Abstract
We report on the design and performance of a time-resolved Coherent Raman spectroscopy system with time resolution of better than 120 fs. The coherent transients can be traced with more than 75 dB dynamic range while accessing and probing Raman active modes across a 250–2400 cm−1 frequency. The system delivers an equivalent spectral resolution of better than 0.1 cm−1 regarding line bandwidth parameters for probed Raman resonances.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Raman spectroscopy is among the most powerful tools and techniques in spectroscopy with important applications ranging from semiconductor nanostructures to biological cells and tissues [1,2]. This is primarily due to its selectivity down to a chemical bond level so that important physical mechanisms and fundamental interactions in condensed matter can be revealed. With the advent of pulsed lasers, coherent Raman spectroscopy methods gained a prominent role with further breakthroughs in understanding interactions in condensed matter and atomic-molecular media [3]. Early efforts in developing time-resolved coherent spectroscopy systems relied on low repetition rate solid-state oscillators and amplifiers that provided a few picoseconds [4–6] or even sub-picosecond time resolution for specially designed laser sources [7,8]. The coherent Raman signals have been traced with picosecond time resolution within 20–40 dB using systems delivering up to milli-Joule energy scale wide pulses at 1–50 Hz repetition rates [3–8]. The advent of broadband laser gain media, like the TiAl2O3 (Ti:S) crystal [9], laid a new foundation in developing spectroscopic systems for condensed matter spectroscopy with ultrafast (∼100 fs) time resolution. One approach is based on femtosecond optical parametric amplifiers (OPA) [10–15], driven by kHz repetition rate amplified Ti:S laser systems, to create separate two- or three-color pulses needed for time-resolved coherent spectroscopy. When it comes to high-repetition rate (tens of MHz) Ti:S laser-based systems, CARS spectroscopy and microscopy with picosecond/femtosecond time resolution rely on the generation of an ultra-broadband continuum in photonic crystal fibers [16–19]. Alternatively, mode-locked 40 MHz repetition rate fiber lasers and subsequent soliton frequency shifts have been used for CARS microscopy with wide tuning range [20,21]. The tailored pulses from the Ti:S/OPA system have been used to trace the decay of the optical phonons within 15–20 dB in semiconductor quantum dots and to resolve fast (∼100 fs) oscillations due to possible beating of the longitudinal optical (LO) phonon mode with its overtone [10]. The OPA system driven by Ti:S kHz amplifier produced three-color 80 fs micro-Joule level pulses and have been used for biological imaging applications [11]. Time-resolved CARS with two-color 100 fs pulses, delivered by a 1kHz repetition rate system, have been shown to be efficient in high resolution spectroscopic studies in molecular gases and thermometry [14]. The Ti:S/OPA system, at a much higher repetition rate of 250 kHz, has been used in demonstrating time-resolved resonant CARS in benzaldehyde and micron size polystyrene beads (1636 cm−1 mode) with 27–36 dB dynamic range using sub-µJ energy pulses in the near-infrared (720–920 nm) [12]. In general, amplified Ti:S laser driven OPA systems for time-resolved CARS can provide superior, down to 40 fs [15], temporal resolution. However, they lack sensitivity and the signal detection range is limited to 25–30 dB. Multi-MHz systems rely on high average power mode-locked oscillators. Time-resolved CARS with 30 dB dynamic range and about 500 fs time resolution have been demonstrated with photonic crystal fiber continuum source driven by high-power femtosecond Ti:S oscillator running at 80 MHz [18,22]. Excellent temporal resolution (∼20 fs) has been achieved with shaped and compressed super-continuum pulses, driven by a high-repetition rate Ti:S oscillator, in time-resolved single beam two-color CARS [16]. Special pulse shaping that induces equal chirp on two-color pulses has been demonstrated for femtosecond CARS to achieve better than 20 cm−1 spectral resolution [17]. The high-repetition rate picosecond OPO based systems showed impressive results in microscopy with increased sensitivity due to phase control [23,24].
