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Annual Meeting Optical Society of America

Raman soliton statistics

John C. Englund, Charles M. Bowden

Published Jan 1, 1989• 0 citations

Abstract

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.

DOI: 10.1364/oam.1989.tuf2

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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.

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 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.

Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.

The origin and statistical behavior of spontaneously generated Raman solitons (SGRSs) are discussed in terms of quantum fluctuations which cause quantum initiation of the Stokes field in a Raman gain medium in the presence of a strong pump field. The macroscopic temporal statistical behavior in superfluorescence, swept-gain superfluorescence, and SGRS is interpreted in terms of the amplification of quantum noise of similar origin. Predictions are presented for the observation of unique macroscopic statistical properties of SGRS as robust direct manifestations of quantum phase fluctuations.

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.