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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Multimode excitation of stimulated light scattering in spherical particles: the angular characteristics of scattered radiation

Аlexander А. Zemlyanov, Yu. É. Geints, E. K. Chistyakova

Published Nov 19, 1999• 0 citations
Publisher

Abstract

We analyze here the influence of multi-mode excitation of stimulated light scattering (SLS) in the spherical particle on the angular intensity distribution in the far-field zone. It is shown that at multi-mode excitation of SLS the scattering diagram becomes asymmetric, unlike the case, when process is realized on single resonant mode of a particle. Degree of its asymmetry significantly depends on combinations of modes excited in the particle that brings either to a significant increase of the intensity of backscattered wave, or to its weakening in the given direction. The comparison with angular intensity distribution at elastic scattering is made.

DOI
10.1117/12.370483

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We analyze here the influence of multi-mode excitation of stimulated light scattering (SLS) in the spherical particle on the angular intensity distribution in the far-field zone. It is shown that at multi-mode excitation of SLS the scattering diagram becomes asymmetric, unlike the case, when process is realized on single resonant mode of a particle. Degree of its asymmetry significantly depends on combinations of modes excited in the particle that brings either to a significant increase of the intensity of backscattered wave, or to its weakening in the given direction. The comparison with angular intensity distribution at elastic scattering is made.
The paper is devoted to the problem of derivation of optimum conditions for the development of stimulated light scattering (SLS) processes in spherical micron-sized particles. The equation for threshold pumping intensity in the case of realization in a particle the conditions of a double SLS resonance for incident and scattered waves was obtained. The coefficient of spatial field overlapping Bc((omega) L, (omega) S) was introduced. The coefficient Bc((omega) L, (omega) S) is shown to be approximately one order of magnitude higher when the mode order of input and output resonances are equal, then when they are different. The main factor determining the value of Bc((omega) L, (omega) S) is the FWHM of excited modes.
The effect of the form change of the intensity correlation function of light scattered back by emulsion or suspension of the particles in liquids is obtained experimentally, when the exciting light intensity increase. The change consists in the appearing in the correlation function of the cosine component with frequency equal to inverse relaxation time of particles concentration fluctuations. The appearance of such cosine component tells about the appearance of the additional spectral line, shifted with respect to exciting light by the half-width of the spectral line of spontaneous polarized Rayleigh scattering by particles. The cosine is caused by beating between exciting radiation and this spectral line. This frequency shift is of about 25-250 Hz depending on particles sizes and characteristic of liquid, in which they are weighted. Together with the scattering relative intensity increase the cosine appearance confirms the obtaining of the stimulated light scattering at variations of the particles concentrations.
An analysis is made of nonlinear nonstationary equations describing dynamics of the stimulated Raman scattering in optical resonators excited by external nonmonochromatic radiation. The threshold of the excitation of the stimulated scattering by nonmonochromatic radiation is found and its dependence on the dispersion of the active medium is deduced. Solutions are obtained for steady-state oscillations in a resonator and their characteristics are investigated as a function of the spectrum of the exciting radiation and of the dispersion of the active medium.
The mode structure of the Stokes component of stimulated Raman scattering (SRS) in a multimode fibre excited by a pump field with statistics corresponding to a narrowband Gaussian noise model is theoretically analysed. The relation is obtained between the number of spatially coherent radiation modes of the Stokes wave and fibre parameters and SRS excitation conditions. It follows from this relation that the degree of spatial coherence of the Stokes radiation at the fibre output is determined by the number of spatial modes of pump radiation and the averaged gain of the Stokes radiation over the interaction length. It is established that there exists the threshold gain at which the number of spatially coherent radiation modes of the Stokes component increases infinitely and, therefore, its spatial coherence tends to zero. The estimates of the number of spatially coherent radiation modes of the Stokes component showed that already at the Raman scattering excitation threshold their number is so great that the degree of spatial coherence of the Stokes component radiation corresponds to the degree of coherence of a thermal source radiation. The measured dispersion of spatial intensity fluctuations of the Stokes component sepa-rated by using an interference filter (with the transmission bandwidth ≈1 nm at 620 nm) proved to be approximately three times higher than the dispersion of radiation intensity fluctuations of a luminescent lamp. The large dispersion of spatial intensity fluctuations of the Stokes component is caused most likely by individual intensity spikes in a small-scale (unresolved by a detector with a spatial resolution of ≈14 μm) speckle pattern produced in the detection plane by monochromatic Stokes radiation.
We conduct a theoretical analysis of the Stokes component mode structure of the Raman scattering. The Raman scattering is excited in a multimode waveguide with pump radiation having statistics corresponding to the model of the narrow-band Gaussian noise. We obtain an analytical relation connecting the number of spatially coherent modes of the Stokes component, characteristics of the waveguide and conditions of the Raman scattering excitation. It follows from the obtained relation that the Raman scattering spatial coherency degree at the waveguide's exit is determined by the number of the spatial modes of pump radiation and the amplification of the Stokes radiation throughout the waveguide's length. There exists a threshold in the amplification corresponding to the unlimited increase of the number of the spatially coherent modes of the Raman scattering and therefore to a zero of spatial coherency. Conducted estimations show that at the Raman scattering threshold value of the radiation intensity the number of the spatially coherent modes of the Raman scattering Stokes component should be comparable to that of the thermal source. Experimentally, measured dispersion of the spatial intensity fluctuations of the Stokes component isolated with an interference filter (spectral bandwidth ~ 1nm, λ = 620nm) is three time smaller than that of the luminescent lamp radiation.
The change in the shape of the correlation function of the intensity of light scattered by particles in liquid, i.e., the appearance of a cosine component, with increasing excitation radiation intensity, is observed. The amplitude of this component increases with the intensity of exciting radiation. A quadratic component appears in the dependence of the scattering intensity on the exciting radiation intensity. These results point to the appearance of stimulated “diffusion” scattering by particle concentration fluctuations.