In this paper we present the design and performance of a time-resolved CARS system that shows better than 120 fs time resolution and dynamic range for signal detection of nearly 80 dB. The system’s design and wavelength tuning range allow tracing vibrations and phonon modes in condensed matter with Raman frequencies within a 250–2450 cm−1 range. The extended dynamic range allowed to achieve better than few percent precision in measuring the phonon decay time constants which in turn yields in better than 0.1 cm−1 equivalent spectral resolution for the corresponding linewidths of the Raman active lattice vibrations.
2. Experimental
The system described in this work is based on simultaneous pumping of two independently tunable optical parametric oscillators (OPOs) that deliver well-synchronized different colors. Key blocks and elements of the experimental set up are shown in Fig. 1(a). The output power of a mode-locked Ti:S oscillator (Coherent Mira HP) at 814 nm is split into three parts. The main part of the beam is split in turn into two, with ∼1W average power in each part, to pump the OPOs that deliver tunable fs pulses at ω1,w2 optical frequencies needed for CARS. Improvements and modifications to the OPO designs have been introduced as compared to the previously reported broadly tunable sources [25,26]. Briefly, one of the OPOs utilizes MgO-doped periodically poled lithium niobate (PPLN) crystal as a gain material for quasi-phase-matched (QPM) operation at a poling period (Λ) of 21.6 µm. In addition, certain measures with the OPO design and operational conditions such as pump power level control, beam spot size in the crystal, output coupler reflectivity (R = 65–75%), amount of intracavity dispersion compensation, and precise PZT cavity length control have been introduced. These are key to producing well shaped Gaussian pulses that are close to transform limited at a central wavelength within 1008–1017 nm. The pulse cross-correlation with the Ti:S oscillator replica shows no detectable satellites within a 60–70 dB span off the main peak. The OPO’s average power is around 350 mW. The second OPO (Fig. 1(b)) utilizes periodically poled stoichiometric lithium tantalate (PPSLT) gain material with a custom fan-out-grating (FOG) design for its quasi-phase-matching (QPM) period sections. The period continuously changes (Λ=22.4–23.3 µm) along the crystal’s height. The third fraction (∼150 mW) of the Ti:S oscillator output serves as the probe pulse beam at ω3 optical frequency. Choice of the PPSLT gain medium with fan-out-grating QPM grating period pattern is advantageous compared to periodically poled lithium niobate (PPLN) material with magnesium oxide doping. Namely, it shows a higher threshold for the photorefractive damage and favorable wavelength-tuning curve (see inset of Fig. 1(b)). This helps to achieve a continuous tuning within the near-infrared wavelengths’ range needed to drive Raman active vibrations in condensed matter.
Possible two-wavelength operation (hysteresis) at a set QPM period was avoided by the Lyot filter rotation and fine scale cavity length adjustment using PZT.
A set of data showing characteristic OPO output spectra is presented in Fig. 2(a) with the OPO output parameters, such us power and bandwidths, stated in the captions. The spectra show that the difference for two optical frequencies, ω1−ω2, covers the 250–2450 cm−1 Raman frequency span. The detected CARS signal wavelengths (λas) are thus within a 678–797 nm range. The three pulses initially travel through separate paths that are designed to adjust linear chirp, beam size, temporal delay, and the vector field polarizations. The beams are combined at dichroic mirrors DM1 and DM2. The pulse wavelengths and shapes of the spectra are detected and controlled with the OSA. The beams are focused with an objective lens (NA = 1.2) to generate a CARS signal in different materials. The incident beam powers have been kept at about 100–150 mW for each beam at the sample position.
