantum well (QW) structures at 10 K. Li et al. have reported 2D spectra of similar QWs and showed that 2D spectroscopy of these systems is very sensitive to many-body interactions [8]. Our sample consists of 10 periods of 10 nm GaAs QWs separated by 10 nm Al0.3Ga0.7As barriers. The heavy-hole and light-hole excitons absorb at around 806 nm and 802 nm, respectively [8]. We have performed so-called rephasing, SI (photon echo), experiments using 40 fs pulses centered at 812 nm from a Ti: sapphire oscillator with a repetition rate of 92 MHz. The details of the signal generation in rephasing experiments and relevant Feynman pathways can be found in Ref. [27]. In this experiment the signal is emitted in the phase-matched direction ks = k1 + k2 + k3 and the pulse with wave vector k1 interacts with the sample first. We have attenuated the LO by using a 3 mm thick neutral density (ND) filter with an optical density of 2. The ND filter delays the LO by about 3.5 ps. This delay is also useful to avoid undesired signal contributions due to coherent interactions of the LO with the nonlinear polarization prepared in the sample by the three interaction pulses. Each excitation beam has a power of 0.5 mW. We calculated an exciton density of about 1010 excitons per cm2 per quantum well.
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In the rephasing scan the pulses with wave vectors k2 and k3 were coincident, while the pulse with wave vector k1 was scanned so that it precedes the other pulses by a time that is varied in 15 fs step sizes through a total range of 4 ps. It is important to note that in this experiment we are trying to resolve the phase evolution of coherences that are resonantly excited at around 805.5 nm (or 802.2 nm for light holes). The oscillation period of these coherences is about 2.7 fs, far too short to resolve with 15 fs step sizes. However, a direct consequence of delaying the pulse envelopes without changing the phases is that the signal phase evolutions are observed in the rotating wave frame, i.e., the resonance is red shifted by the carrier frequency [28]. We have set the carrier wavelength to 812.4 nm; this corresponds to a frequency of 369 THz. Resonances at 805.5 nm (372.2 THz) and 802.2 nm (373.7 THz) are therefore observed as beat frequencies against the LO at 3.2 THz and 4.7 THz, respectively. These beat frequencies correspond to oscillation periods much larger than 100 fs, easily resolved with a 15 fs step size. 4. Data Fig. 2 shows the data acquired by the CCD camera through spectral interferometry. The total data acquisition time was about 10 min including four-step phase cycling to reduce the noise level. The data are plotted as a function of time delay (x-axis) and frequency (y-axis). The evolution of the phase of the coherences at the heavy hole and light hole during the time between the interaction with the first pulse and non-conjugate pulses can be observed as beat periods along the x-axis. Fig. 3 shows the 2D power spectrum obtained using the spectral interferometry algorithm on the raw data [26]. The contours are plotted as a function of two frequencies; the yaxis represents the frequencies that evolved during the time delay that is scanned between the first and second pulses
374.7
6000
emission frequency [THz]
374.2
4000
373.7 2000 373.2 0 372.7 —2000 372.2 —4000 371.7 371.2 —4
—6000 —3.5
—3
—2.5
—2
—1.5
—1
—0.5
0
tau [ps] Fig. 2. Raw data acquired by the 2D spectrometer. The signal is detected using spectral interferometry. 2D spectra are obtained upon analysis of the raw data by the spectral interferometry algorithm.
Fig. 3. 2D spectral surface of GaAs quantum wells corresponding to S1 (photon echo) diagrams, obtained by analyzing the raw data shown in Fig. 2. The two diagonal peaks are heavy hole and light hole resonances and the off-diagonal peaks appear are due to coupling of heavy-hole and light-hole bands.
