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Femtosecond coherent Raman system with >75 dB dynamic range for probing vibration modes across 250-2400 cm−1

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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 [46] 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 [38]. 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) [1015], 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 [1619]. 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.

 figure: Fig. 1.

Fig. 1. (a). TiS - Coherent Mira (model 900-F) femtosecond TiAl2O3 laser, OPO1 and OPO2 – synchronously pumped femtosecond optical parametric oscillators. λ/2 – half-wave plate, DM1,2 – dichroic mirrors, DM1,2 – dichroic mirrors, CC - corner cube, OSA – optical spectrum analyzer, CCD – charge coupled device detector array, OBJ – objective lens (NA = 1.2), S-sample, CND – condenser lens, ATT – light intensity attenuator, BPF – band pass filter, GTP – Glan-Thompson prism polarizer, MONO – diffraction grating monochromator. (b). Broadly tunable OPO based on PPSLT crystal with variable QPM-period (Λ=22.3–23.4µm). LF-Lyot filter, PZT-computer controlled piezo-electric transducer, OC – output coupler. The inset shows the theoretical (blue line) wavelength-tuning curve for the resonating signal wave (λs) for different QPM periods and experimentally detected central wavelengths (black circles).

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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.

 figure: Fig. 2.

Fig. 2. (a). OPO1,2 output spectra taken with the OSA (Anritsu model MS9710C). OPO1 central wavelength (λ1) is normally set within 1008–1017 nm. OPO2 is widely tunable within 1030–1350 nm range. The OPOs central wavelengths can be maintained within ±1.5 nm while the pulse bandwidths are kept below 130 cm−1 across the tuning range. 2(b). Spectrum of the coherent amplitude Q (red line) for the input pulsed fields (E1, E2) at two optical carrier frequencies 1 and ω2). The corresponding OPO1 and OPO2 pulse intensity spectra are shown in the inset in blue (OPO1) and red (OPO2) lines. The two fields produce the broadband (∼170 cm−1) coherent excitation that can be calculated using the convolution integral. The data shown in black dots correspond to spontaneous Raman scattering spectra for KTP crystal in the vicinity of ∼400–1000 cm−1.

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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,

$$P_{as}^{(3)} = 6{\varepsilon _0}{\chi ^{(3)}}({\omega _{as}},{\omega _1} - {\omega _2},{\omega _3}){E_{10}}{E_{20}}{E_{30}}{e^{i[{({\omega_1} - {\omega_2} + {\omega_3})t - ({k_1} - {k_2} + {k_3})z} ]}} + c.c.$$
where third order optical nonlinearity (χ(3)) is a material constant. The detected wave is at the anti-Stokes frequency (ωas = ω123) with the corresponding field amplitude Eas. The CARS process can be considered as scattering of the probe pulse (E3(t)) on the coherent excitation in a material created by the first two (E1(t), E2(t)) in the vicinity of Raman resonances. For the case of ultrashort pulses with broad spectra the material excitation at the difference frequency ω1−ω2 is given by a double convolution integral that is applied to the first two broadband fields in the spectral domain. The excitation results in a coherent amplitude (Q(ω1−ω2)) [27] that is an ensemble average of the atomic displacements within the volume of interaction and decays freely after the action of the excitation pulses. Figure 2(b) shows how broadband the excitation can be in our case. The data shows an absolute value of the coherent amplitude (red line) in frequency domain that is as broad as ∼170 cm−1 when the two pulses with bandwidths of ∼95–120 cm−1 (see inset) are used to coherently drive vibrations at around 820 cm−1.

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:

$${\xi _{as}} = \frac{{48\ln 2}}{{\sqrt 3 \pi {c^2}\varepsilon _0^2}}\frac{{{{|{{\chi^{(3)}}} |}^2}}}{{{n_1}{n_2}{n_3}{n_{as}}}}{\xi _1}{\xi _2}{\xi _3}\frac{{{L^2}}}{{\lambda _{as}^2w_0^4t_p^2}}$$

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:

$${S_{\max }} = \frac{{{\lambda _{as}}\nu {\xi _{as}}}}{{2\pi c\hbar }}{\eta _D}{\eta _T}{t_{{\mathop{\rm int}} }}$$

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.

 figure: Fig. 3.

Fig. 3. (a) Time-resolved CARS signal (transients) obtained from BSO crystal (blue circles) and silica glass (red circles). OPO1,2 have been tuned to 1014 nm and 1158 nm for the measurement in BSO and 1011 nm and 1049 nm for glass experiment to create coherent excitations centered at about 1265 cm−1 and 360 cm−1 correspondingly. The measurement in BSO demonstrates 77 dB dynamic range in detecting CARS signal versus time delay. The dotted and dash dotted lines represent simulations for the CARS transients assuming ultrafast electronic nonlinearity relaxation time (<10 fs) and 120 fs correspondingly. (b) CARS spectra at different delay times for the measurement in BSO. The broadband OPO1,2 fields produce coherence that stretch to ∼1400 cm−1.

