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Physical Review Letters

Spontaneous Generation of Raman Solitons from Quantum Noise

John C. Englund, Charles M. Bowden

Published Nov 24, 1986• 74 citations
Publisher

Abstract

Large phase shifts that arise during the quantum initiation of stimulated Raman scattering are shown to induce solitons in the pump intensity. These phase shifts are associated with phase waves, which were previously discovered in quantum superfluorescence theory.
DOI
10.1103/physrevlett.57.2661

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Conditions For The Spontaneous Generation Of Solitons In Stimulated Raman Scattering

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Quantum phase fluctuations may be amplified into large, sudden phase shifts in the Stokes field, which subsequently give rise to solitons in the pump intensity. Ensemble simulations indicate that increased dissipation due to collisional dephasing within the medium significantly increases the frequency of soliton generation. The statistical distribution of soliton heights and positions is described.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 8, 1988•4 citations

Spontaneous generation of phase waves and solitons in stimulated Raman scattering. II. Quantum statistics of Raman-soliton generation

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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.

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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.

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Spontaneously generated Raman solitons

Charles M. Bowden, John C. Englund

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.

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Raman Solitons and Raman spikes

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Stimulated Raman scattering of a laser pump pulse seeded by a Stokes pulse generically leaves a two-level medium initially at rest in an excited state constituted of static solitons and radiation. The soliton birth manifests as sudden very large variations of the phase of the output pump pulse. This is proved by building the IST solution of SRS on the semi-line, which shows moreover that initial Stokes phase flips induce Raman spikes in the pump output also for short pulse experiments.

arXiv:solv-int/9703007•Mar 10, 1997•1 citation
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.
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.
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.