and the x-axis is for the emission frequencies. As described earlier, the y-axis frequencies are observed in the rotating wave frame. Therefore, the heavy-hole peak corresponds to 3.2 THz and the light-hole peak to 4.7 THz. We have also shifted the x-axis by the carrier frequency, so that we could label the peaks as diagonal and off-diagonal for convenience. The 2D power spectrum of GaAs QWs exhibits four distinct spectral features. The diagonal peaks are heavy-hole and light-hole exciton resonances, and the off-diagonal peaks indicate the couplings between these states. The heavy-hole and light-hole excitons are coupled through the conduction band [8]. The separation of these spectral features on a two-dimensional surface allows one to discriminate the quantum mechanical pathways that the optically excited coherences evolved through, which is inaccessible information via conventional FWM experiments. One can also use complex Fourier analysis to obtain the real and imaginary 2D spectral surfaces. It is important to note that the features in a real and imaginary 2D spectral surfaces are not purely absorptive or purely dispersive. Ref. [23] describes the experimental analysis procedure to obtain mainly absorptive or dispersive lineshapes in a 2D spectrum. These procedures involve both rephasing (SI) and non-rephasing (SII) experiments. In this communication we only present the 2D surface that corresponds to rephasing diagrams. The results of a comprehensive study will be presented subsequently. Fig. 4a and b show the real and imaginary 2D spectral surfaces obtained via complex Fourier analysis of the raw data. One striking observation is that the diagonal and off-diagonal features in the real 2D spectra are highly dispersive, consistent with earlier measurements of GaAs quantum wells [8] but not usually seen in 2D measurements
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5. Conclusions We have demonstrated a design based on 2D spatiotemporal pulse shaping coupled to a 2D spatial beam shaper that is capable of modulating the phase and amplitude profiles of non-collinear excitation pulses for fully coherent multi-wave mixing spectroscopy. This design has the potential to empower researchers from many different backgrounds to harness the capabilities of 2D FT spectroscopy, for applications ranging from small molecules to biological systems to semiconductors. The approach demonstrated here can be extended to the measurement of higher dimensional spectra in resonant and non-resonant experiments through the use of different phase mask patterns or, more generally, an SLM for the 2D spatial shaping to produce more than four beams in a phase-matched geometry when necessary. The approach also will be applicable to multidimensional coherent spectroscopy in different regions of the electromagnetic spectrum. Acknowledgements The authors acknowledge S. Cundiff for the quantum well sample. This work was supported in part by National Science Foundation Grant CHE-0616939. D. Turner thanks the NDSEG Fellowship Program for financial support. References
Fig. 4. (a) Real and (b) imaginary 2D spectral surfaces.
of dilute systems [23]. Li et al. showed through simulations using the optical Bloch equations that the dispersive character is mainly due to excitation induced shifts of the exciton energy, as opposed to excitation induced exciton dephasing. The clear indication of many-body interactions and the further sensitivity to particular interaction mechanisms illustrates the value of 2D FT spectroscopy compared to conventional FWM techniques. The present demonstration illustrates that the fully coherent multidimensional spectrometer introduced in this paper is capable of producing the 2D FT experimental results similar to those obtained via conventional methods using optical delay lines. The new approach also makes new classes of measurements possible. Although we have only demonstrated the rephasing measurement, non-rephasing and SIII measurements are conducted as easily. In addition, full phase coherence among all the beams enables new capabilities like 3D FT spectroscopy and observation of higher coherences, which will be reported shortly.