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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:

$$P_{as}^{(3)}(t - {t_d}) = N\frac{{\partial \alpha }}{{\partial q}}\frac{i}{2}Q(z,t){E_{30}}(t - {t_d}){e^{i[{({\omega_1} - {\omega_2} + {\omega_3})t - ({k_1} - {k_2} + {k_3})z} ]}}{e^{ - i{\omega _3}{t_d}}}$$

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:

$$S({t_d}) = 2{S_{\max }}{\left|{\frac{{2\ln 2}}{{t_p^2}}\int\limits_{ - \infty }^\infty {g(t^{\prime} - {t_d})\left[ {\int\limits_{ - {t_0}}^\infty {{e^{ - \frac{{(t^{\prime} - \vartheta )}}{{{T_2}}}}}{g^2}(\theta )H(t^{\prime} - \theta )d\theta } } \right]dt^{\prime}} } \right|^2}$$

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.

 figure: Fig. 4.

Fig. 4. Time-domain CARS signal measured in KTP crystal. The OPO1,2 wavelengths have been set to 1013 nm and 1089 nm to create broadband coherence centered at ω1−ω2∼692 cm−1. The time-domain CARS signal has been integrated within the spectral window of ∼30 nm centered at 772 nm. The initial part decays with a constant of 420 fs while the decay at longer delays slows down significantly with a characteristic time constant of 1.68 ps. (b,c) CARS spectra for the sample taken at different delay times. The dashed vertical lines indicate the spectral windows the CARS transients have been traced within.

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 figure: Fig. 5.

Fig. 5. CARS transient obtained from KTP crystal when Raman active vibrations in the vicinity of 692 cm−1 are targeted. (a) Data shown in blue circles represent CARS signal decay for the case of spectrally selective acquisition within 767–777 nm range for the anti-Stokes wavelength. The spectral segment corresponds to probing the Raman active vibration at ∼630 cm−1. (b) Red circles represent CARS signal decay for the case of spectrally selective acquisition that corresponds to probing the Raman active vibration at ∼830 cm−1. The dashed lines represent simulated curves for the CARS signals.

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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.

 figure: Fig. 6.

Fig. 6. CARS transient (blue and red circles) obtained from KTP crystal when Raman active vibrations in the vicinity of ∼400 cm−1 (red) and ∼1600 cm−1 (blue) are targeted. The black dotted dashed line represents theoretical fit for the signal assuming single channel phonon decay with the decay time of T2 = 1.18 ± 0.02 ps. The data in red circles represent the CARS transient obtained from the crystal when targeting the ∼377 cm−11 vibration) phonon mode. The black dashed line represents the theoretical fit for the isolated line with the decay time of T2 = 1.72 ps.

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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.

 figure: Fig. 7.

Fig. 7. CARS transient (blue circles) obtained from BSO crystal by targeting crystal vibration in the vicinity of ∼800 cm−1. The black dotted dashed line represents the theoretical fit assuming single exponential decay at longer delay times with the T2 time of 1.29 ps. The red-circled data represent the time-domain CARS signal obtained from the crystal while targeting phonon vibration at around 1600 cm−1. The black dashed line represents a simulation for the CARS signal with single exponential decay for the phonon mode with T2 = 1.42 ps.

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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.

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Supplementary Material (1)