Time-delayed CARS was achieved by controlling the probe pulse delay in the Ti:S beam path at the corner cube. The signal is guided to the grating monochromator after passing through a condenser, attenuator, and lens trail. A band-pass filter was used to eliminate or substantially reduce the residual probe beam (at 814 nm). The Glan-Thompson prism polarizer was introduced for various polarization sensitive experiments. The signal at anti-Stokes wavelength passed through the monochromator and was detected by a cooled CCD. The CCD chip (2048 × 70 pixel area) delivers excellent sensitivity with about 8–12 electron counts (rms) noise level (ND) measured for 100 ms integration time. A 200 kHz 16-bit analog-to-digital converter digitizes the CCD’s charge/voltage signal and the CCD signal saturation level is about ∼65000 counts. For detection of strong light, we exploited a set of calibrated neutral density filters to attenuate the light input into the monochromator. The control and data acquisition program is used to record various data such as the time-dependent CARS signal and spectra at anti-Stokes wavelength. Spectrally selective acquisition is done by adjusting settings for the CCD detector areas. CARS signal beam loss within the detection optics trail, starting with the condenser lens, was estimated using a white light source and resulted in ηT =15–25% light transmission to the detector, depending on the wavelength. Successful spatial and temporal overlap was finely adjusted and optimized by observing the CARS signal spectra using the data acquisition programs. We assign the corresponding optical frequencies ω1, w2, w3 (or wavelengths λ1, l2, l3) for the OPO1, OPO2, and probe beam fields E1(t), E2(t), and E3(t). Those serve as the driving and delayed probe pulses in the time-resolved CARS process. The process is driven by a third order polarization,
The dotted trace represents spontaneous Raman data taken in the potassium titanyl phosphate (KTP) crystal. The data clearly shows that at least two Raman resonances are well within the excitation envelope created by the ultrashort pulses with the characteristic bandwidths.
CARS signal magnitude and the potential dynamic range in tracing the signal in time for our experimental conditions can be provided by solving the wave-equation for Eas. The field is driven by the nonlinear polarization provided by formula (1). Assuming Gaussian pulse shape and spatial beam profiles we derive that the pulse energy (ξas) at the anti-Stokes frequency, in the case of perfect phase-matching, can be given by the following expression:
In the formula, the focused beam spot size (w0) and pulsewidths (tp) are assumed to be uniform for all three beams and pulses; n1,2,3,as are the linear refractive indices, ξ1,2,3 are incident pulse energies, and L is the sample thickness. We must note that the phase-matching condition is automatically fulfilled for thin samples (L<<1/[kas-((k1-k2)+k3)] and for sample thicknesses less than the laser wavelength the CARS signal increases nonlinearly with the reciprocal spot size. Details of the derivation that resulted in formula (2) and other information are provided in the Supplement 1. The CCD detector signal can be straightforwardly estimated for a known laser pulse repetition rate (ν=76 MHz), detector quantum efficiency (ηD = 0.5), optical loss/transmission coefficient for the anti-Stokes signal (ηT = 0.2), and the detector’s integration time (tint = 100 ms) using the following expression:
We assume incident beam power of ∼125 mW for each beam, pulsewidth of ∼150 fs, estimated interaction volume created by a high numerical aperture objective lens [28] yielding in a spot-size of w0∼210 nm and on-axis interaction length of L = 1.1 µm. We also assume that the third order nonlinearity characteristic value for condensed matter is χ(3)∼4×10−23 m2/V2 [29]. Then formula (2) yields in the pulse energy of ∼5.1 fJ at the anti-Stokes frequency which is ∼1.4 × 1010 CCD detector counts for 100 ms integration time. Provided that attenuation for the signal at maximum levels is introduced to avoid the CCD detector saturation, the attainable dynamic range in CARS signal tracing can be as high as 10log10(S/ND) ∼ 90–95 dB. In addition to the intrinsic CCD readout noise, signals of different origins will contribute to the overall noise level (NΣ) that may significantly affect the attainable dynamic range. The light signals in the vicinity of the anti-Stokes wavelengths are primarily broad band amplified spontaneous emission (ASE) from Ti:S laser source, spectral broadening of the interacting pulsed fields due to strong self-phase modulation and frequency shift in the foci, and second order nonlinear processes at interfaces, such as second harmonic and sum-frequency generation.