[1] O. Golonzka, M. Khalil, N. Demirdoven, A. Tokmakoff, J. Chem. Phys. 115 (2001) 10814. [2] O. Golonzka, M. Khalil, N. Demirdoven, A. Tokmakoff, Phys. Rev. Lett. 86 (2001) 2154. [3] M.T. Zanni, S. Gnanakaran, J. Stenger, R.M. Hochstrasser, J. Phys. Chem. B 105 (2001) 6520. [4] J. Zheng, K. Kwak, J. Asbury, X. Chen, I.R. Piletic, M.D. Fayer, Science 309 (2005) 1338. [5] H.S. Chung, M. Khalil, A.W. Smith, Z. Ganim, A. Tokmakoff, PNAS 102 (2005) 612. [6] M.L. Cowan, B.D. Bruner, N. Huse, J.R. Dwyer, B. Chugh, E.T. J Nibbering, T. Elsaesser, R.J.D. Miller, Nature 434 (2005) 199. [7] T. Brixner, J. Stenger, H.M. Vaswani, M. Cho, R.E. Blankenship, G.R. Fleming, Nature 434 (2005) 625. [8] X. Li, T. Zhang, C.N. Borca, S.T. Cundiff, Phys. Rev. Lett. 96 (2006) 057406. [9] J.A. Rogers, M. Fuchs, M.J. Banet, J.B. Hanselman, R. Logan, K.A. Nelson, Appl. Phys. Lett. 71 (1997) 225. [10] A.A. Maznev, K.A. Nelson, J.A. Rogers, Opt. Lett. 23 (1998) 1319. [11] G.D. Goodno, G. Dadusc, R.J.D. Miller, J. Opt. Soc. Am. B 15 (1998) 1791. [12] G.D. Goodno, V. Astinov, R.J.D. Miller, J. Phys. Chem. B 103 (1999) 603. [13] M.L. Cowan, J.P. Ogilvie, R.J.D. Miller, Chem. Phys. Lett. 386 (2004) 184. [14] F. Ding, P. Mukherjee, M.T. Zanni, Opt. Lett. 31 (2006) 2918. [15] V. Volkov, R. Schanz, P. Hamm, Opt. Lett. 30 (2005) 2010. [16] J.J. Loparo, S.T. Roberts, A. Tokmakoff, J. Chem. Phys. 125 (2006) 194521. [17] P. Tian, D. Keusters, Y. Suzaki, W.S. Warren, Science 300 (2003) 1553.
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[18] S. Shim, D.B. Strasfeld, E.C. Fulmer, M.T. Zanni, Opt. Lett. 31 (2006) 838. [19] M. Roth, M. Mehendale, A. Bartelt, H. Rabitz, Appl. Phys. B 80 (2005) 441. [20] T. Hornung, J.C. Vaughan, T. Feurer, K.A. Nelson, Opt. Lett. 29 (2004) 2052. [21] J.C. Vaughan, T. Hornung, T. Feurer, K.A. Nelson, Opt. Lett. 30 (2005) 323. [22] J.C. Vaughan, T. Hornung, K.A.W. Stone, K.A. Nelson, J. Phys. Chem. 111 (2007) 4873.
[23] M. Khalil, N. Demirdoven, A. Tokmakoff, J. Phys. Chem. A 107 (2003) 5258. [24] J.C. Vaughan, T. Feurer, K.A. Nelson, Opt. Lett. 28 (2003) 2408. [25] T. Feurer, J.C. Vaughan, R.M. Koehl, K.A. Nelson, Opt. Lett. 27 (2002) 652. [26] L. Lepetit, G. Cheriaux, M. Joffre, J. Opt. Soc. Am. B 12 (1995) 2467. [27] Shaul Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press, 1995. [28] A.W. Albrecht, J.D. Hybl, S.M. G Faeder, D.M. Jonas, J. Chem. Phys. 111 (1999) 10934.
Chemical Physics 341 (2007) 89–94 www.elsevier.com/locate/chemphys
Multidimensional coherent spectroscopy made easy Kenan Gundogdu, Katherine W. Stone, Daniel B. Turner, Keith A. Nelson
*
Department of Chemistry, Massachusetts Institute of Technology, 77 Mass Ave. 6-026 Cambridge, MA 02139, United States Received 13 March 2007; accepted 7 June 2007 Available online 27 June 2007
Abstract We have demonstrated a highly efficient fully coherent 2D spectrometer based on 2D pulse shaping and Fourier beam shaping. The versatility of the design allows one to measure different 2D spectral surfaces consecutively. Easy alignment, inherent phase stability, rotating wave frame detection, and arbitrary waveform generation in all of the beams are important features of this design. We have demonstrated the functionality of the 2D spectrometer by measuring a 2D spectral surface of a GaAs quantum well. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Multidimensional spectroscopy; Four-wave mixing; Coherent; Ultrafast spectroscopy; Pulse shaping
1. Introduction Two-dimensional Fourier transform (2D FT) spectroscopy is a very powerful tool for probing electronic and vibrational dynamics in molecules and complex systems. 2D FT spectroscopy in the IR regime has been used to study both intramolecular and intermolecular vibrational dynamics such as vibrational couplings, anharmonicities, dephasing, solvation dynamics and transient molecular structures of small molecules and proteins [1–6]. Application in the optical regime has been used to study exciton dynamics in light harvesting complexes and in semiconductors, revealing information regarding exciton delocalization, couplings and many-body interactions [7,8]. These dynamics are in general highly convolved and therefore, difficult or impossible to retrieve by any other spectroscopic method. 2D FT spectroscopy is an enhancement to four-wave mixing (FWM) experiments. In conventional FWM techniques the spectral and/or temporal dependence of the signal is analyzed but the phase information is ignored. The introduction of diffractive optics enabled heterodyne detec-
*
Corresponding author. Tel.: +1 617 253 1423. E-mail address: [email protected] (K.A. Nelson).
