Theory of femtosecond coherent anti-Stokes Raman scattering spectroscopy of gas-phase transitions

A theoretical analysis of coherent anti-Stokes Raman scattering (CARS) spectroscopy of gas-phase resonances using femtosecond lasers is performed. The time-dependent density matrix equations for the femtosecond CARS process are formulated and manipulated into a form suitable for solution by direct numerical integration (DNI). The temporal shapes of the pump, Stokes, and probe laser pulses are specified as an input to the DNI calculations. It is assumed that the laser pulse shapes are 70 fs Gaussians and that the pulses are Fourier-transform limited. A single excited electronic level is defined as an effective intermediate level in the Raman process, and transition strengths are adjusted to match the experimental Raman polarizability. The excitation of the Raman coherence is investigated for different Q-branch rotational transitions in the fundamental 2330 cm(-1) band of diatomic nitrogen, assuming that the pump and Stokes pulses are temporally overlapped. The excitation process is shown to be virtually identical for transitions ranging from Q2 to Q20. The excitation of the Raman coherences is also very efficient; for laser irradiances of 5x10(17) W/m2, corresponding approximately to a 100 microJ, 70 fs pulse focused to 50 microm, approximately 10% of the population of the ground Raman level is pumped to the excited Raman level during the impulsive pump-Stokes excitation, and the magnitude of the induced Raman coherence reaches 40% of its maximum possible value. The theoretical results are compared with the results of experiments where the femtosecond CARS signal is recorded as a function of probe delay with respect to the impulsive pump-Stokes excitation.     

Chirped coherent anti-stokes Raman scattering for high spectral resolution spectroscopy and chemically selective imaging

We describe a simple multiplex vibrational spectroscopic imaging technique based on employing chirped femtosecond pulses in a coherent anti-Stokes Raman scattering (CARS) scheme. Overlap of a femtosecond Stokes pulse with chirped pump/probe pulses introduces a temporal gate that defines the spectral resolution of the technique, allowing single-shot acquisition of high spectral resolution CARS spectra over a several hundred wavenumber bandwidth. Simulated chirped (c-) CARS spectra match the experimental results, quantifying the dependence of the high spectral resolution on the properties of the chirped pulse. c-CARS spectromicroscopy offers promise as a simple and generally applicable high spatial resolution, chemically specific imaging technique for studying complex biological and materials samples.     

Optimal coherent control of coherent anti-Stokes Raman scattering: signal enhancement and background elimination

The ability to enhance resonant signals and eliminate the non-resonant background is analyzed for coherent anti-Stokes Raman scattering (CARS). The analysis is done at a specific frequency as well as for broadband excitation using femtosecond pulse-shaping techniques. An appropriate objective functional is employed to balance resonant signal enhancement against non-resonant background suppression. Optimal enhancement of the signal and minimization of the background can be achieved by shaping the probe pulse alone while keeping the pump and Stokes pulses unshaped. In some cases analytical forms for the probe pulse can be found, and numerical simulations are carried out for other circumstances. It is found that a good approximate optimal solution for resonant signal enhancement in two-pulse CARS is a superposition of linear and arctangent-type phases for the pump. The well-known probe delay method is shown to be a quasi-optimal scheme for broadband background suppression. The results should provide a basis to improve the performance of CARS spectroscopy and microscopy.     

Chemical imaging by single pulse interferometric coherent anti-stokes Raman scattering microscopy

A single pulse interferometric coherent anti-Stokes Raman (CARS) spectroscopy method is used to obtain broadband CARS spectra and microscopy images of liquid and polymer samples. The pump, Stokes, and probe pulses are all selected inside a single broadband ultrafast pulse by a phase- and polarization-controlled pulse shaping technique and used to generate two spectral interference CARS signals simultaneously. The normalized difference of these two signals provides an amplified background-free broadband resonant CARS spectrum over the 400-1500 cm(-1) range with 35 cm(-1) spectral resolution. Chemically selective microscopy images of multicomponent polymer and liquid samples are investigated with this new CARS method. Multiplex CARS spectra at 10,000 spatial points are measured within a few minutes, and used to construct chemically selective microscopy images with a spatial resolution of 400 nm. The spectral bandwidth limits, sensitivity, homodyne amplification advantages, spatial resolution, depolarization, chromatic aberration, and chemical imaging aspects of this new technique are discussed in detail.     

