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Journal of Experimental and Theoretical Physics

Multifrequency Stimulated Raman Scattering on Rotational Transitions of Molecules

Victor P. Kochanov

Published Jan 1, 2019• 1 citation
Publisher

Abstract

Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.

DOI
10.1134/s1063776119010023

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Abstract The theory of multifrequency stimulated Raman scattering (SRS) of light on rotational transitions of molecules, which are simulated by a three-level quantum system, is developed. It is shown that the application of bichromatic pumping increases the scattered radiation spectrum width. The exact algebraic solution for the wave amplitudes is obtained in the simplest version of synchronous SRS on transitions with a negligibly low eigenfrequency. It is found that an increase in the ratio of the Raman transition frequency to the pump radiation frequency leads to predominance of the anti-Stokes scattering branch. The effect of wave asynchronism emerging due to linear and nonlinear dispersion of the medium as well as the phase difference of the pump waves on SRS is considered. All types of asynchronism narrow generated frequency spectrum and suppress the anti-Stokes scattering branch. Nonlinear dispersion ensures positive values of wave amplitudes due to phase jumps by π during the propagation of waves in a medium.
The stimulated Raman scattering (SRS), arising from the interaction between molecules of a medium and two strong light fields - a resonant field and a pumping field - is studied theoretically. The transitions of molecules between a given pair of levels is assumed to be both Raman active and infrared active. A semiclassical approach, in which the density matrix method is used for the quantum mechanical description for the medium, is employed. We expand the density matrix in various orders within which the zeroth-order is referred to as the solution of the equation of motion of the density matrix when only the resonant field is applied. -- We obtain a set of equations in second order of the density matrix element p₁₀⑵ (ω) from which the gain function can be derived. This set of equations in the special case of steady state is accidentally similar to those obtained by Mollow in his study of the power spectrum of a strong driven two-level system. We have shown that the SRS in the steady state under the resonant field interaction, is drastically reduced in general. When the flopping frequency is larger than the relaxation constants (Ω > r), we find there appears both weak positive and weak negative gains on both sides of the ordinary SRS components. Since we retain our second-order equations in a general form rather than the form for steady state, we are able to take account of the dependence on the transient zeroth solution. By employing the Laplace transform technique with the help of convolution products, we are able to solve for ρ₁₀⑵(ω) in the stationary flopping state. When the intensity of the resonant field is high, we have found theoretically that both the Stokes and anti-Stokes component become doublets and equally displaced by the amount of the flopping frequency, Ω, on the opposite sides of ordinary Stokes and anti-Stokes components, respectively. The gain maxima are approximately the order of Ω/4r times the ordinary gain of the Stokes component, where Ω/r >> 1 if the flopping exists. The gains are therefore large in comparison with the ordinary gain for SRS in the steady state.
An analysis is made of the propagation of a short coherent optical pulse in a three-level resonant medium with an essentially nonequidistant spectrum as a function of the degree of preexcitation of the medium. It is found that in addition to self-induced transparency and resonance scattering, stimulated Raman scattering (Stokes or anti-Stokes) should be observed under certain spatial phase-matching conditions. The area theorem is formulated for all radiation components. An analysis is made of the case of propagation of a resonant electromagnetic pulse of frequency ω in a system of three-level atoms having an equidistant spectrum. Under conditions of preexcitation of the medium at the frequency 2ω by longitudinal acoustic pulses, a scattered transverse acoustic wave at the frequency ω may be observed.
A calculation is made of the intensity of the Stokes radiation in the stimulated Raman scattering of ultrashort light pulses in a dispersive medium employing the asymptotic approximation for arbitrary modulation of the amplitude and phase of the pump pulse. Particular attention was paid to the effect of phase modulation on the stimulated Raman scattering. Calculations were also made of the intensity of the anti-Stokes component in the scattering of an ultrashort pulse in a dispersive medium and of the optimal angle for the observation of the anti-Stokes rings.
A theoretical analysis is made of the stimulated Raman scattering in gases in the presence of spatial degeneracy of the energy levels. Saturation of the population difference and influence of anti-Stokes radiation are allowed for. Various polarizations of the pump fields and of the Stokes and anti-Stokes radiation are considered. It is shown that the profile of the stimulated Raman line is generally a sum of three Lorentzian lines and the scattering includes scalar, symmetric, and antisymmetric components. The use of circularly polarized pump radiation suppresses the influence of anti-Stokes radiation on the gain of the Stokes wave.
An analysis is made of the laws governing amplification of the Stokes wave in stimulated Raman scattering (STRS) in a dispersive medium for different models of wide-band pump radiation. An accurate solution of the STRS equations is obtained for pump radiation having a quadratically time-modulated phase. It is shown that for pump radiation for which the width of the instantaneous frequency spectrum is much less than the Raman scattering line width, the laws governing amplification of the Stokes wave differ substantially from those predicted by statistical STRS theory. Solutions of STRS equations in a dispersive medium are found for a model of temporally periodic pump radiation having a high intermode beat frequency.