Frequency shifts in stimulated Raman scattering

Abstract

The nonresonant contributions to the nonlinear susceptibility x (3) produce a frequency chirp during stimulated Raman scattering. In the case of transient stimulated Raman scattering, the spectrum of the generated Stokes pulse is found at higher frequencies than expected from spontaneous Raman data. The frequency difference can be calculated from the theory of stimulated Raman scattering.It has been shown in numerous papers that an intense electromagnetic wave of frequency COL, travelling through a Raman active medium, is able to generate a strong Stokes shifted collinear wave at frequency coS. In most experimental investigations the Stokes shift coo = col --coS of the stimulated Raman process was found to be equal to the Stokes shift known from spontaneous Raman measurements [ 1 ]. In contradiction, there exists a number of papers where deviations in the Stokes shifts between stimulated and spontaneous Raman scattering were reported [2].In this note we present a theoretical and experimental study of the stimulated Raman process taking into account the self-phase modulation of the laser and Stokes wave. It will be shown that under quasistationary conditions the stimulated Stokes emission has the same Stokes shift as spontaneous Raman scattering. For the transient stimulated Raman process the situation is different. Theory predicts and experiments confirm a smaller Stokes shift, i.e. a higher Stokes frequency. For clarity, we consider here a specific case, Raman scattering of a molecular vibration in liquids. The theoretical discussion is quite general being applicable to other Raman type process as well.The nonlinear response of the molecules is represented by the nonlinear polarisation pNL, which may be separated into two parts: A resonant contribution PR NL due to the molecular transition of interest with a Raman susceptibility ~a/~q and a nonresonant part NL PNR due to the electronic states of the molecules [3].N is the number density of the molecules and <q> denotes the expectation value of the normal mode operator q for the transition. For simplicity we make two assumptions: (i) A highly polarized Raman line is investigated, i.e. Oa/aq is a scalar. coO and m represent the transition frequency and the reduced mass, respectively, T 2 the dephasing time and n' is the occupation probability of the first excited vibrational level. For the system considered here we have a small population, i.e. n' < 1.For the light fields and the coherent material excitation, we make the ansatz of plane waves propagating in the x-direction: E = ~ {~ Ejexp(-ico/t + ikix + i~b/) + cc 1and ~q) = -~i{Q exp(-icoqt + ikqx + i~bq) + cc}.

Generation of Multiple Phase-Locked Stokes and Anti-Stokes Components in an Impulsively Excited Raman Medium

“…In these conditions self-focusing and self-phase modulation due to fast electronic response, medium ionization, and other competing processes can make the phase relationships between the components irregular. Note that spectral broadening of Stokes and anti-Stokes frequencies [7], continuum generation in SRS [6], and Kerr-induced shift of the Stokes line [8] were recently reported. In addition, amplitude modulation of the Stokes field (leading to Stokes pulse shortening) was observed even in the first SRS experiments [9].…”

“…First, pumping with a pulse shorter than the molecular vibrational period enables synchronization of the injection pulse scattering on a time scale less than one vibrational period. Second, the SRS gain of an impulsively pumped medium is determined by the integral characteristic of the pump pulse (full energy) and thus not sensitive to its temporal structure (in contrast to the conventional schemes of SRS [6][7][8][9]).…”

Fiber-based ultraviolet frequency sweep laser

“…In addition, some scattered light belongs to Raman scattering [2], which has a negative or positive frequency shift relative to the incident light. Intensities and frequency shifts of Raman scattering are related to vibration or rotation energy levels of molecules of detected objects [3]. Hence, Raman spectroscopy can be used to obtain the information on molecular vibration or rotation and then study the structure of molecules.…”