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Soviet Journal of Quantum Electronics

Influence of the profile of the spectral line of vibrations of a medium on the time characteristics of stimulated scattering

Igor' M Bel'dyugin, Mark V. Zolotarev, K. A. Sviridov

Published Jan 31, 1985• 1 citation
Publisher

Abstract

A theoretical analysis is made of the problem of the time taken to establish steady-state lasing as a result of various types of stimulated scattering (Raman, Brillouin, and excited by heat evolution in a medium) and of the law governing amplification of Stokes waves after times much shorter than the relaxation time of vibrations of the medium for an arbitrary spectral line profile. It is shown that the characteristic times for the establishment of steady-state lasing in the case of stimulated scattering near the maximum of the gain profile are of the same type for different spectral lines profiles and have similar values.

DOI
10.1070/qe1985v015n01abeh005897

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A theoretical analysis is made of the problem of the time taken to establish steady-state lasing as a result of various types of stimulated scattering (Raman, Brillouin, and excited by heat evolution in a medium) and of the law governing amplification of Stokes waves after times much shorter than the relaxation time of vibrations of the medium for an arbitrary spectral line profile. It is shown that the characteristic times for the establishment of steady-state lasing in the case of stimulated scattering near the maximum of the gain profile are of the same type for different spectral lines profiles and have similar values.
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.
An analysis is made of the influence of the width of the pump line on the stimulated scattering in Fabry–Perot and ring resonators which are tuned both to the pump frequency and to the frequency of the Stokes component. It is shown that the excitation threshold of the stimulated scattering in dispersion-free media is independent of the width of the pump line, because of the parametric interaction between the modes, whereas in media with a considerable dispersion the threshold is Δω p /Δω sp greater than the stimulated emission threshold under monochromatic pumping conditions (the subscripts "p" and "sp" refer to the pump wave and to the spontaneous Raman scattering). Analytic expressions are given for the amplitudes of the pump and Stokes fields at the excitation threshold and under steady-state conditions.
The development of the Stokes spectrum and the dependence of Raman gain upon pump laser bandwidth in a narrow linewidth Raman medium are analyzed in terms of a closed set of multimode equations. The analysis predicts that the Stokes gain coefficient takes on its maximum value, which is independent of bandwidth, when the Stokes spectrum replicates the pump spectrum. It is also shown that in the absence of dispersion the spectrum of a weak Stokes wave is driven to duplicate the pump spectrum, and that for noise input the average power generated in the Stokes wave is independent of the pump bandwidth.
A theoretical and experimental investigation was made of the amplification of a Stokes signal in a multimode pump field when the ratio of the spectral widths of the interacting fields was varied. In the pump intensity range I p < I cr ( I cr was a critical intensity) the gain increment was considerably less than the static value and it was governed entirely by the spectral distributions of the pump and Stokes signal. In the range I p > I cr the gain increment tended to the static value. An anomalous scatter of the Raman amplifier gain was observed experimentally for Δ ν s ≈Δ ν p ≫Δ ν l (Δ ν s ,Δ ν p , and Δ ν l were the line widths of the Stokes signal, pump, and spontaneous stimulated Raman scattering). A theory developed for the purpose indicated that the scatter was observed because the phase relationships between the interacting waves at the input into the medium varied from one measurement to another.
The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.