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.     

Wave packet theory of dynamic stimulated Raman spectra in femtosecond pump-probe spectroscopy

The quantum theory for stimulated Raman spectroscopy from a moving wave packet using the third-order density matrix and polarization is derived. The theory applies, in particular, to the new technique of femtosecond broadband stimulated Raman spectroscopy (FSRS). In the general case, a femtosecond actinic pump pulse first prepares a moving wave packet on an excited state surface which is then interrogated with a coupled pair of picosecond Raman pump pulse and a femtosecond Raman probe pulse and the Raman gain in the direction of the probe pulse is measured. It is shown that the third-order polarization in the time domain, whose Fourier transform governs the Raman gain, is given simply by the overlap of a first-order wave packet created by the Raman pump on the upper electronic state with a second-order wave packet on the initial electronic state that is created by the coupling of the Raman pump and probe fields acting on the molecule. Calculations are performed on model potentials to illustrate and interpret the FSRS spectra.     

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.     

Polarization dependence of vibrational coupling signals in femtosecond stimulated Raman spectroscopy

The polarization dependence of vibrational coupling signals seen in femtosecond stimulated Raman spectroscopy (FSRS) is investigated. Changing the polarization of a pulse used to impulsively excite coherent low frequency chlorine bending motion in CDCl(3) has a dramatic effect on the line shape of vibrational sidebands which arise from the anharmonic coupling of the pumped modes at 262 and 365 cm(-1) with the higher frequency symmetric stretching mode at 652 cm(-1). The asymmetric bend sideband (652+262 cm(-1)) changes sign and magnitude as the impulsive pulse polarization is rotated relative to the Raman pulses, while the symmetric bend sideband (652+365 cm(-1)) is relatively polarization independent. These experiments demonstrate the ability of FSRS to obtain time-resolved information on not only the vibrational coupling strength but also the symmetry of anharmonically coupled modes.     

Femtosecond Stimulated Raman Line Shapes: Dependence on Resonance Conditions of Pump and Probe Pulses?

Resonance enhancement has been increasingly employed in the emergent femtosecond stimulated Raman spectroscopy (FSRS) to selectively monitor molecular structure and dynamics with improved spectral and temporal resolutions and signal-to-noise ratios. Such joint efforts by the technique-and application-oriented scientists and engineers have laid the foundation for exploiting the tunable FSRS methodology to investigate a great variety of photosensitive systems and elucidate the underlying functional mechanisms on molecular time scales. During spectral analysis, peak line shapes remain a major concern with an intricate dependence on resonance conditions. Here, we present a comprehensive study of line shapes by tuning the Raman pump wavelength from red to blue side of the ground-state absorption band of the fluorescent dye rhodamine 6G in solution. Distinct line shape patterns in Stokes and anti-Stokes FSRS as well as from the low to high-frequency modes highlight the competition between multiple third-order and higher-order nonlinear pathways, governed by different resonance conditions achieved by Raman pump and probe pulses. In particular, the resonance condition of probe wavelength is revealed to play an important role in generating circular line shape changes through oppositely phased dispersion via hot luminescence (HL) pathways. Meanwhile, on-resonance conditions of the Raman pump could promote excited-state vibrational modes which are broadened and red-shifted from the coincident ground-state vibrational modes, posing challenges for spectral analysis. Certain strategies in tuning the Raman pump and probe to characteristic regions across an electronic transition band are discussed to improve the FSRS usability and versatility as a powerful structural dynamics toolset to advance chemical, physical, materials, and biological sciences.     

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.     

Elucidating the spectral and temporal contributions from the resonant and nonresonant response to femtosecond coherent anti-Stokes Raman scattering

A theoretical expression is developed for femtosecond coherent anti-Stokes Raman scattering (CARS) to quantitatively account for the vibrational line shape in the presence of nonresonant signal. The contributions of the resonant and nonresonant components are extracted from the emitted signal line shape as a function of Stokes wavelength and as a function of the temporal overlap of the two pump pulses (for spectrally resolved femtosecond CARS). The theory is compared to the measured spectra of the oxygen vibrational transition DeltaG(01)=1556.4 cm(-1) for temporal detunings of 0 and 700 fs.     

Wavelength-modulated femtosecond stimulated Raman spectroscopy-approach towards automatic data processing

A new wavelength modulator based on a custom-made chopper blade and a slit placed in the Fourier plane of a pulse shaper was used to detect explicitly the first derivative of the time-resolved femtosecond stimulated Raman spectroscopy (FSRS) signals. This approach resulted in an unprecedented reduction of the non-coherent background that results from population transfer by the Raman pump inherent to FSRS experiments. The method of Fourier peak filtering was implemented as a powerful tool for reducing both the remaining non-coherent and coherent background associated with FSRS experiments. The method was demonstrated on β-carotene and a similar synthetic aryl carotenoid. The experiments confirm earlier FSRS results on β-carotene but suggest some reinterpretation. Strong bleaching signals of ground state vibrations were observed and interpreted as an inseparable part of the time-resolved FSRS experiment. New long-lived Raman features were observed in β-carotene and the synthetic aryl carotenoid and assigned to a combination of conformational changes and solvent rearrangement. More complex wavelength modulation methods are proposed in the development of more robust FSRS experiments.     

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.     

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.     

