Simultaneous time and frequency detection in femtosecond coherent Raman spectroscopy. II. Application to acetonitrile

The preceding paper showed that, in principle, a high-resolution coherent Raman spectrum can be recovered using femtosecond probe pulses by combined detection in both time and frequency. This measurement is possible even when the pulses are too broad in frequency for conventional frequency-domain spectroscopy and too broad in time for conventional time-domain spectroscopy. In this paper, the method is tested on experimental coherent anti-stokes Raman spectroscopy data from acetonitrile. Compared to theoretical models, experimental data are complicated by noise and incomplete knowledge of the pulse structure. Despite these complications, most of the information in the Raman spectrum is recovered from the data: weak transitions are detected and natural-linewidth resolution is achieved across an 800 cm(-1) spectral range. However, circumstances in which experimental limitations result in missed features or ambiguities in the recovered spectrum are also identified. These results suggest where improvements in measurement and data analysis can be made.     

Complete characterization of molecular vibration using frequency resolved gating

The authors propose a new approach to vibration spectroscopy based on the coherent anti-Stokes Raman scattering of broadband ultrashort laser pulses. The proposed method reveals both the amplitude and the phase of molecular vibrations by utilizing the cross-correlation frequency resolved optical gating (XFROG) technique. The spectrum of the anti-Stokes pulse is measured as a function of the time delay between the laser-induced molecular vibrations and a well characterized broadband femtosecond probe pulse. The iterative XFROG algorithm provides a simultaneous complete characterization of molecular vibrations both in frequency and time domains with high resolution. They demonstrate experimentally the feasibility of the proposed method and show one of its potential applications in disentangling the time behavior of a mixture of vibrationally excited molecules. The technique of femtosecond pulse shaping is used for further improvement of accuracy and stability against noise.     

Influence of electronic resonances on mode selective excitation with tailored laser pulses

Femtosecond time-resolved coherent anti-Stokes Raman scattering (fs-CARS) gives access to ultrafast molecular dynamics. However, the gain of the temporal resolution entails a poor spectral resolution due to the inherent spectral width of the femtosecond excitation pulses. Modifications of the phase shape of one of the exciting pulses results in dramatic changes of the mode distribution reflected in coherent anti-Stokes Raman spectra. A feedback-controlled optimization of specific modes making use of phase and/or amplitude modulation of the pump laser pulse is applied to selectively influence the anti-Stokes signal spectrum. The optimization experiments are performed under electronically nonresonant and resonant conditions. The results are compared and the role of electronic resonances is analyzed. It can be clearly demonstrated that these resonances are of importance for a selective excitation by means of phase and amplitude modulation. The mode selective excitation under nonresonant conditions is determined mainly by the variation of the spectral phase of the laser pulse. Here, the modulation of the spectral amplitudes only has little influence on the mode ratios. In contrast to this, the phase as well as amplitude modulation contributes considerably to the control process under resonant conditions. A careful analysis of the experimental results reveals information about the mechanisms of the mode control, which partially involve molecular dynamics in the electronic states.     

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.     

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.     

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.     

Electronic coherences and vibrational wave-packets in single molecules studied with femtosecond phase-controlled spectroscopy

Employing femtosecond pulse-shaping techniques we investigate ultrafast, coherent and incoherent dynamics in single molecules at room temperature. In first experiments single molecules are excited into their purely electronic 0-0 transition by phase-locked double-pulse sequences with pulse durations of 75 fs and 20 nm spectral band width. Their femtosecond kinetics can then be understood in terms of a 2-level system and modelled with the optical Bloch equations. We find that we observe the coherence decay in single molecules, and the purely electronic dephasing times can be retrieved directly in the time domain. In addition, the Rabi-frequencies and thus the transition dipole moments of single molecules are determined from these data. Upon excitation of single molecules into a vibrational level of the electronically excited state also incoherent intra-molecular vibrational relaxation is recorded. Increasing the spectral band width of the excitation pulses to up to 120 nm (resulting in a transform-limited pulse width of 15 fs) coherent superpositions of excited state vibrational modes, i.e. vibrational wave packets, are excited. The wave-packet oscillations in the excited state potential energy surface are followed in time by a phase-controlled pump-probe scheme, which permits to record wave packet interference, and to determine the energies of vibrational modes and their coupling strengths to the electronic transition.     

