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Physical Review A

Soliton initiation and decay in stimulated Raman scattering

David C. MacPherson, R. C. Swanson, John L. Carlsten

Published Jun 1, 1989• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.6078

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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.
Recent studies of soliton formation in a Raman amplifier by a \ensuremath{\pi} phase shift have shown that the soliton will decay if the input Stokes beam is off resonance. Initial experiments indicated that this soliton decay is related to frequency shifts of the input Stokes beam that result from quantum fluctuations. In this paper we use the quantum statistics of the Raman spectral fluctuations to compare the predicted decay statistics of the soliton decay with the experimentally measured distribution. We find that, as conjectured, the soliton decay is directly related to the statistics of the initiating quantum fluctuations.
Measurements on soliton decay in stimulated Raman scattering have led to the study of frequency fluctuations in the single shot Stokes linewidth. These spectral measurements show that the spectrum of a single shot can be considerably narrower than the gain narrowed profile predicted by quantum mechanics for the ensemble average. However when spectra of many shots are averaged together the predicted result is recovered. The fluctuations seen are thought to be related to the quantum fluctuations associated with the initiating spontaneous emission. Theoretical results based on coherent mode theory are shown to be in agreement with the data.
In our studies of soliton formation in stimulated Raman scattering (SRS), we have discovered that a fully quantum mechanical theory predicts large shot-to-shot fluctuations in the SRS power spectrum, which leads to soliton decay. This theory, which includes a Langevin operator to simulate collision-induced fluctuations and maintain operator consistency, can be used to generate the statistics of the macroscopic SRS output. We have also studied a simpler model which uses a random vacuum field as an input to the semiclassical SRS equations. The vacuum field was numerically generated by summing a set of electromagnetic field modes that spanned the collisional Raman linewidth. Each mode was separated in frequency by less than the resolution of the system and given a random phase for each shot. Despite the lack of Langevin terms, the shot-to-shot variations and two-frequency correlation function from the simple approach were essentially indistinguishable from the fully quantum mechanical theory. This suggests that a simulation of SRS from spontaneous emission does not always require Langevin terms in the quantum noise.
Stimulated Raman scattering is a quantum macroscopic process starting from unstable state. Any fluctuations, initial or boundary, classical or quantum in nature, lead to the macroscopic output fluctuations of the Stokes amplitude. Manifestation of these fluctuations in the statistics of the Stokes pulse energy and its spectrum have been studied extensively for the linear stage of the SRS [1]. Another fluctuation phenomena arises in nonlinear stage of the SRS - the random spikes, usually called soliton-like, are observed in the depleted pump [2]. Here we shown that the reason for these soliton-like spikes is the conservation of the relative phase Δϕ=ϕL−ϕS+ϕQ of the laser, Stokes and the polarization wanes [3].