3. Results and discussions
To explore and determine experimentally maximum signal levels, attainable dynamic ranges in tracing CARS signals, and time resolution in measuring ultrafast decay processes, we have carried out experiments in different media and at different conditions. Figure 3(a) shows CARS transients when OPO1,2 central wavelengths are tuned such that potential Raman bands at ∼1265 cm−1 in BaSnO3 (BSO) and ∼360 cm−1 in KTP crystals can be excited and probed. Considering the light signal attenuation that was used to detect strong light at the corresponding anti-Stokes wavelength we can generate CARS signals as high as 0.7–1.6 × 109 in CCD counts. The detected signal maximum is about one order of magnitude lower than the theoretical estimates provided above. We believe that matching pulsewidths and spotsizes for the three incident light sources are primary issues that need to be solved in order to generate stronger CARS signals that are closer to the estimate. The experimental signal plot for BSO crystal is shown in blue circles and it demonstrates high dynamic range of about 77 dB. Our background noise signal (NΣ) did not exceed 25–35 counts, which is only a factor of three above the CCD detector’s sensitivity level (ND). The experimental CARS transient obtained from a measurement that targeted possible bands in microscope slide glass at ∼360 cm−1 is shown in red circles. The trace has been artificially shifted on time and intensity scale for better viewing and comparison with the transient in BSO. Both measurements show primarily resolution limited signal decay over decades in signal decay. The black lines show simulated time-resolved CARS signal when using a model that will be discussed further below. Comparisons of the experimental and theoretical curves show that a time resolution of better than 120 fs can be achieved for the signals that are traced within multiple decades for the different conditions outlined above. A noticeably lower dynamic range (∼57 dB) has been observed for the case of CARS that targeted lower energy frequencies in glass material compared to the case of BSO material. The difference is primarily due to a much higher background signal (NΣ ∼700–800 counts) detected for the case of the lower frequency targeting. Indeed, the background was not dependent on OPO1,2 pulse action and persisted at much longer time delays. The background is primarily due to the Ti:S laser ASE output and other processes that have been mentioned above. The strong contribution cannot be eliminated in principle since the anti-Stokes wavelength of 791 nm is only about 23 nm shifted from the delayed probe beam’s wavelength. Resolution limited response indicates that CARS signals are primarily due to the non-resonant contribution to the optical nonlinearity since there are no Raman active bands within at the particular excitation conditions in glass and BSO crystal material. Indeed, the spontaneous Raman data do not show optical phonon contributions in the vicinity of targeted frequencies for the samples. For BSO crystal, however, the CARS data show faint resonant features that are resolved by tracing CARS spectra at different time delays.
The ∼1400 cm−1 phonon mode that exists in BSO Raman spectra is still weakly excited by the high frequency component of the broadband pulse spectra within its shoulder part of our E1,2(t) pulses. Figure 3(b) shows significant spectral shift of the CARS signal maximum at ∼700 fs delay time. The non-resonant signal (blue line) has decayed substantially at the delay time of 700 fs and the remaining weak signal (red line) is getting clearly detected at ∼730 nm.
As we have mentioned above, the CARS process can be considered as a scattering of the probe pulse (E3(t)) on the coherent excitation in a material created by the first two pulses (E1(t), E2(t)). In this approach, for time-resolved measurements, excitation and probing processes are separated in time by a delay (td) and the time-dependent nonlinear polarization can be expressed with the help of the coherent amplitude (Q) created in the material:
In the equation above, the coupling constant between the material excitation (Q) and the probe field E3(t) is the Raman scattering tensor component. The rate equations for Q(t) are presented and solved for several different cases in Ref. [27]. Obviously, for td = 0 the above expression should result in Eq. (1) and the relationship between the Raman tensor components and the resonant part of χ(3) can be straightforwardly established. In a simple case of phonon decay with a characteristic time constant T2 we arrive at the following solution for the anti-Stokes pulse energy at time delay td:
In the equations above, Smax - detector counts at zero delay that can be calculated using formula (2) and (3), H(t) is Heaviside’s step function, g(t) is a Gaussian time-dependent envelope of the pulsed electric field with pulsewidth tp. By measuring T2 one can arrive at the homogeneously broadened Raman linewidth (Δν) using a simple relationship such as Δν=1/πcT2 [27].
