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Soviet Journal of Quantum Electronics

Statistical characteristics of the energies of pulses of forward and backward stimulated Raman scattering under linear, intermediate, and nonlinear scattering conditions

Pavel A Apanasevich, D. E. Gakhovich, A. S. Grabchikov, S. Ya. Kilin, Valery P. Kozich, B. L. Kontsevoi, Valentine A. Orlovich

Published Sep 30, 1992• 6 citations
Publisher

Abstract

An experimental investigation was made of the distribution of the energies of pulses of forward (concurrent) and backward first Stokes components of stimulated Raman scattering (STRS), and of pump (exciting) radiation pulses, transmitted by a scattering medium. The study was carried out under linear, intermediate, and nonlinear scattering conditions. The dependences of the coefficients of variation and of the asymmetry of the distributions on the energy of the pump pulses were determined. The statistical properties of the energy of the backward STRS pulses differed in a number of respects from the forward STRS pulses, including a relatively high coefficient of variation in the former case. An interpretation of these differences was developed. It was found that STRS gave rise to fluctuations of the energy of the transmitted pump pulses and the statistical characteristics of these pulses were determined. The results obtained for forward STRS were in satisfactory agreement with the conclusions reached on the basis of a quantum theory.

DOI
10.1070/qe1992v022n09abeh003607

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An experimental investigation was made of the distribution of the energies of pulses of forward (concurrent) and backward first Stokes components of stimulated Raman scattering (STRS), and of pump (exciting) radiation pulses, transmitted by a scattering medium. The study was carried out under linear, intermediate, and nonlinear scattering conditions. The dependences of the coefficients of variation and of the asymmetry of the distributions on the energy of the pump pulses were determined. The statistical properties of the energy of the backward STRS pulses differed in a number of respects from the forward STRS pulses, including a relatively high coefficient of variation in the former case. An interpretation of these differences was developed. It was found that STRS gave rise to fluctuations of the energy of the transmitted pump pulses and the statistical characteristics of these pulses were determined. The results obtained for forward STRS were in satisfactory agreement with the conclusions reached on the basis of a quantum theory.
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.
The results of the investigation of Stokes energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump are presented. The pulse-energy distributions and their standard deviations were measured. The comparison of the experimental data with known ones for coherent pump shows the strong difference in the distribution shape and the standard deviation value. This difference is explained as a manifestation of the non-Gaussian (super-Gaussian) statistics in stimulated scattering with a broad-band pump. The results of numerical calculations for statistics of Stokes intensity are in a qualitative agreement with the experimental findings.
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.
A study is made of the problem of stimulated Raman scattering (STRS) in a resonant medium pumped by a strong pulse satisfying the adiabaticity condition. It is shown that in the absence of relaxation the maximum STRS gain is reached during the tail (trailing edge) of the pump pulse, which is the reason for the absence of the Stark shift. If the pump pulse is considerably longer than the relaxation time, the lag of the STRS pulse behind the pump pulse is short and then the Stark shift is manifested in the spectrum and a characteristic interference structure is formed. Noise and monochromatic "seeding" variants are considered.
An experimental study of stimulated Raman scattering (SRS) has been performed using a subnanosecond pulse to investigate the statistical properties of Stokes light generation.1 There are macroscopic fluctuations of Stokes pulse energy as well as random generation of spatial mode patterns. When the scattering volume has a low Fresnel number, the spatial patterns of the SRS resemble cavity modes. When the Fresnel number is large, there are irregular structures appearing across the Stokes profile in a random fashion. A theoretical study of the spatial and temporal coherence properties of Raman generation using a Gaussian-profile pump pulse has also been carried out. Using a Gaussian-Laguerre mode expansion technique,2 it is found that the higher-order spatial coherence modes1 experience different gain than the lower-order spatial coherence modes, and consequently the temporal coherence associated with each individual spatial coherence mode is different.
An investigation was made of the influence of the geometric excitation conditions on the energy dependences of the stimulated scattering of focused laser pulses of ~ 10 −8 sec duration when the sharpness and depth of focusing were varied. The experimental results obtained in this study were interpreted theoretically on the basis of a quantum analysis of stimulated Raman scattering in a two-level system. The experimental relationships could be explained only if an allowance was made for the changes in the populations of the levels participating in the Raman transition. It was possible to select the experimental conditions so that reconstruction of the wavefront of the pump radiation was observed under stimulated scattering conditions in a wide energy range.