Optical control of coherent lattice motions probed by femtosecond electron diffraction

We report the study of laser-induced coherent lattice motions using femtosecond electron diffraction. The oscillations of Bragg peak positions associated with a damped lattice vibration along the surface normal were directly observed in real time and with sub-milli-angstrom spatial resolution. In addition, by using a pair of optical excitation pulses and varying their time delay and relative pulse intensities, we demonstrated the successful control of coherent lattice motions.     

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.     

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.     

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.     

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.     

Communication: Time-domain measurement of high-pressure N2 and O2 self-broadened linewidths using hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering

The direct measurement of self-broadened linewidths using the time decay of pure-rotational hybrid femtosecond/picosecond coherent anti-Stokes Raman scattering (fs/ps RCARS) signals is demonstrated in gas-phase N(2) and O(2) from 1-20 atm. Using fs pump and Stokes pulses and a spectrally narrowed ps probe pulse, collisional dephasing rates with time constants as short as 2.5 ps are captured with high accuracy for individual rotational transitions. S-branch linewidths of N(2) and O(2) from ~0.06 to 2.2 cm(-1) and the line separation of O(2) triplet states are obtained from the measured dephasing rates and compared with high-resolution, frequency-domain measurements and S-branch approximations using the modified exponential gap model. The accuracy of the current measurements suggests that the fs/ps RCARS approach is well suited for tracking the collisional dynamics of gas-phase mixtures over a wide range of pressures.     

Communication: Comment on the effective temporal and spectral resolution of impulsive stimulated Raman signals

A compact correlation-function expression for time-resolved stimulated Raman signals, generated by combining a spectrally narrow (picosecond) with a broad (femtosecond) pulse, is derived using a closed time path loop diagrammatic technique that represents forward and backward time evolution of the vibrational wave function. We show that even though the external spectral and temporal parameters of the pulses may be independently controlled, the effective temporal and spectral resolution of the experiment may not exceed the fundamental bandwidth limitation.     

Use of the Gerchberg–Saxton algorithm in optimal coherent anti-Stokes Raman spectroscopy

We are utilizing recent advances in ultrafast laser technology and recent discoveries in optimal shaping of laser pulses to significantly enhance the stand-off detection of explosives via control of molecular processes at the quantum level. Optimal dynamic detection of explosives is a method whereby the selectivity and sensitivity of any of a number of nonlinear spectroscopic methods are enhanced using optimal shaping of ultrafast laser pulses. We have recently investigated the Gerchberg–Saxton algorithm as a method to very quickly estimate the optimal spectral phase for a given analyte from its spontaneous Raman spectrum and the ultrafast laser pulse spectrum. Results for obtaining selective coherent anti-Stokes Raman spectra (CARS) for an analyte in a mixture, while suppressing the CARS signals from the other mixture components, are compared for the Gerchberg–Saxton method versus previously obtained results from closed-loop machine-learning optimization using evolutionary strategies.     

Communication: hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering thermometry using a narrowband time-asymmetric probe pulse

A narrowband, time-asymmetric probe pulse is introduced into the hybrid femtosecond/picosecond rotational coherent anti-Stokes Raman scattering (fs/ps RCARS) technique to provide accurate and precise single-shot, high-repetition-rate gas-phase thermometric measurements. This narrowband pulse-generated by inserting a Fabry-Pe?rot e?talon into the probe-pulse beam path-enables frequency-domain detection of pure-rotational transitions. The unique time-asymmetric nature of this pulse, in turn, allows for detection of resonant Raman-active rotational transitions free of signal contamination by nonresonant four-wave-mixing processes while still allowing detection at short probe-pulse delays, where collisional dephasing processes are negligible. We demonstrate that this approach provides excellent single-shot thermometric accuracy (<1% error) and precision (~2.5%) in gas-phase environments.     

Molecular vibrational dynamics of rhodamine B dye in solution studied by femtosecond CARS

Spectrally dispersed femtosecond time-resolved coherent anti-Stokes Raman spectroscopy is utilized to study the ultrafast vibrational dynamics in rhodamine B dye in solution at room temperature. The anti-Stokes intensities are monitored as a function of time and wavenumber. By simply changing the timing of laser pulses, the vibrational dynamics of excited Raman transitions in rhodamine B molecules can be tracked and detected.     

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.     

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.     

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.