The effect of the broadband excitation, for which more than one Raman active band can contribute to the time-resolved CARS signal, is well illustrated by data in Fig. 4. The OPO1,2 wavelengths for this case are tuned to produce broadband coherence in KTP crystal, centered at 692 cm−1, that is similar in shape and bandwidth to the one shown by the red curve in Fig. 2(b). The broad spectral envelope covers three Raman active lines characteristic for the crystal though favoring resonant excitation for the phonon mode at ∼640 cm−1. Time-domain CARS data shown in Fig. 4(a) indicates that at least two Raman resonances can make a pronounced contribution. Spectra for CARS signal at different delay times are shown in Fig. 4(b,c). The CARS transient, shown in Fig. 4(a), has been measured as an integrated value across the entire 30 nm wide spectral window for the anti-Stokes signal centered at ∼771 nm. There are clear fast and slow decaying contributions that have distinctly different decay times of about 420 fs and 1.67 ps. The two components are also clearly resolved in CARS spectra detected for different time delays (td) as shown in Fig. 4(b,c). CARS spectra at short delay times (<700 fs) have maxima at the anti-Stokes wavelengths around 772 nm, corresponding to the signal from the 637 cm−1 energy phonon, one of the main vibrations within Ti-O octahedron in KTP [30,31]. At longer delays (∼1200 fs) the characteristic double line in the CARS spectra can be detected with peak positions at 772 nm and 759 nm. The latter corresponds to the KTP optical phonon vibration at ∼830 cm−1. The peak at 772 nm vanishes as the time delay increases while the peak at 759 nm can be still detected for delay times beyond few picoseconds. We have performed time-resolved CARS measurements while detecting the signal within the wavelength segments shown in Fig. 4(c) by two pairs of dashed vertical lines. The corresponding CARS transients are shown in Fig. 5(a,b). The CARS transients, that correspond to detection of the spectrally separated contributions, can be well fitted with the single exponential decay functions with T2 - times of ∼420 fs and ∼1.68 ps. These times correspond to the 640 cm−1 and ∼830 cm−1 lattice vibrations with the corresponding bandwidths (Δν) of 24.4 cm−1 and 6.1 cm−1.
An efficient overtone decay channel, with high density of states for the phonons of lower energy, explains much faster decay of the lower energy phonon.
Time-resolved CARS signals when one of the lowest and highest energy phonon modes in KTP crystal are excited and probed are presented in Fig. 6. The best fits to the experimental results allowed us to conclude that the phonon decay times are 1.72 ± 0.04 ps and 1.18 ± 0.02 ps for the crystal phonon modes frequencies of 420 cm−1 and 1650 cm−1 correspondingly. The phonon decay times to bandwidths conversion, using the formula stated previously, yields 6.2 ± 0.18 cm−1 and 8.9 ± 0.1 cm−1 correspondingly. The results show that we can obtain precise information on Raman line bandwidths across the entire spectrum of vibrations in condensed matter. Opposite to the case discussed above (Fig. 5) the higher frequency mode decays faster here. This again is explained by the fact that decay channels for the low frequency mode at ∼420 cm−1 are less efficient since there are no lower energy optical phonons that will result in momentum conservation and have high enough density of states at the same time. Thus, more complex multistep decay processes that involve acoustic phonons are the only channels for the lattice energy dissipation and those lead to the longer decay times observed in the experiment.
Results of tracing two different phonon vibrations in BSO crystal are presented in Fig. 7. In this case, we focused our attention on crystal vibrations at around ∼1600 cm−1 and at about half of that energy. Clearly, this is a situation when both higher and lower energy vibrations have a direct route to decay into two half-energy optical phonons. It is of interest to compare efficiencies of the decay channels of the similar nature. We note again that a high dynamic range (∼72 dB) in tracing the CARS signals and low signal to noise ratio allow us to obtain phonon decay times with an excellent precision. The data allows using an algorithm that has been demonstrated in our earlier paper [32] for obtaining line shapes from the time-domain data. We arrive at perfect Lorentzian line shapes with the bandwidths of 8.2 ± 0.1 cm−1 and 7.5 ± 0.08 cm−1 for the optical phonon lines at 805 cm−1 and 1610 cm−1 correspondingly. Thus, the expectation of the similar decay rates has been confirmed.
4. Conclusion
In conclusion, we have presented a time-resolved coherent Raman spectroscopy system design approach and demonstrated its performance in a variety of experimental conditions that are of interest and importance in spectroscopy of condensed matter. The system is based on broadly tunable optical parametric oscillators in the near infrared. The design allows selecting and tracing Raman active vibrations across the entire vibrational spectrum (250–2400 cm−1) in condensed matter. Time decay for the vibrations have been traced with better than 120 fs resolution and an unprecedented dynamic range that is close eight decades. By tracing the time decay of the vibrations within a 60–80 dB dynamic range, we showed that the important information on crystal vibration damping rates and the corresponding Raman linewidths can be obtained with excellent precision. The achieved equivalent spectral resolution of better than 0.1 cm−1 is an order of magnitude better than current commercially available spontaneous Raman spectroscopy systems.
