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Optics Letters

Bright–bright 2π solitons in stimulated Raman scattering

A. E. Kaplan, P. L. Shkolnikov, B. A. Akanaev

Published Apr 1, 1994• 15 citations
Publisher

Abstract

We found conditions for excitation of bright-bright 2pi solitons in stimulated Raman scattering that involves nutation of population at Raman quantum levels, for two (laser-Stokes) and three (e.g., laser-Stokes-anti-Stokes) components. The soliton components at all participating frequencies are bright solitons of the same, Lorentzian, shape, in contrast to the well-known bright-dark soliton combination in stimulated Raman scattering.

DOI
10.1364/ol.19.000445

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Physical Review A•Nov 1, 1993•2 citations
We found conditions for excitation of bright-bright 2pi solitons in stimulated Raman scattering that involves nutation of population at Raman quantum levels, for two (laser-Stokes) and three (e.g., laser-Stokes-anti-Stokes) components. The soliton components at all participating frequencies are bright solitons of the same, Lorentzian, shape, in contrast to the well-known bright-dark soliton combination in stimulated Raman scattering.
A system of Maxwell-Bloch type equations (MBE's), describing stimulated Raman scattering with both Stokes and anti-Stokes waves taken into account, is investigated. We introduce variables S3{\mathit{S}}_{3}S3​ and ${\mathit{S}}_{\ifmmode\pm\else\textpm\fi{}}$, which are bilinear in the electromagnetic fields, and prove that the corresponding equations possess Lax representation. This fact is used to obtain additional solutions for S3{\mathit{S}}_{3}S3​, ${\mathit{S}}_{\ifmmode\pm\else\textpm\fi{}}$ and for the MBE's which include solitons, periodical waves, and self-similarity solutions. The transient and bright threshold solitons are also analyzed. \textcopyright{} 1996 The American Physical Society.
Although \ensuremath{\pi} phase shifts in an input Stokes beam are known to initiate soliton formation in a Raman amplifier, the observed shot-to-shot amplitude fluctuations have gone unexplained. It has been suggested that recently observed frequency shifts caused by quantum fluctuations may be related to the observed soliton decay. We show that frqequency shifts of the magnitude observed from these quantum fluctuations lead to soliton decay, and thus, are indeed the probable cause of observed soliton decay.
Optical nutation at the Raman-active transition 6P 1/2−6P 3/2 of thallium atoms (ω R /2πc=7793 cm −1) under resonant Raman excitation by a biharmonic picosecond pulsed field, giving rise to substantial motion of the population, is detected. Optical nutation appears as an oscillatory behavior of the energy of the anti-Stokes scattering of probe pulses, which follow with a fixed delay, as a function of the product of the energies of the excitation pulses. As a result of the dynamic Stark effect, which decreases the frequency of the transition under study, resonance excitation conditions are satisfied for negative initial detunings of the Raman excitation frequency from resonance. The Raman scattering cross section for the transition under study is estimated by comparing the experimental data with the calculations.
We have studied the diffractive coupling of Stokes, anti-Stokes, and pump fields in stimulated Raman scattering. We find that, depending on the strength of the anti-Stokes field relative to that of the Stokes, both soliton dynamics and beam-pointing fluctuations are affected for finite Fresnel numbers. The generation of the anti-Stokes waves can inhibit a gain-focusing mechanism that we predicted for the Stokes field, when a soliton propagates in the medium. Although no qualitative differences arise in the beam-pointing fluctuations of the Stokes field, we predict that the anti-Stokes beam may be much more stable than the Stokes counterpart. Our analysis shows that for a Fresnel number of 5, the difference can be as large as 70%, while for Fresnel numbers of order unity, it is nearly 10%.