0301-0104/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.06.027
tion of phase-matched signals and complete determination of the complex signal fields, measured as a function of a single variable time delay (i.e., 1D measurements) between the two time-coincident, phase-locked excitation pulses and the time-coincident, phase-locked probe and reference pulses [9–12]. The power of 2D FT spectroscopy originates from its ability to track and correlate phase evolutions during two independent time periods. This requires the introduction of specified time delays between the non-collinear excitation pulses and the non-collinear probe and reference, without loss of control over the phase relationships between pulse pairs. Therefore, the primary challenge in constructing optical FT experiments is maintaining phase stability between the pulse pairs at about k/50 (16 nm for 800 nm pulses) while delaying pulses by steps smaller than k/2. Depending on the excitation wavelength (IR or visible), several approaches have been developed. For instance, using multiple high precision delay lines or refractive optics for accurately delaying the pulses, active interferometric feedback loops for improving the phase stability, and He–Ne tracer beams to correct both phase instabilities and inaccurate time steps are common approaches, all of which substantially increase the complexity of the setup [8,13–16]. In the visible spectral range especially, these approaches impose substantial limitations on capabilities. For example, phase stability is maintained within each
90
K. Gundogdu et al. / Chemical Physics 341 (2007) 89–94
pulse pair but not between the two pairs, i.e., the measurement is not fully phase-coherent, and in many cases two time delays are linked by a common delay stage, foregoing independent variation. Using a collinear geometry for excitation and phase cycling with an acousto-optic modulator addresses these problems, however, the signal is not background-free [17–19]. Although the strength of 2D FT spectroscopy promises important advances in many fields, the spread of this highly powerful technique beyond the group of specialized and experienced ultrafast spectroscopists who have worked actively on its development and its full realization even within this group are strongly hindered by its technical difficulty. At present, there are only a handful of research groups that are able to perform these experiments, especially in the visible spectral range. Recently, it was demonstrated that reconfigurable, automated modulation of the temporal and spatial profiles of femtosecond laser fields through 2D pulse shaping can be used to perform 2D FT spectroscopy. In contrast to conventional multi-wave mixing setups, multiple delay lines are not required. All the time delays between the non-collinear optical fields are implemented with a 2D pulse shaper [20–22]. The pulse envelope can be delayed with no shift in the optical phases and successive time delay steps can be extremely uniform; both of these are important features for Fourier transform experiments. A key element of the apparatus is its inherent phase stability, arising from common path optics for all the beams. Phase stability of k/67 among all four beams was measured recently over an 8 h period with no enclosure around the setup [22]. Finally, arbitrary waveform generation (i.e., shaping of the phase and amplitude temporal profiles) is enabled for all four fields. This novel design makes the experimental setup compact, easily aligned, robust and versatile. For instance, one
can easily perform the experiments that corresponds to socalled SI (photon echo), SII (virtual echo) and SIII diagrams [23] in a homodyne or heterodyne detected fashion consecutively without any realignment of the setup. There is also no consideration of uneven time delay steps, which is an important issue for Fourier transform experiments. The simplicity of the 2D pulse shaping-based experimental alignment combined with all these advantages suggests this approach for a turn-key, fully coherent multidimensional optical spectrometer that could be used for routine materials characterization and analysis as well as fundamental research. However, the experimental system described earlier had two significant limitations arising from the use of a spatial mask with four holes to isolate the four phase-matched beams from a spatially extended laser field [22]. Most of the light was blocked, resulting in poor throughput, and diffraction from the edges of the holes led to cross-talk between various incident beams and the outgoing signal. In this letter, we describe a new experimental design that overcomes these limitations and also greatly facilitates high-order measurements that involve more than four input beams. Our ‘‘fully coherent multidimensional Fourier transform spectrometer’’ may be easily replicated and may serve as a prototype for a manufacturable instrument. 2. Experimental design Fig. 1 illustrates the multidimensional spectrometer. It is composed of a 2D spatial beam shaper to arrange the BOXCARS geometry, and a 2D spatiotemporal pulse shaper based on a 2D liquid crystal spatial light modulator (LC SLM) to implement the relative time delays and phase shifts as well as any other temporal shaping of the pulses.
