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Annual Meeting Optical Society of America

Phase waves and the statistics of Raman solitons

John C. Englund, Charles M. Bowden

Published Jan 1, 1988• 0 citations
Publisher

Abstract

When vacuum fluctuations at the Stokes frequency are amplified through the interaction of a coherent pump with a Raman medium, large phase shifts in the Stokes field may survive well into its macroscopic regime. Because the response time of the medium’s polarizability is finite, the relative phase of the polarizability and the Stokes field exhibits a peak, called a phase wave. Correspondingly, the pump reacts to a sufficiently large phase shift by briefly repleting before continuing its depletion, thus forming a solitary wave or soliton. It is possible to use the statistical properties of phase waves to predict such observables as the frequency of soliton production, the distribution of soliton amplitudes, and the soliton delay-time statistics.

DOI
10.1364/oam.1988.fv2

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When vacuum fluctuations at the Stokes frequency are amplified through the interaction of a coherent pump with a Raman medium, large phase shifts in the Stokes field may survive well into its macroscopic regime. Because the response time of the medium’s polarizability is finite, the relative phase of the polarizability and the Stokes field exhibits a peak, called a phase wave. Correspondingly, the pump reacts to a sufficiently large phase shift by briefly repleting before continuing its depletion, thus forming a solitary wave or soliton. It is possible to use the statistical properties of phase waves to predict such observables as the frequency of soliton production, the distribution of soliton amplitudes, and the soliton delay-time statistics.
The statistical properties of spontaneously generated Raman solitons are of significant interest because they reflect the statistics of the photon vacuum. These solitons arise when the fluctuating vacuum nearly vanishes at a space-time point (i.e., its expectation values nearly vanish). At such a point, a near phase reversal takes place, so that molecules that are phased to absorb incident radiation instead emit radiation at that frequency; with subsequent phase disruption caused by molecular collisions, phase locking is reestablished, and the radiation is again absorbed. The sequence of pump-frequency absorption, emission, and absorption produces a peak in the pump signal whose width is approximately the mean collision time. Such peaks are shaped by further propagation and show remarkable stability. Although they eventually decay, many survive into the macroscopic regime and may be detected. Specifically, using parameters consistent with ongoing experiments, we have found that solitons having peak intensities greater than one-tenth the pump-pulse maximum can be detected in ~12% of the pulses sent through the Raman medium. The delay time distribution of the solitons decays quasiexponentially, while the soliton height distribution appears to be bimodal.
The formalism of Englund and Bowden [Phys. Rev. A 42, 2870 (1990)] is used to conduct a detailed investigation into the statistics of spontaneously generated Raman solitons and their origin in phase waves. Two approaches are adopted. In one, a Monte Carlo simulation of the stochastic differential equations describing stimulated Raman scattering is carried out, with quantum noise entering through the Stokes vacuum. The other involves determining analytically the field statistics in the quantum-initiation regime, finding the corresponding phase-wave statistics, and determining numerically the class of phase waves that appear in the nonlinear regime as solitons. Computations involving quasi-Gaussian and rectangular pump-pulse profiles consistently indicate soliton yields of roughly 10% and 4%, respectively; differences in the distributions of soliton delay times and peak intensities are also indicated. The Monte Carlo method is adapted to the experimental parameter values of MacPherson et al. [Phys. Rev. A 40, 6745 (1989)], and gives yields and distribution in good accord with the experiment.
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.
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].
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%.