Probing avoided crossings and conical intersections by two-pulse femtosecond stimulated Raman spectroscopy: Theoretical study.

This study leverages two-pulse femtosecond stimulated Raman spectroscopy (2FSRS) to characterize molecular systems with avoided crossings (ACs) and conical intersections (CIs) in their low-lying excited electronic states. By simulating 2FSRS spectra of microscopically inspired ACs and CIs models, we demonstrate that 2FSRS not only delivers valuable information on the molecular parameters characterizing ACs and CIs but also helps distinguish between these two systems.

Selective suppression of CARS signal with two competing stimulated Raman scattering processes.

Coherent anti-Stokes Raman scattering (CARS) spectroscopy and microscopy have been used in studying the structure and dynamics of a wide range of chemical and biological systems. However, the spatial resolution of CARS microscopy is still limited by the diffraction barrier, and hence a suitable scheme to selectively switch off the CARS imaging signal is essential for super-resolution CARS microscopy. Here, we present theoretical descriptions about three different ways to selectively suppress the pump-Stokes-pump two-beam CARS signal by employing three-beam double stimulated Raman scattering (SRS) schemes. Using a semiclassical theory for the interaction of radiation with the Raman-active molecule, we obtain coupled differential equations for the intensities of the pump, Stokes, depletion, and the generated CARS signal fields. We find approximate solutions of these coupled differential equations. They are then used to show that the pump-Stokes-pump CARS signal can be selectively suppressed by increasing the added depletion beam intensity, when the three injected beam frequencies are tuned in such a way that they can induce two SRS processes simultaneously. To show that these switching-off methods can be used to develop super-resolution CARS imaging techniques, we numerically calculate the full-width-at-half-maximum of the CARS imaging point spread function assuming that the spatial profiles of the pump and Stokes beams are Gaussian functions and that the spatial profile of the depletion beam is doughnut-shaped. We anticipate that the proposed selective CARS suppression schemes will be of use in developing super-resolution, label-free CARS microscopy.

Selective suppression of CARS signal with three-beam competing stimulated Raman scattering processes.

Coherent Raman scattering spectroscopy and microscopy are useful methods for studying the chemical and biological structures of molecules with Raman-active modes. In particular, coherent anti-Stokes Raman scattering (CARS) microscopy, which is a label-free method capable of imaging structures by displaying the vibrational contrast of the molecules, has been widely used. However, the lack of a technique for switching-off the CARS signal has prevented the development of the super-resolution Raman imaging method. Here, we demonstrate that a selective suppression of the CARS signal is possible by using a three-beam double stimulated Raman scattering (SRS) scheme; the three beams are the pump, Stokes, and depletion lights in order of frequency. Both pump-Stokes and pump-depletion beam pairs can generate SRS processes by tuning their beat frequencies to match two different vibrational modes, then two CARS signals induced by pump-Stokes-pump and pump-depletion-pump interactions can be generated, where the two CARS signals are coupled with each other because they both involve interactions with the common pump beam. Herein, we show that as the intensity of the depletion beam is increased, one can selectively suppress the pump-Stokes-pump CARS signal because the pump-depletion SRS depletes the pump photons. A detailed theoretical description of the coupled differential equations for the three incident fields and the generated CARS signal fields is presented. Taking benzene as a molecular system, we obtained a maximum CARS suppression efficiency of about 97% with our experimental scheme, where the ring breathing mode of the benzene is associated with pump-Stokes-pump CARS, while the C-H stretching mode is associated with the competing pump-depletion SRS process. We anticipate that this selective switching-off scheme will be of use in developing super-resolution label-free CARS microscopy.

Three-beam double stimulated Raman scatterings: Cascading configuration.

Two-beam stimulated Raman scattering (SRS) has been used in diverse label-free spectroscopy and imaging applications of live cells, biological tissues, and functional materials. Recently, we developed a theoretical framework for the three-beam double SRS processes that involve pump, Stokes, and depletion beams, where the pump-Stokes and pump-depletion SRS processes compete with each other. It was shown that the net Stokes gain signal can be suppressed by increasing the depletion beam intensity. The theoretical prediction has been experimentally confirmed recently. In the previous scheme for a selective suppression of one SRS by making it compete with another SRS, the two SRS processes occur in a parallel manner. However, there is another possibility of three-beam double SRS scheme that can be of use to suppress either Raman gain of the Stokes beam or Raman loss of the pump beam by depleting the Stokes photons with yet another SRS process induced by the pair of Stokes and another (second) Stokes beam. This three-beam double SRS process resembles a cascading energy transfer process from the pump beam to the first Stokes beam (SRS-1) and subsequently from the first Stokes beam to the second Stokes beam (SRS-2). Here, the two stimulated Raman gain-loss processes are associated with two different Raman-active vibrational modes of solute molecule. In the present theory, both the radiation and the molecules are treated quantum mechanically. We then show that the cascading-type three-beam double SRS can be described by coupled differential equations for the photon numbers of the pump and Stokes beams. From the approximate solutions as well as exact numerical calculation results for the coupled differential equations, a possibility of efficiently suppressing the stimulated Raman loss of the pump beam by increasing the second Stokes beam intensity is shown and discussed. To further prove a potential use of this scheme for developing a super-resolution SRS microscopy, we present a theoretical expression and numerical simulation results for the full-width-at-half-maximum of SRS imaging point spread function, assuming that the pump and Stokes beam profiles are Gaussian and the second Stokes beam has a doughnut-shaped spatial profile. It is clear that the spatial resolution with the present 3-beam cascading SRS method can be enhanced well beyond the diffraction limit. We anticipate that the present work will provide a theoretical framework for a super-resolution stimulated Raman scattering microscopy that is currently under investigation.