Femtosecond time resolved coherent anti-Stokes Raman spectroscopy: experiment and modelization of speed memory effects on H2-N2 mixtures in the collision regime

With the aim of temperature diagnostic, femtosecond time-resolved CARS (coherent anti-Stokes Raman spectroscopy) is applied to probe H2 in H2-N2 mixtures. In a first part, a Lorentzian profile is used to model the femtosecond CARS response. A difference between the experimental broadening and the expected one is observed in the collision regime. The observed broadening increases strongly in an inhomogeneous way with respect to the perturber concentration. This is of considerable importance for temperature measurements. In a second part, we show that in the collision regime, this inhomogeneous broadening is due to the speed dependence of the collisional parameters and the memory effects of the radiator speed. A new modelization of the time-resolved CARS response taking into account the speed memory effects is presented and applied to the temperature diagnostic in H2-N2 mixtures. The numerical results are in good agreement with experiments.     

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.     

Coherent anti-Stokes Raman scattering: Spectroscopy and microscopy

In this review the basis, recent developments and applications of coherent anti-Stokes Raman scattering (CARS) in the fields of spectroscopy and microscopy are dialed with. The nonlinear susceptibility of the investigated molecule induced by pump and Stokes laser beams employed in the CARS technique is discussed. The relation between the nonlinear susceptibility, the different CARS laser intensities and the phase matching condition between them is also presented. The structure of CARS spectrum is analyzed as a function of the physical characteristics of the different employed lasers. This includes laser half widths, interference effects, cross-coherence and saturation of the resultant CARS signal by stimulated Raman scatter process (SRS). The different broadening mechanisms for CARS spectral line such as pressure and Doppler broadening are demonstrated. The recent progress in CARS for the in situ reaction flame diagnosis due to its suitability for detection of vibrational-rotational excited gas molecules present in the electronic ground state is discussed. CARS diagnosis for liquid- and solid-phases including the progress in polymeric materials is considered. The applications of CARS microscopy are reviewed in the view of its recent advances to study chemical and biological systems.     

Hybrid four-wave mixing in liquid pyridine

Four-wave mixing spectra for liquid pyridine are obtained with broadband laser beam. A comparison of Stokes and anti-Stokes spectra allows the assignment of several lines (951, 991, 1030 cm^?1) to CARS and CSRS processes. Two additional moderately intense lines on the Stokes side between 951 and 991 cm^?1 as well as 991 and 1030 cm^?1 , which do not appear on the anti-Stokes side, are assigned to a “hybrid four-wave mixing” process, in which two active Raman modes of pyridine are involved. This process previously unrevealed in experiment seems to be important for correct assignment of the spectral lines in four-wave mixing experiments with a broadband laser beam.     

The ketene intermediate in the photochemistry of ortho-nitrobenzaldehyde

The first intermediate of the photochemical transformation of ortho-nitrobenzaldehyde to ortho-nitrosobenzoic acid in acetonitrile solvent has been characterized by femtosecond spectroscopy and time-dependent density functional theory (TDDFT) calculations. Femtosecond stimulated Raman spectroscopy (FSRS) indicates that this intermediate adopts a ketene structure. This assignment is supported by the TDDFT results. A kinetic analysis of FSRS and transient absorption data points to two channels for the formation of the ketene. For the predominating first channel the formation takes 0.4 ps. For the second channel it is much slower and takes 220 ps. We assign the first channel to a reaction via an excited singlet state. The second one might involve a triplet state.     

Development of a tunable femtosecond stimulated raman apparatus and its application to beta-carotene

We have developed a tunable femtosecond stimulated Raman spectroscopy (FSRS) apparatus and used it to perform time-resolved resonance Raman experiments with <100 fs temporal and <35 cm(-1) spectral resolution. The key technical change that facilitates this advance is the use of a tunable narrow-bandwidth optical parametric amplifier (NB-OPA) presented recently by Shim et al. (Shim, S.; Mathies, R. A. Appl. Phys. Lett. 2006, 89, 121124). The practicality of tunable FSRS is demonstrated by examining the photophysical dynamics of beta-carotene. Using 560 nm Raman excitation, the resonant S1 state modes are enhanced by a factor of approximately 200 compared with 800 nm FSRS experiments. The improved signal-to-noise ratios facilitate the measurement of definitive time constants for beta-carotene dynamics including the 180 fs appearance of the S1 vibrational features due to direct internal conversion from S2 and their characteristic 9 ps decay to S0. By tuning the FSRS system to 590 nm Raman excitation, we are able to selectively enhance vibrational features of the hot ground state S hot 0 and monitor its approximately 5 ps cooling dynamics. This tunable FSRS system is valuable because it facilitates the direct observation of structural changes of selected resonantly enhanced states and intermediates during photochemical and photobiological reactions.     

Vibrational structure of the S(2) (1B(u)) excited state of diphenyloctatetraene observed by femtosecond stimulated Raman spectroscopy

Femtosecond time-resolved stimulated Raman spectroscopy (FSRS) is used to study the vibrational structure and dynamics of the S(2) state of diphenyloctatetraene. Strong vibrational features at 1184, 1259 and 1578 cm(-1) whose linewidths are determined by the S(2) electronic lifetime are observed at early times after photoexcitation at 397 nm. Kinetic analysis of the integrated Raman intensities as well as the transient absorption reveals an exponential decay of the S(2) state on the order of 100 fs. These results demonstrate the ability of FSRS to study the vibrational structure of excited state and chemical reaction dynamics on the femtosecond timescale.