Fig. 1. Schematic illustration of the fully phase-coherent spectrometer design. A single beam from an ultrafast laser source is focused onto a diffractive optic (2D Phase Mask ‘‘PM’’) designed to split it into four beams arranged at the corners of a square. This beam arrangement is sent to a 2D spatiotemporal pulse shaper consisting of a diffraction grating (G), a cylindrical lens (CL) and a 2D SLM configured for diffraction-based pulse shaping. The first-order diffracted outputs from the 2D pulse shaper are separated from the input by a beamsplitter (BS) and then focused through a spatial filter (SF) in order to reject the undesired diffraction orders. The filtered output is then focused onto the sample where the nonlinear signal is generated in the phase-matched direction and detected by a monochrometer and CCD camera (not shown).
K. Gundogdu et al. / Chemical Physics 341 (2007) 89–94
2.1. 2D Spatial beam shaper The beam shaper apparatus takes a single beam as input and generates four beams in the BOXCARs geometry to satisfy the phase-matching requirement for heterodyned FWM measurements. The critical element in the beam shaper is a 2D phase mask, PM in Fig. 1. In the present demonstration, we used two diffractive optical elements with a groove spacing of 7.5 lm, attached face to face with the grooves perpendicular to each other. When a beam is focused on the phase mask, four first-order diffracted beams diverge from the focus with equal angles of diffraction with respect to the incident beam. Weak higher-order and zero-order beams are blocked. A lens collimates the four first-order diffracted beams. The beam shaper has a power efficiency of 50%, and the output beams have the same Gaussian spatial profile as the input beam. More generally, a 2D SLM could be used to reconfigurably generate the four beams or more beams for higher-order measurements. 2.2. 2D Spatiotemporal pulse shaper We have described spatiotemporal femtosecond pulse shaping, through which an incident light field is tailored as a function of time and one spatial coordinate (vertical in the present case), in various forms through which it may be executed [21,24,25]. Our present needs are relatively simple since only four independently controlled temporal profiles are needed and the primary characteristics of the profiles that need to be controlled are the pulse delay (changing of the envelope position in time without changing the optical phase) and, when desired, the optical phase. More generally, many independent beams can be shaped and complex temporal profiles may be crafted. For control over both phase and amplitude temporal profiles, we use the spatiotemporal pulse shaper in diffraction mode [21]. The frequency components of an incident beam are dispersed in the horizontal dimension by a diffraction grating and imaged with a lens onto a 2D liquid crystal SLM. Each frequency component encounters a vertical sawtooth grating pattern of phase shifts. The phase and amplitude of the resulting first-order diffraction may be controlled by specifying the spatial phase of the grating pattern (i.e., the positions of the grating ‘‘teeth’’) and the amplitude of the pattern, respectively. The diffracted frequency components are recombined with a second lens and grating, yielding the specified shaped waveform. In this configuration, time delays (within the 12 ps window of our current pulse shaper) are introduced by applying a linear spectral phase variation as a function of frequency, executed through a linear variation of the sawtooth spatial phase as a function of horizontal position. In the current spectrometer configuration, the two orthogonal phase masks are oriented at roughly 25° angles relative to the horizontal and vertical so that the four beams form a square that is tilted at a similar angle. In
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this manner, each of the four beams arrives at a vertically distinct region of the 2D SLM so it can be temporally shaped independently of the others. See Fig. 1. The four first-order diffracted fields are selected by a spatial filter situated at the focal plane of lens L1 and collimated by a second lens, L2. The sample is located at the focal plane of lens L3. We arbitrarily choose one of the beams as the local oscillator (LO) and delay the pulse to positive times so that it transmits through the sample long after the three excitation pulses. The signal that emerges from the sample at the phase-matching direction is spatially overlapped with the local oscillator and is heterodyne