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.     

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.     

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.     

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 stimulated Raman study of excited-state evolution in bacteriorhodopsin

Femtosecond time-resolved stimulated Raman spectroscopy (FSRS) is used to examine the photoisomerization dynamics in the excited state of bacteriorhodopsin. Near-IR stimulated emission is observed in the FSRS probe window that decays with a 400-600-fs time constant. Additionally, dispersive vibrational lines appear at the locations of the ground-state vibrational frequencies and decay with a 260-fs time constant. The dispersive line shapes are caused by a nonlinear effect we term Raman initiated by nonlinear emission (RINE) that generates vibrational coherence on the ground-state surface. Theoretical expressions for the RINE line shapes are developed and used to fit the spectral and temporal evolution of the spectra. The rapid 260-fs decay of the RINE peak intensity, compared to the slower evolution of the stimulated emission, indicates that the excited-state population moves in approximately 260 fs to a region on the potential energy surface where the RINE signal is attenuated. This loss of RINE signal is best explained by structural evolution of the excited-state population along multiple low-frequency modes that carry the molecule out of the harmonic photochemically inactive Franck-Condon region and into the photochemically active geometry.     

Quantum theory of time-resolved femtosecond stimulated Raman spectroscopy: direct versus cascade processes and application to CDCl3

We present a quantum mechanical wave packet treatment of time-resolved femtosecond stimulated Raman spectroscopy (FSRS), or two-dimensional (2D) FSRS, where a vibrational coherence is initiated with an impulsive Raman pump which is subsequently probed by FSRS. It complements the recent classical treatment by Mehlenbacher et al. [J. Chem. Phys. 131, 244512 (2009)]. In this 2D-FSRS, two processes can occur concurrently but with different intensities: a direct fifth-order process taking place on one molecule, and a cascade process comprising two third-order processes on two different molecules. The cascade process comprises a parallel and a sequential cascade. The theory is applied to the 2D-FSRS of CDCl(3) where calculations showed that: (a) the cascade process is stronger than the direct fifth-order process by one order of magnitude, (b) the sidebands assigned to C-Cl E and A(1) bends, observed on both sides of the Stokes C-D stretch frequency, are not due to anharmonic coupling between the C-D stretch and the C-Cl bends, but are instead due to the coherent anti-Stokes Raman spectroscopy (CARS) and coherent Stokes Raman spectroscopy (CSRS) fields produced in the first step of the cascade process, (c) for each delay time between the femtosecond impulsive pump and FSRS probe pulses, the line shape of the sidebands shows an inversion symmetry about the C-D stretch frequency, and this is due to the 180(°) phase difference between the CARS and CSRS fields that produced the left and right sidebands, and (d) for each sideband, the line shape changes from positive Lorentzian to dispersive to negative Lorentzian, then to negative dispersive and back to positive Lorentzian with the period of the bending vibration, and it is correlated with the momentum of the wave packet prepared on the ground-state surface by the impulsive pump along the sideband normal coordinate.     

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.     

Development of simultaneous frequency- and time-resolved coherent anti-Stokes Raman scattering for ultrafast detection of molecular Raman spectra

The development of a time-resolved coherent anti-Stokes Raman scattering (CARS) variant for use as a probe of excited electronic state Raman-active modes following excitation with an ultrafast pump pulse is detailed. Application of this technique involves a combination of broadband fs-time scale pulses and a narrowband pulse of ps duration that allows multiplexed detection of the CARS signal, permitting direct observation of molecular Raman frequencies and intensities with time resolution dictated by the broadband pulses. Thus, this nonlinear optical probe, designated fs/ps CARS, is suitable for observation of Raman spectral evolution following excitation with a pump pulse. Because of the spatial separation of the CARS output signal relative to the three input beams inherent in a folded BOXCARS arrangement, this technique is particularly amenable to probing low-frequency vibrational modes, which play a significant role in accepting vibrational energy during intramolecular vibrational energy redistribution within electronically excited states. Additionally, this spatial separation allows discrimination against strong fluorescence signal, as demonstrated in the case of rhodamine 6G.     

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.     

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.     

On the Resolution Limit of Femtosecond Stimulated Raman Spectroscopy: Modelling Fifth‐Order Signals with Overlapping Pulses

Femtosecond stimulated Raman scattering (FSRS) spectroscopy is a powerful pump–probe technique that can track electronic and vibrational dynamics with high spectral and temporal resolution. The investigation of extremely short‐lived species, however, implies deciphering complex signals and is ultimately hampered by unwanted nonlinear effects once the time resolution limit is approached and the pulses overlap temporally. Using the loop diagrams formalism we calculate the fifth‐order response of a model system and address the limiting case where the relevant dynamics timescale is comparable to the pump–pulse duration and, consequently, the pump and the probe overlap temporally. We find that in this regime, additional diagrams that do not contribute for temporally well separated pulses need to be taken into account, giving rise to new time‐dependent features, even in the absence of photoinduced dynamics and for negative delays.     