异硫氰基孔雀石绿受激拉曼光谱研究

本文报道了具有时间分辨能力的全频宽带受激拉曼（BBSRS）系统和关于异硫氰基孔雀石绿（MGITC）受激拉曼光谱（sRs）的研究．BBSRS系统的探测光为450-800nm宽带连续白光,泵浦光为280～900nm范围内连续可调谐的ps窄带可见光（带宽≈7．5cm-1,脉宽≈2．5ps）．在合适的泵浦波长下,该系统可同时获取拉曼损失和拉曼增益光谱．MGITC的SRS研究结果表明,当拉曼损失谱峰出现在最大吸收波长（≈627nm）时,共振SRS谱峰强度最大;当泵浦或增益谱峰在最大吸收波长附近时,未观察到明显的共振拉曼信号;共振峰强度随浓度增大而增大,随泵浦功率增大而迅速增大,后趋于饱和;共振和非共振峰强在延时零点附近达到最大值,并随延时绝对值的增大而减小．     

Quantum theory of (femtosecond) time-resolved stimulated Raman scattering

We present a complete perturbation theory of stimulated Raman scattering (SRS), which includes the new experimental technique of femtosecond stimulated Raman scattering (FSRS), where a picosecond Raman pump pulse and a femtosecond probe pulse simultaneously act on a stationary or nonstationary vibrational state. It is shown that eight terms in perturbation theory are required to account for SRS, with observation along the probe pulse direction, and they can be grouped into four nonlinear processes which are labeled as stimulated Raman scattering or inverse Raman scattering (IRS): SRS(I), SRS(II), IRS(I), and IRS(II). Previous FSRS theories have used only the SRS(I) process or only the "resonance Raman scattering" term in SRS(I). Each process can be represented by an overlap between a wave packet in the initial electronic state and a wave packet in the excited Raman electronic state. Calculations were performed with Gaussian Raman pump and probe pulses on displaced harmonic potentials to illustrate various features of FSRS, such as high time and frequency resolution; Raman gain for the Stokes line, Raman loss for the anti-Stokes line, and absence of the Rayleigh line in off-resonance FSRS from a stationary or decaying v=0 state; dispersive line shapes in resonance FSRS; and the possibility of observing vibrational wave packet motion with off-resonance FSRS.     

Femtosecond Time-Resolved Stimulated Raman Spectroscopy: Application to the Ultrafast Internal Conversion in beta-Carotene

We have developed the technique of femtosecond stimulated Raman spectroscopy (FSRS), which allows the rapid collection of high-resolution vibrational spectra on the femtosecond time scale. FSRS combines a sub-50 fs actinic pump pulse with a two-pulse stimulated Raman probe to obtain vibrational spectra whose frequency resolution limits are uncoupled from the time resolution. This allows the acquisition of spectra with <100 fs time resolution and <30 cm(-1) frequency resolution. Additionally, FSRS is unaffected by background fluorescence, provides rapid (100 ms) acquisition times, and exhibits traditional spontaneous Raman line shapes. FSRS is used here to study the relaxation dynamics of beta-carotene. Following optical excitation to S(2) (1B(u) (+)) the molecule relaxes in 160 fs to S(1) (2A(g) (-)) and then undergoes two distinct stages of intramolecular vibrational energy redistribution (IVR) with 200 and 450 fs time constants. These processes are attributed to rapid (200 fs) distribution of the internal conversion energy from the S(1) C=C modes into a restricted bath of anharmonically coupled modes followed by complete IVR in 450 fs. FSRS is a valuable new technique for studying the vibrational structure of chemical reaction intermediates and transition states.     