Funding
Air Force Office of Scientific Research (FA9550-18-1-0273).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. M. Cardona and R. Merlin, Light Scattering in Solids IX: Novel Materials and Techniques, Topics in Applied Physics (Springer Berlin Heidelberg, 2006).
2. A. Kunstar, A. M. Leferink, P. I. Okagbare, M. D. Morris, B. J. Roessler, C. Otto, M. Karperien, C. A. van Blitterswijk, L. Moroni, and A. A. van Apeldoorn, “Label-free Raman monitoring of extracellular matrix formation in three-dimensional polymeric scaffolds,” J. R. Soc. Interface. 10(86), 20130464 (2013). [CrossRef]
3. A. Laubereau and W. Kaiser, “Coherent Picosecond Interactions,” in Coherent Nonlinear Optics: Recent Advances, M. S. Feld and V. S. Letokhov, eds. (Springer Berlin Heidelberg, 1980), pp. 271–292.
4. D. von der Linde, A. Laubereau, and W. Kaiser, “Molecular vibrations in liquids: Direct measurement of the molecular dephasing time; determination of the shape of picosecond light pulses,” Phys. Rev. Lett. 26(16), 954–957 (1971). [CrossRef]
5. F. Vallée and C. Flytzanis, “Temporal and spatial evolution of picosecond phonon-polariton pulses in crystals,” Phys. Rev. B 46(21), 13799–13812 (1992). [CrossRef]
6. S. A. Akhmanov, N. I. Koroteev, S. A. Magnitskii, V. B. Morozov, A. P. Tarasevich, and V. G. Tunkin, “Time-domain coherent active Raman spectroscopy of a free-nitrogen jet,” J. Opt. Soc. Am. B 2(4), 640–648 (1985). [CrossRef]
7. S. Hogiu, W. Werncke, M. Pfeiffer, A. Lau, and T. Steinke, “Picosecond time-resolved CARS spectroscopy of a mixed excited singlet state of diphenylhexatriene,” Chem. Phys. Lett. 287(1-2), 8–16 (1998). [CrossRef]
8. P. Heinz, W. Kriegleder, and A. Laubereau, “Feedback control of an actively-passively mode-locked Nd:Glass laser,” Appl. Phys. A 43(3), 209–212 (1987). [CrossRef]
9. P. F. Moulton, “Spectroscopic and laser characteristics of Ti:Al2O3,” J. Opt. Soc. Am. B 3(1), 125–133 (1986). [CrossRef]
10. P. Waltner, A. Materny, and W. Kiefer, “Phonon relaxation in CdSSe semiconductor quantum dots studied by femtosecond time-resolved coherent anti-Stokes Raman scattering,” J. Appl. Phys. 88(9), 5268–5271 (2000). [CrossRef]
11. A. Zumbusch, G. R. Holtom, and X. S. Xie, “Three-dimensional vibrational imaging by coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 82(20), 4142–4145 (1999). [CrossRef]
12. A. Volkmer, L. D. Book, and X. S. Xie, “Time-resolved coherent anti-Stokes Raman scattering microscopy: Imaging based on Raman free induction decay,” Appl. Phys. Lett. 80(9), 1505–1507 (2002). [CrossRef]
13. H. Tran, F. Chaussard, N. le Cong, B. Lavorel, O. Faucher, and P. Joubert, “Femtosecond time resolved coherent anti-Stokes Raman spectroscopy of H2 - N2 mixtures in the Dicke regime: Experiments and modeling of velocity effects,” J. Chem. Phys. 131(17), 174310 (2009). [CrossRef]
14. T. Lang, M. Motzkus, and H. M. Frey, “High resolution femtosecond coherent anti-Stokes Raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys. 115(12), 5418–5426 (2001). [CrossRef]
15. M. M. Kazemi, M. Namboodiri, P. Donfack, A. Materny, D. Kerlé, B. Rathke, and J. Kiefer, “Influence of the alkyl side-chain length on the ultrafast vibrational dynamics of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide (CnmimNTf2) ionic liquids,” Phys. Chem. Chem. Phys. 19(24), 15988–15995 (2017). [CrossRef]