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Data availability

Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. (a). TiS - Coherent Mira (model 900-F) femtosecond TiAl2O3 laser, OPO1 and OPO2 – synchronously pumped femtosecond optical parametric oscillators. λ/2 – half-wave plate, DM1,2 – dichroic mirrors, DM1,2 – dichroic mirrors, CC - corner cube, OSA – optical spectrum analyzer, CCD – charge coupled device detector array, OBJ – objective lens (NA = 1.2), S-sample, CND – condenser lens, ATT – light intensity attenuator, BPF – band pass filter, GTP – Glan-Thompson prism polarizer, MONO – diffraction grating monochromator. (b). Broadly tunable OPO based on PPSLT crystal with variable QPM-period (Λ=22.3–23.4µm). LF-Lyot filter, PZT-computer controlled piezo-electric transducer, OC – output coupler. The inset shows the theoretical (blue line) wavelength-tuning curve for the resonating signal wave (λs) for different QPM periods and experimentally detected central wavelengths (black circles).
Fig. 2.
Fig. 2. (a). OPO1,2 output spectra taken with the OSA (Anritsu model MS9710C). OPO1 central wavelength (λ1) is normally set within 1008–1017 nm. OPO2 is widely tunable within 1030–1350 nm range. The OPOs central wavelengths can be maintained within ±1.5 nm while the pulse bandwidths are kept below 130 cm−1 across the tuning range. 2(b). Spectrum of the coherent amplitude Q (red line) for the input pulsed fields (E1, E2) at two optical carrier frequencies 1 and ω2). The corresponding OPO1 and OPO2 pulse intensity spectra are shown in the inset in blue (OPO1) and red (OPO2) lines. The two fields produce the broadband (∼170 cm−1) coherent excitation that can be calculated using the convolution integral. The data shown in black dots correspond to spontaneous Raman scattering spectra for KTP crystal in the vicinity of ∼400–1000 cm−1.
Fig. 3.
Fig. 3. (a) Time-resolved CARS signal (transients) obtained from BSO crystal (blue circles) and silica glass (red circles). OPO1,2 have been tuned to 1014 nm and 1158 nm for the measurement in BSO and 1011 nm and 1049 nm for glass experiment to create coherent excitations centered at about 1265 cm−1 and 360 cm−1 correspondingly. The measurement in BSO demonstrates 77 dB dynamic range in detecting CARS signal versus time delay. The dotted and dash dotted lines represent simulations for the CARS transients assuming ultrafast electronic nonlinearity relaxation time (<10 fs) and 120 fs correspondingly. (b) CARS spectra at different delay times for the measurement in BSO. The broadband OPO1,2 fields produce coherence that stretch to ∼1400 cm−1.
Fig. 4.
Fig. 4. Time-domain CARS signal measured in KTP crystal. The OPO1,2 wavelengths have been set to 1013 nm and 1089 nm to create broadband coherence centered at ω1−ω2∼692 cm−1. The time-domain CARS signal has been integrated within the spectral window of ∼30 nm centered at 772 nm. The initial part decays with a constant of 420 fs while the decay at longer delays slows down significantly with a characteristic time constant of 1.68 ps. (b,c) CARS spectra for the sample taken at different delay times. The dashed vertical lines indicate the spectral windows the CARS transients have been traced within.
Fig. 5.
Fig. 5. CARS transient obtained from KTP crystal when Raman active vibrations in the vicinity of 692 cm−1 are targeted. (a) Data shown in blue circles represent CARS signal decay for the case of spectrally selective acquisition within 767–777 nm range for the anti-Stokes wavelength. The spectral segment corresponds to probing the Raman active vibration at ∼630 cm−1. (b) Red circles represent CARS signal decay for the case of spectrally selective acquisition that corresponds to probing the Raman active vibration at ∼830 cm−1. The dashed lines represent simulated curves for the CARS signals.
Fig. 6.
Fig. 6. CARS transient (blue and red circles) obtained from KTP crystal when Raman active vibrations in the vicinity of ∼400 cm−1 (red) and ∼1600 cm−1 (blue) are targeted. The black dotted dashed line represents theoretical fit for the signal assuming single channel phonon decay with the decay time of T2 = 1.18 ± 0.02 ps. The data in red circles represent the CARS transient obtained from the crystal when targeting the ∼377 cm−11 vibration) phonon mode. The black dashed line represents the theoretical fit for the isolated line with the decay time of T2 = 1.72 ps.
Fig. 7.
Fig. 7. CARS transient (blue circles) obtained from BSO crystal by targeting crystal vibration in the vicinity of ∼800 cm−1. The black dotted dashed line represents the theoretical fit assuming single exponential decay at longer delay times with the T2 time of 1.29 ps. The red-circled data represent the time-domain CARS signal obtained from the crystal while targeting phonon vibration at around 1600 cm−1. The black dashed line represents a simulation for the CARS signal with single exponential decay for the phonon mode with T2 = 1.42 ps.

Equations (5)

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P a s ( 3 ) = 6 ε 0 χ ( 3 ) ( ω a s , ω 1 ω 2 , ω 3 ) E 10 E 20 E 30 e i [ ( ω 1 ω 2 + ω 3 ) t ( k 1 k 2 + k 3 ) z ] + c . c .
ξ a s = 48 ln 2 3 π c 2 ε 0 2 | χ ( 3 ) | 2 n 1 n 2 n 3 n a s ξ 1 ξ 2 ξ 3 L 2 λ a s 2 w 0 4 t p 2
S max = λ a s ν ξ a s 2 π c η D η T t int
P a s ( 3 ) ( t t d ) = N α q i 2 Q ( z , t ) E 30 ( t t d ) e i [ ( ω 1 ω 2 + ω 3 ) t ( k 1 k 2 + k 3 ) z ] e i ω 3 t d
S ( t d ) = 2 S max | 2 ln 2 t p 2 g ( t t d ) [ t 0 e ( t ϑ ) T 2 g 2 ( θ ) H ( t θ ) d θ ] d t | 2
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