Fourth-order Raman spectroscopy of wide-band gap materials

Low-frequency surface vibrations were observed on a rutile TiO(2)(110) surface covered with trimethyl acetate (TMA) by using fourth-order Raman spectroscopy. The TMA-covered surface interfaced to air was irradiated with 18-fs light at a wavelength of 630 nm. A pump pulse excited vibrational coherence of Raman-active modes and a probe pulse interacts with the coherently excited surface to generate second harmonic light (315 nm), the intensity of which oscillated as a function of the pump-probe delay. Four bands were recognized at 180, 357, 444, and 826 cm(-1) in the Fourier transformation spectrum of the oscillation and assigned to bulk phonons modified by the presence of the surface boundary condition. The Raman transition for the pump was nonresonant to the band gap excitation of TiO(2), as evidenced by the oscillation phase relative to the pump irradiation and by the oscillation amplitude as a function of the pump power. The observable range of this surface-selective spectroscopy is extended to wide-band gap materials on which one-photon resonance enhancement of the Raman-pump efficiency cannot be expected.     

Instantaneous vibrational frequencies of diffusing and desorbing adsorbates: CO/Pt(111)

Electronic excitation of metal by intense laser pulses stimulates nuclear motions of adsorbates through nonadiabatic coupling, resulting in diffusion and desorption of adsorbates. These processes take place via precursor states: adsorbates whose vibrational modes with respect to substrate are highly excited. This paper reports the dynamics of precursor states of CO on Pt(111) probed by use of infrared-visible sum frequency generation with phase-sensitive detection, which allows us to obtain the second-order nonlinear susceptibility and thus the vibrational response function. Without pump pulses at 400 nm, the inverse Fourier transformation of the vibrational response function reveals a free induction decay of vibrational polarization of C-O stretching created by a short infrared pulse. The free induction decay is perturbed when an intense 400-nm pump pulse following the infrared pulse is irradiated, because diffusion and desorption of CO are induced by the pump pulse. The time evolution of instantaneous C-O stretching frequency retrieved from the perturbed free induction decay shows a redshift followed by a rapid reverse shift when the fluence of pump pulse is high enough to desorb CO. This indicates that the frustrated modes of CO is first substantially excited and then the parallel momentum of CO is converted to the normal one through mutual collisions, leading to substantial excitation of the external stretching mode of CO.     

Molecular vibrations at a liquid-liquid interface observed by fourth-order Raman spectroscopy

Interface-selective, Raman-based observation of molecular vibrations is demonstrated at a liquid-liquid interface. An aqueous solution of oxazine 170 dye interfaced with hexadecane is irradiated with pump and probe light pulses of 630-nm wavelengths in 17-fs width. The ultrashort pulses are broadened due to group velocity dispersion when traveling through the hexadecane layer. The dispersion is optically corrected to give an optimized instrumental response. The pump pulse induces a vibrational coherence of the dye via impulsive stimulated Raman scattering. The probe pulse generates second-harmonic light at the interface. The efficiency of the generation is modulated as a function of the pump-probe delay by the coherently excited molecules. Fourier transformation of the modulated efficiency presents the frequency spectrum of the vibrations. Five bands are recognized at 534, 557, 593, 619, and 683 cm(-1). The pump-and-probe process induces a fourth-order optical response that is forbidden in a centrosymmetric media. The contribution of an undesired, cascaded optical process is quantitatively considered and excluded.     

Analysis of time resolved femtosecond and femtosecond/picosecond coherent anti-Stokes Raman spectroscopy: application to toluene and Rhodamine 6G

The third-order polarization for coherent anti-Stokes Raman scattering (CARS) from a pure state is described by 48 terms in perturbation theory, but only 4 terms satisfy the rotating wave approximation. They are represented by Feynman dual time-line diagrams and four-wave mixing energy level diagrams. In time-resolved (tr) fs and fs/ps CARS from the ground vibrational state, one resonant diagram, which is the typical CARS term, with three field interactions-pump, Stokes, followed by probe-on the ket is dominant. Using the separable, displaced harmonic oscillators approximation, an analytic result is obtained for the four-time correlation function in the CARS third-order polarization. Dlott's phenomenological expression for off-resonance CARS from the ground vibrational state is derived using a three-state model. We calculated the tr fs and fs/ps CARS for toluene and Rhodamine 6G (R6G), initially in the ground vibrational state, to compare with experimental results. The observed vibrational features and major peaks for both tr fs and fs/ps CARS, from off-resonance (for toluene) to resonance (for R6G) pump wavelengths, can be well reproduced by the calculations. The connections between fs/ps CARS, fs stimulated Raman spectroscopy, and impulsive stimulated scattering for toluene and R6G are discussed.     