16. B. von Vacano and M. Motzkus, “Time-resolved two color single-beam CARS employing supercontinuum and femtosecond pulse shaping,” Opt. Comm. 264(2), 488–493 (2006). [CrossRef]
17. N. Muller, L. Bruckner, and M. Motzkus, “Invited Article: Coherent Raman and mid-IR microscopy using shaped pulses in a single-beam setup,” APL Photonics 3(9), 092406 (2018). [CrossRef]
18. T. W. Kee and M. T. Cicerone, “Simple approach to one-laser, broadband coherent anti-Stokes Raman scattering microscopy,” Opt. Lett. 29(23), 2701 (2004). [CrossRef]
19. G. I. Petrov and V. V. Yakovlev, “Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy,” Opt. Express 13(4), 1299 (2005). [CrossRef]
20. O. Burkacky, A. Zumbusch, C. Brackmann, and A. Enejder, “Dual-pump coherent anti-Stokes-Raman scattering microscopy,” Opt. Lett. 31(24), 3656 (2006). [CrossRef]
21. G. Krauss, T. Hanke, A. Sell, D. Träutlein, A. Leitenstorfer, R. Selm, M. Winterhalder, and A. Zumbusch, “Compact coherent anti-Stokes Raman scattering microscope based on a picosecond two-color Er:fiber laser system,” Opt. Lett. 34(18), 2847–2849 (2009). [CrossRef]
22. Y. J. Lee, S. H. Parekh, J. A. Fagan, and M. T. Cicerone, “Phonon dephasing and population decay dynamics of the G-band of semiconducting single-wall carbon nanotubes,” Phys. Rev. B 82(16), 165432 (2010). [CrossRef]
23. M. Jurna, J. P. Korterik, C. Otto, J. L. Herek, and H. L. Offerhaus, “Vibrational phase contrast microscopy by use of coherent anti-stokes Raman scattering,” Phys. Rev. Lett. 103(4), 043905 (2009). [CrossRef]
24. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006). [CrossRef]
25. K. V. Bhupathiraju, A. D. Seymour, and F. Ganikhanov, “Femtosecond optical parametric oscillator based on periodically poled stoichiometric LiTaO3 crystal,” Opt. Lett. 34(14), 2093–2095 (2009). [CrossRef]
26. J. D. Rowley, S. Yang, and F. Ganikhanov, “Power and tuning characteristics of a broadly tunable femtosecond optical parametric oscillator based on periodically poled stoichiometric lithium tantalate,” J. Opt. Soc. Am. B 28(5), 1026–1036 (2011). [CrossRef]
27. A. Laubereau and W. Kaiser, “Vibrational dynamics of liquids and solids investigated by picosecond light pulses,” Rev. Mod. Phys. 50(3), 607–665 (1978). [CrossRef]
28. L. Moreaux, O. Sandre, and J. Mertz, “Membrane imaging by second-harmonic generation microscopy,” J. Opt. Soc. Am. B 17(10), 1685–1694 (2000). [CrossRef]
29. R. W. Boyd, “Order-of-magnitude estimates of the nonlinear optical susceptibility,” J. Mod. Opt. 46(3), 367–378 (1999). [CrossRef]
30. G. H. Watson, “Polarized Raman spectra of KTiOAsO4 and isomorphic nonlinear-optical crystals,” J. Raman Spectrosc. 22(11), 705–713 (1991). [CrossRef]
31. R.Z. Shneck, U. Argaman, and Z. Burshtein, “Anomalous LO-TO splitting observed by combined IR reflectance and Raman scattering in KTiOPO4 (KTP) single crystal,” Vibrational Spectroscopy, (to be published) (2022).
32. S. Yang and F. Ganikhanov, “Dispersion of the resonant nonlinear optical susceptibility obtained with femtosecond time-domain coherent anti-Stokes Raman scattering,” Opt. Lett. 38(22), 4754–4757 (2013). [CrossRef]