detected through spectral interferometry [26]. In this experimental design, once the LO is chosen, one can determine the interaction order of three excitation pulses to perform the experiments corresponding to SI (photon echo), SII (virtual echo) and SIII diagrams without changing the experimental alignment. Flexibly alternating between heterodyne detected transient grating and SIII scans in the conventional design using optical delay lines is not possible because the partners in each pair of time-coincident pulses must be exchanged. In order to reduce spurious interferences of the signal with scattered light (mainly from the SLM or the sample), phase cycling [22] is executed by varying the phases of selected beams by p and subtracting signals, thereby suppressing signals that do not depend on each of the three excitation fields. 3. Experimental demonstration In order to demonstrate the performance of the device, we have measured 2D spectra of GaAs quantum well (QW) structures at 10 K. Li et al. have reported 2D spectra of similar QWs and showed that 2D spectroscopy of these systems is very sensitive to many-body interactions [8]. Our sample consists of 10 periods of 10 nm GaAs QWs separated by 10 nm Al0.3Ga0.7As barriers. The heavy-hole and light-hole excitons absorb at around 806 nm and 802 nm, respectively [8]. We have performed so-called rephasing, SI (photon echo), experiments using 40 fs pulses centered at 812 nm from a Ti: sapphire oscillator with a repetition rate of 92 MHz. The details of the signal generation in rephasing experiments and relevant Feynman pathways can be found in Ref. [27]. In this experiment the signal is emitted in the phase-matched direction ks = k1 + k2 + k3 and the pulse with wave vector k1 interacts with the sample first. We have attenuated the LO by using a 3 mm thick neutral density (ND) filter with an optical density of 2. The ND filter delays the LO by about 3.5 ps. This delay is also useful to avoid undesired signal contributions due to coherent interactions of the LO with the nonlinear polarization prepared in the sample by the three interaction pulses. Each excitation beam has a power of 0.5 mW. We calculated an exciton density of about 1010 excitons per cm2 per quantum well.
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In the rephasing scan the pulses with wave vectors k2 and k3 were coincident, while the pulse with wave vector k1 was scanned so that it precedes the other pulses by a time that is varied in 15 fs step sizes through a total range of 4 ps. It is important to note that in this experiment we are trying to resolve the phase evolution of coherences that are resonantly excited at around 805.5 nm (or 802.2 nm for light holes). The oscillation period of these coherences is about 2.7 fs, far too short to resolve with 15 fs step sizes. However, a direct consequence of delaying the pulse envelopes without changing the phases is that the signal phase evolutions are observed in the rotating wave frame, i.e., the resonance is red shifted by the carrier frequency [28]. We have set the carrier wavelength to 812.4 nm; this corresponds to a frequency of 369 THz. Resonances at 805.5 nm (372.2 THz) and 802.2 nm (373.7 THz) are therefore observed as beat frequencies against the LO at 3.2 THz and 4.7 THz, respectively. These beat frequencies correspond to oscillation periods much larger than 100 fs, easily resolved with a 15 fs step size. 4. Data Fig. 2 shows the data acquired by the CCD camera through spectral interferometry. The total data acquisition time was about 10 min including four-step phase cycling to reduce the noise level. The data are plotted as a function of time delay (x-axis) and frequency (y-axis). The evolution of the phase of the coherences at the heavy hole and light hole during the time between the interaction with the first pulse and non-conjugate pulses can be observed as beat periods along the x-axis. Fig. 3 shows the 2D power spectrum obtained using the spectral interferometry algorithm on the raw data [26]. The contours are plotted as a function of two frequencies; the yaxis represents the frequencies that evolved during the time delay that is scanned between the first and second pulses
374.7
6000
emission frequency [THz]
374.2
4000
373.7 2000 373.2 0 372.7 —2000 372.2 —4000 371.7 371.2 —4
—6000 —3.5
—3
—2.5
—2
—1.5
—1
—0.5
0
tau [ps] Fig. 2. Raw data acquired by the 2D spectrometer. The signal is detected using spectral interferometry. 2D spectra are obtained upon analysis of the raw data by the spectral interferometry algorithm.