Determination of intermolecular energy transfer by time resolved CARS measurements

Energy transfer in methyl isocyanide following i.r. multiphoton excitation has been examined with a CARS probe. Results show that CARS is an effective technique both for measuring the fraction of molecules receiving energy from the laser and for monitoring intermolecular energy transfer following laser irradiation. In addition, the Raman transition at 2169 cm⁻¹ shows a vibrational progression due to hot bands of the ν₈ bend. Since the ν₈, bend is the only low energy mode of the molecule, it is an effective vibrational “thermometer”. Utilizing this thermometer, results show that the vibrational state distribution does not fit a Boltzmann distribution for 7 μs following i.r. multiphoton excitation.     

Inverse Raman bands in ultrafast Raman loss spectroscopy

Ultrafast Raman loss spectroscopy (URLS) is equivalent to anti-Stokes femtosecond stimulated Raman spectroscopy (FSRS), using a broadband probe pulse that extends to the blue of the narrow bandwidth Raman pump, and can be described as inverse Raman scattering (IRS). Using the Feynman dual time-line diagram, the third-order polarization for IRS with finite pulses can be written down in terms of a four-time correlation function. An analytic expression is obtained for the latter in the harmonic approximation which facilitates computation. We simulated the URLS of crystal violet (CV) for various resonance Raman pump excitation wavelengths using the IRS polarization expression with finite pulses. The calculated results agreed well with the experimental results of S. Umapathy et al., J. Chem. Phys. 133, 024505 (2010). In the limit of monochromatic Raman pump and probe pulses, we obtain the third-order susceptibility for multi-modes, and for a single mode we recover the well-known expression for the third-order susceptibility, χ(IRS) ((3)), for IRS. The latter is used to understand the mode dependent phase changes as a function of Raman pump excitation in the URLS of CV.     

Chirp dependence of wave packet motion in oxazine 1

The motion of vibrational wave packets in the system oxazine 1 in methanol is investigated by spectrally resolved transient absorption spectroscopy. The spectral properties of the probe pulse from 600 to 700 nm were chosen to cover the overlap region where ground-state bleach and stimulated emission signals are detected. The spectral phase of the pump pulse was manipulated by a liquid crystal display based pulse-shaping setup. Chirped excitation pulses of negative and positive chirp can be used to excite vibrational modes predominantly in the ground or excited state, respectively. To distinguish the observed wave packets in oxazine 1 moving in the ground or excited state, spectrally resolved transient absorption experiments are performed for various values of the linear chirp of the pump pulses. The amplitudes of the wave packet motion show an asymmetric behavior with an optimum signal for a negative chirp of -0.75 +/- 0.2 fs/nm, which indicates that predominantly ground-state wave packets are observed.     

Optimal laser pulse shaping for interferometric multiplex coherent anti-stokes Raman scattering microscopy

We present a significant sensitivity improvement of interferometric multiplex coherent anti-Stokes Raman scattering (CARS) by optimizing the power, bandwidth and phase of the pump, Stokes, and probe pulses independently. Fourier transform spectral interferometry (FTSI) is used to retrieve the entire complex quantity of the CARS spectrum by utilizing the non-resonant background as a local oscillator. Background-free spontaneous Raman-like vibrational spectra can be measured over the 500-1400 cm(-1) range with 20 cm(-1) spectral resolution within a tens of microseconds time scale. Chemically selective microscopy of a multicomponent polymer film is performed to demonstrate the feasibility of its microscopy application. A systematic analysis of the signal recovery method and several technical issues are discussed.     