Resonant femtosecond stimulated Raman spectroscopy with an intense actinic pump pulse: Application to conical intersections.

We theoretically investigate the feasibility of characterizing conical intersections with time-resolved resonant femtosecond stimulated Raman spectroscopy (FSRS) using an intense actinic pump pulse. We perform nonperturbative numerical simulations of FSRS signals for a three-electronic-state two-vibrational-mode model, which is inspired by the S2(ππ*)-S1(nπ*) conical intersection in pyrazine. Our results show that moderately strong actinic pulses increase the intensity of vibrational fingerprint lines in FSRS transients. They facilitate the extraction of useful spectroscopic information by enhancing peaks revealing the coupling and tuning modes of the conical intersection.

Femtosecond stimulated Raman spectroscopy as a tool to detect molecular vibrations in ground and excited electronic states.

We give a detailed theoretical analysis of the simplest variant of femtosecond stimulated Raman spectroscopy, where a picosecond Raman pump pulse and a femtosecond Raman probe pulse are applied resonantly to a chromophore in thermal equilibrium in the ground electronic state. We demonstrate that this technique is capable of the detection of dephasing-free Raman-like lines revealing vibrational modes not only in the electronic ground state but also in the excited electronic state of the chromophore. The analytical results obtained with simplifying assumptions for the shape of the laser pulses are substantiated by numerical simulations with realistic laser pulses, employing the equation-of-motion phase-matching approach.

Resonant Femtosecond Stimulated Raman Spectra: Theory and Simulations.

We present a description of resonant femtosecond stimulated Raman spectra, which is based on the solution of the nonperturbative equation of motion of the chromophore in the laser fields. The theory is applicable for arbitrary shapes and durations of the Raman pulses, accounts for excited-state absorption, and describes nonstationary preparation of the system by an actinic pulse. The method is illustrated by the calculation of femtosecond stimulated Raman spectra of a model system with a conical intersection.

Effect of Initial Vibrational-State Excitation on Subfemtosecond Photodynamics of Water.

We discuss the effect of initial vibrational-state excitation on the subfemtosecond photodynamics of water. Photoelectron spectra of Franck-Condon ionization to the (2)B1 state of the H2O(+) (D2O(+)) from the ground and several vibrationally excited states of the neutral are reported. Also calculated are ratios of the high-order harmonic generation (HHG) signals as a function of time for each initial vibrational state of the neutral molecule as predicted from the ratios of the square of the autocorrelation functions for D2O(+) and H2O(+). They reveal maxima as a function of time for each vibrational state of the neutral molecule. In turn, the HHG signals are found to be enhanced with vibrational excitation, with the calculated expectation values of the bond lengths and bond angle revealing quasiperiodic oscillations in time for all initial vibrational states of the neutral species. Although the bond lengths show only a marginal increase, the bond angle is found to be enhanced markedly by vibrational excitation, this being therefore responsible for the observed rise in the HHG signal.

Subfemtosecond quantum nuclear dynamics in water isotopomers.

Subfemtosecond quantum dynamics studies of all water isotopomers in the X̃ (2)B1 and à (2)A1 electronic states of the cation formed by Franck-Condon ionization of the neutral ground electronic state are reported. Using the ratio of the autocorrelation functions for the isotopomers as obtained from the solution of the time-dependent Schrödinger equation in a grid representation, high-order harmonic generation signals are calculated as a function of time. The results are found to be in agreement with the available experimental findings and with our earlier study for D2O(+)/H2O(+). Maxima are predicted in the autocorrelation function ratio at various times. Their origin and occurrence is explained by calculating expectation values of the bond lengths and bond angle of the water isotopomers as a function of time. The values so calculated for the (2)B1 and (2)A1 electronic states of the cation show quasiperiodic oscillations that can be associated with the time at which the nuclear wave packet reaches the minima of the potential energy surface, there being responsible for the peaks in the HHG signals.

Domain of validity of the perturbative approach to femtosecond optical spectroscopy.

We have performed numerical nonperturbative simulations of transient absorption pump-probe responses for a series of molecular model systems. The resulting signals as a function of the laser field strength and the pump-probe delay time are compared with those obtained in the perturbative response function formalism. The simulations and their theoretical analysis indicate that the perturbative description remains valid up to moderately strong laser pulses, corresponding to a rather substantial depopulation (population) of the initial (final) electronic states.