Fig. 3. 2D spectral surface of GaAs quantum wells corresponding to S1 (photon echo) diagrams, obtained by analyzing the raw data shown in Fig. 2. The two diagonal peaks are heavy hole and light hole resonances and the off-diagonal peaks appear are due to coupling of heavy-hole and light-hole bands.
and the x-axis is for the emission frequencies. As described earlier, the y-axis frequencies are observed in the rotating wave frame. Therefore, the heavy-hole peak corresponds to 3.2 THz and the light-hole peak to 4.7 THz. We have also shifted the x-axis by the carrier frequency, so that we could label the peaks as diagonal and off-diagonal for convenience. The 2D power spectrum of GaAs QWs exhibits four distinct spectral features. The diagonal peaks are heavy-hole and light-hole exciton resonances, and the off-diagonal peaks indicate the couplings between these states. The heavy-hole and light-hole excitons are coupled through the conduction band [8]. The separation of these spectral features on a two-dimensional surface allows one to discriminate the quantum mechanical pathways that the optically excited coherences evolved through, which is inaccessible information via conventional FWM experiments. One can also use complex Fourier analysis to obtain the real and imaginary 2D spectral surfaces. It is important to note that the features in a real and imaginary 2D spectral surfaces are not purely absorptive or purely dispersive. Ref. [23] describes the experimental analysis procedure to obtain mainly absorptive or dispersive lineshapes in a 2D spectrum. These procedures involve both rephasing (SI) and non-rephasing (SII) experiments. In this communication we only present the 2D surface that corresponds to rephasing diagrams. The results of a comprehensive study will be presented subsequently. Fig. 4a and b show the real and imaginary 2D spectral surfaces obtained via complex Fourier analysis of the raw data. One striking observation is that the diagonal and off-diagonal features in the real 2D spectra are highly dispersive, consistent with earlier measurements of GaAs quantum wells [8] but not usually seen in 2D measurements
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5. Conclusions We have demonstrated a design based on 2D spatiotemporal pulse shaping coupled to a 2D spatial beam shaper that is capable of modulating the phase and amplitude profiles of non-collinear excitation pulses for fully coherent multi-wave mixing spectroscopy. This design has the potential to empower researchers from many different backgrounds to harness the capabilities of 2D FT spectroscopy, for applications ranging from small molecules to biological systems to semiconductors. The approach demonstrated here can be extended to the measurement of higher dimensional spectra in resonant and non-resonant experiments through the use of different phase mask patterns or, more generally, an SLM for the 2D spatial shaping to produce more than four beams in a phase-matched geometry when necessary. The approach also will be applicable to multidimensional coherent spectroscopy in different regions of the electromagnetic spectrum. Acknowledgements The authors acknowledge S. Cundiff for the quantum well sample. This work was supported in part by National Science Foundation Grant CHE-0616939. D. Turner thanks the NDSEG Fellowship Program for financial support. References
Fig. 4. (a) Real and (b) imaginary 2D spectral surfaces.
of dilute systems [23]. Li et al. showed through simulations using the optical Bloch equations that the dispersive character is mainly due to excitation induced shifts of the exciton energy, as opposed to excitation induced exciton dephasing. The clear indication of many-body interactions and the further sensitivity to particular interaction mechanisms illustrates the value of 2D FT spectroscopy compared to conventional FWM techniques. The present demonstration illustrates that the fully coherent multidimensional spectrometer introduced in this paper is capable of producing the 2D FT experimental results similar to those obtained via conventional methods using optical delay lines. The new approach also makes new classes of measurements possible. Although we have only demonstrated the rephasing measurement, non-rephasing and SIII measurements are conducted as easily. In addition, full phase coherence among all the beams enables new capabilities like 3D FT spectroscopy and observation of higher coherences, which will be reported shortly.
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