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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Conditions For The Spontaneous Generation Of Solitons In Stimulated Raman Scattering

John C. Englund, Charles M. Bowden

Published Apr 8, 1988• 4 citations
Publisher

Abstract

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.

DOI
10.1117/12.943857

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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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Theoretical and experimental details of initiating and amplifying a Stokes pulse using stimulated Raman scattering in H2 are presented.Statistics associated with the spectral fluctuations of a Stokes seed pulse have been measured and theoretically calculated.The spectral fluctuations are shown to result from quantum noise associated with spontaneous initiation.These spectral fluctuations are an example of an easily measurable macroscopic fluctuation of quantum origin.The effects of frequency fluctuations on the generation of solitons in the nonlinear regime of stimulated Raman scattering are calculated and measured.A detailed derivation of the fully quantum mechanical stimulated Raman scattering equations is given along with their solution for various approximations.The driven Maxwell's equation for the Raman system is derived from the system Hamiltonian.For treating the quantum initiation of stimulated Raman scattering, the radiation field is expanded in localized coherent modes.The details of calculating and using these modes to generate an ensemble of Stokes pulses are presented along with specific examples and ensemble average statistics.The use of localized modes for treating the pulsed cavityless Raman laser gives insight into the spontaneous initiation of Stokes pulses.iv ACKNOWLEDGMENTS I feel very fortunate to have had Dr. John Carlsten for my thesis adviser.I would like to thank John for making graduate school an enjoyable part of life and for the many hours o f stimulating discussions on fundamental physics.I am also greatly indebted to my wife, Susie, for filling my big lunch bag every morning and for her many hours spent typing this thesis

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Generation of solitons in transient stimulated Raman scattering by optical phase shift

David C. MacPherson, John L. Carlsten

Several groups1,2 are studying the use of optical phase shifts to initiate soliton formation in transient stimulated Raman scattering. Our experiments use a generator-amplifier Raman laser pumped by a frequency-doubled Nd:YAG laser at 532 nm. The Raman medium is hydrogen at 1-100 atm. We use an electrooptic crystal to place a π phase shift in the Stokes beam between the generator and amplifier. This shift momentarily reverses the direction of gain. The phase shift is produced by modulating the amplitude of the Stokes envelope through zero using polarizers and a Pockels cell. Numerical calculations indicate that solitons can be initiated by switching the Pockels cell voltage over a time of several nanoseconds. Development of the temporal pulse is shown in Fig. 1. Once initiated the soliton pulse can narrow to a width of a few picoseconds if the collisional dephasing time (1/Γ) is 60 ps. The width W (HWHM) of the evolving pulse is shown in Fig. 2 (⨉). The solid curve is the pulse width predicted by steady- state theory, which is initially valid because the field envelopes change slowly compared with 1/Γ.

•Apr 26, 1987•0 citations
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.
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.
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.
Theoretical and experimental details of initiating and amplifying a Stokes pulse using stimulated Raman scattering in H2 are presented.Statistics associated with the spectral fluctuations of a Stokes seed pulse have been measured and theoretically calculated.The spectral fluctuations are shown to result from quantum noise associated with spontaneous initiation.These spectral fluctuations are an example of an easily measurable macroscopic fluctuation of quantum origin.The effects of frequency fluctuations on the generation of solitons in the nonlinear regime of stimulated Raman scattering are calculated and measured.A detailed derivation of the fully quantum mechanical stimulated Raman scattering equations is given along with their solution for various approximations.The driven Maxwell's equation for the Raman system is derived from the system Hamiltonian.For treating the quantum initiation of stimulated Raman scattering, the radiation field is expanded in localized coherent modes.The details of calculating and using these modes to generate an ensemble of Stokes pulses are presented along with specific examples and ensemble average statistics.The use of localized modes for treating the pulsed cavityless Raman laser gives insight into the spontaneous initiation of Stokes pulses.iv ACKNOWLEDGMENTS I feel very fortunate to have had Dr. John Carlsten for my thesis adviser.I would like to thank John for making graduate school an enjoyable part of life and for the many hours o f stimulating discussions on fundamental physics.I am also greatly indebted to my wife, Susie, for filling my big lunch bag every morning and for her many hours spent typing this thesis
The π phase jump generated spontaneously in stimulated Raman scattering, which is the origin of Raman soliton formation, has been investigated. The probability of Raman soliton generation is measured as a function of the pressure of the Raman medium and the pump intensity. The relation between the soliton’s shape and the magnitude of the phase jump has been revealed by homodyne phase detection of the Stokes phase. These results are compared with numerical calculation, and qualitative agreement is obtained. The stochastic nature of Raman soliton generation is discussed in terms of the phase jump’s magnitude and evolution through the Raman medium.
Several groups1,2 are studying the use of optical phase shifts to initiate soliton formation in transient stimulated Raman scattering. Our experiments use a generator-amplifier Raman laser pumped by a frequency-doubled Nd:YAG laser at 532 nm. The Raman medium is hydrogen at 1-100 atm. We use an electrooptic crystal to place a π phase shift in the Stokes beam between the generator and amplifier. This shift momentarily reverses the direction of gain. The phase shift is produced by modulating the amplitude of the Stokes envelope through zero using polarizers and a Pockels cell. Numerical calculations indicate that solitons can be initiated by switching the Pockels cell voltage over a time of several nanoseconds. Development of the temporal pulse is shown in Fig. 1. Once initiated the soliton pulse can narrow to a width of a few picoseconds if the collisional dephasing time (1/Γ) is 60 ps. The width W (HWHM) of the evolving pulse is shown in Fig. 2 (⨉). The solid curve is the pulse width predicted by steady- state theory, which is initially valid because the field envelopes change slowly compared with 1/Γ.