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.     

Femtosecond Time-Resolved Stimulated Raman Spectroscopy of the S(2) (1B(u)) Excited State of beta-Carotene

The electronic and vibrational structure of beta-carotene's early excited states are examined using femtosecond time-resolved stimulated Raman spectroscopy. The vibrational spectrum of the short-lived ( approximately 160 fs) second excited singlet state (S(2),1B(u) (+))of beta-carotene is obtained. Broad, resonantly enhanced vibrational features are observed at approximately 1100, 1300, and 1650 cm(-1) that decay with a time constant corresponding to the electronic lifetime of S(2). The temporal evolution of the vibrational spectra are consistent with significant population of only two low-lying excited electronic states (1B(u) (+) and 2A(g) (-)) in the ultrafast relaxation pathway of beta-carotene.     

The vibrational Stokes shift of water (HOD in D2O)

The vibrational Stokes shift of the OH stretching transition nu(OH) of water is the shift between the ground-state absorption and the excited-state (v=1) emission. A recent measurement on HOD in D(2)O solvent [S. Woutersen and H. J. Bakker, Phys. Rev. Lett. 83, 2077 (1999)] of a 70 cm(-1) redshift, and a subsequent calculation of a 57 cm(-1) redshift using equilibrium molecular dynamics simulations [C. P. Lawrence and J. L. Skinner, J. Chem. Phys. 117, 8847 (2002)] were in good agreement. We now report extensive measurements of the vibrational Stokes shift in HOD/D(2)O using an ultrafast IR pump, Raman probe method. The vibrational Stokes shift is seen to depend on the pump pulse frequency and on time delay; by varying these parameters it can be made to range from 112 to -32 cm(-1) (negative values indicate a blueshift in the excited state). The equilibrium vibrational Stokes shift is actually a negative rather than a positive quantity. Possible reasons for the disagreement between experiment and theory are briefly discussed.     

Perturbative theory and modeling of electronic-resonance-enhanced coherent anti-Stokes Raman scattering spectroscopy of nitric oxide

A theory is developed for three-laser electronic-resonance-enhanced (ERE) coherent anti-Stokes Raman scattering (CARS) spectroscopy of nitric oxide (NO). A vibrational Q-branch Raman polarization is excited in the NO molecule by the frequency difference between visible Raman pump and Stokes beams. An ultraviolet probe beam is scattered from the induced Raman polarization to produce an ultraviolet ERE-CARS signal. The frequency of the ultraviolet probe beam is selected to be in electronic resonance with rotational transitions in the A (2)Sigma(+)<--X (2)Pi (1,0) band of NO. This choice results in a resonance between the frequency of the ERE-CARS signal and transitions in the (0,0) band. The theoretical model for ERE-CARS NO spectra has been developed in the perturbative limit. Comparisons to experimental spectra are presented where either the probe laser was scanned with fixed Stokes frequency or the Stokes laser was scanned with fixed probe frequency. At atmospheric pressure and an NO concentration of 100 ppm, good agreement is found between theoretical and experimental spectral peak locations and relative intensities for both types of spectra. Factors relating to saturation in the experiments are discussed, including implications for the theoretical predictions.     

Ultrafast spectroscopy with sub-10 fs deep-ultraviolet pulses

Time-resolved transient absorption spectroscopy with sub-9 fs ultrashort laser pulses in the deep-ultraviolet (DUV) region is reported for the first time. Single 8.7 fs DUV pulses with a spectral range of 255-290 nm are generated by a chirped-pulse four-wave mixing technique for use as pump and probe pulses. Electronic excited state and vibrational dynamics are simultaneously observed for an aqueous solution of thymine over the full spectral range using a 128-channel lock-in detector. Vibrational modes of the electronic ground state and excited states can be observed as well as the decay dynamics of the electronic excited state. Information on the initial phase of the vibrational modes is extracted from the measured difference absorbance trace, which contains oscillatory structures arising from the vibrational modes of the molecule. Along with other techniques such as time-resolved infrared spectroscopy, spectroscopy with sub-9 fs DUV pulses is expected to contribute to a detailed understanding of the photochemical dynamics of biologically significant molecules that absorb in the DUV region such as DNA and amino acids.     

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.