Shaping femtosecond coherent anti-Stokes Raman spectra using optimal control theory

Optimal control theory is used to tailor laser pulses which enhance a femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) spectrum in a certain frequency range. For this aim the optimal control theory has to be applied to a target state distributed in time. Explicit control mechanisms are given for shaping either the Stokes or the probe pulse in the four-wave mixing process. A simple molecule for which highly accurate potential energy surfaces are available, namely molecular iodine, is used to test the procedure. This approach of controlling vibrational motion and delivering higher intensities to certain frequency ranges might also be important for the improvement of CARS microscopy.     

Optical control of excited-state vibrational coherences of a molecule in solution: The influence of the excitation pulse spectrum and phase in LD690

Spectral and phase shaping of femtosecond laser pulses is used to selectively excite vibrational wave packets on the ground (S0) and excited (S1) electronic states in the laser dye LD690. The transient absorption signals observed following excitation near the peak of the ground-state absorption spectrum are characterized by a dominant 586 cm(-1) vibrational mode. This vibration is assigned to a wave packet on the S0 potential energy surface. When the excitation pulse is tuned to the blue wing of the absorption spectrum, a lower frequency 568 cm(-1) vibration dominates the response. This lower frequency mode is assigned to a vibrational wave packet on the S1 electronic state. The spectrum and phase of the excitation pulse also influence both the dephasing of the vibrational wave packet and the amplitude profiles of the oscillations as a function of probe wavelength. Excitation by blue-tuned, positively chirped pulses slows the apparent dephasing of the vibrational coherences compared with a transform-limited pulse having the same spectrum. Blue-tuned negatively chirped excitation pulses suppress the observation of coherent oscillations in the ground state.     

Time- and frequency-resolved coherent anti-Stokes Raman scattering spectroscopy with sub-25 fs laser pulses

In general, many different diagrams can contribute to the signal measured in broadband four-wave mixing experiments. Care must therefore be taken when designing an experiment to be sensitive to only the desired diagram by taking advantage of phase matching, pulse timing, sequence, and the wavelengths employed. We use sub-25 fs pulses to create and monitor vibrational wavepackets in gaseous iodine, bromine, and iodine bromide through time- and frequency-resolved femtosecond coherent anti-Stokes Raman scattering (CARS) spectroscopy. We experimentally illustrate this using iodine, where the broad bandwidths of our pulses, and Boltzmann population in the lower three vibrational levels conspire to make a single diagram dominant in one spectral region of the signal spectrum. In another spectral region, however, the signal is the sum of two almost equally contributing diagrams, making it difficult to directly extract information about the molecular dynamics. We derive simple analytical expressions for the time- and frequency-resolved CARS signal to study the interplay of different diagrams. Expressions are given for all five diagrams which can contribute to the CARS signal in our case.     

Single-Shot Gas-Phase Thermometry by Time-to-Frequency Mapping of Coherence Dephasing

We demonstrate a single-beam coherent anti-Stokes Raman scattering (CARS) technique for gas-phase thermometry that assesses the species-specific local gas temperature by single-shot time-to-frequency mapping of Raman-coherence dephasing. The proof-of-principle experiments are performed with air in a temperature-controlled gas cell. Impulsive excitation of molecular vibrations by an ultrashort pump/Stokes pulse is followed by multipulse probing of the 2330 cm(-1) Raman transition of N(2). This sequence of colored probe pulses, delayed in time with respect to each other and corresponding to three isolated spectral bands, imprints the coherence dephasing onto the measured CARS spectrum. For calibration purposes, the dephasing rates are recorded at various gas temperatures, and the relationship is fitted to a linear regression. The calibration data are then used to determine the gas temperature and are shown to provide better than 15 K accuracy. The described approach is insensitive to pulse energy fluctuations and can, in principle, gauge the temperature of multiple chemical species in a single laser shot, which is deemed particularly valuable for temperature profiling of reacting flows in gas-turbine combustors.