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Optics Letters

Spectral quantum fluctuations in a stimulated Raman generator: a description in terms of temporally coherent modes

Ian A. Walmsley

Published Mar 15, 1992• 6 citations
Publisher

Abstract

The probability density of the single-shot mean Stokes frequency from a linear Raman generator is calculated. It is shown that the fluctuations in the Stokes pulse energy spectrum that arise from the quantum initiation of the Stokes light are reduced in the transient regime of amplification. Also, it appears that saturation of the Raman gain does not reduce the phase fluctuations of the Stokes light below those present in the unsaturated gain (linear) regime.

DOI
10.1364/ol.17.000435

Related papers

A model of the quantum noise in the Stokes pulse energy spectrum from a transient-stimulated Raman generator

Ian A. Walmsley

Recently Swanson et al.1 have shown that, even in the transient regime of a Raman generator, when the Stokes pulses are nominally transform-limited, the mean frequency of the pulses fluctuates from pulse to pulse. The coherent modes model2 provides a simple, intuitive and computationally efficient method for determining the statistics of the Stokes light from a Raman generator. We use this model to calculate the probability density of the mean frequency of the Stokes pulse energy spectrum and show that it gives reasonable agreement with Swanson et al.'s experimental results. The spectral fluctuations in the transient regime arise because the excitation of high-order temporally coherent modes produces a time-dependent phase structure in the Stokes pulse. The phase of the Stokes field is more sensitive to the excitation of these high-order modes than is its amplitude, so that the pulse energy spectrum exhibits measurable fluctuations in the transient regime, even though the pulse temporal shape does not.3

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Quantum Fluctuations in Picosecond Transient Stimulated Raman Scattering

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From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.

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Quantum fluctuations and soliton generation in stimulated Raman scattering

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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

•Jan 1, 1989•0 citations
The probability density of the single-shot mean Stokes frequency from a linear Raman generator is calculated. It is shown that the fluctuations in the Stokes pulse energy spectrum that arise from the quantum initiation of the Stokes light are reduced in the transient regime of amplification. Also, it appears that saturation of the Raman gain does not reduce the phase fluctuations of the Stokes light below those present in the unsaturated gain (linear) regime.
Recently Swanson et al.1 have shown that, even in the transient regime of a Raman generator, when the Stokes pulses are nominally transform-limited, the mean frequency of the pulses fluctuates from pulse to pulse. The coherent modes model2 provides a simple, intuitive and computationally efficient method for determining the statistics of the Stokes light from a Raman generator. We use this model to calculate the probability density of the mean frequency of the Stokes pulse energy spectrum and show that it gives reasonable agreement with Swanson et al.'s experimental results. The spectral fluctuations in the transient regime arise because the excitation of high-order temporally coherent modes produces a time-dependent phase structure in the Stokes pulse. The phase of the Stokes field is more sensitive to the excitation of these high-order modes than is its amplitude, so that the pulse energy spectrum exhibits measurable fluctuations in the transient regime, even though the pulse temporal shape does not.3
From a classical point of view the generation of Stokes light by stimulated Raman scattering (SRS) is not possible unless a Stokes input signal is supplied. On the other hand, the gain in SRS can be so large that without input the spontaneous build-up of strong Stokes waves can be observed. A proper quantum theoretical description1 shows that this spontaneous initiation of Stokes generation is due to microscopic random fluctuations originating from quantum noise associated with the dynamical variable Q(t) which is active in the Raman process, e.g., a molecular normal mode coordinate. In highly transient SRS -when the duration of the excitation pulse is shorter than the dephasing time- the Stokes field is proportional to the initial Heisenberg operator Q(0) describing the state of the system just before the excitation pulse is turned on (t=0). In this case the statistics of the final Stokes pulse energy is determined by quantum mechanical uncertainties associated with the random Raman polarization of the initial state2. On the other hand, in a steady state situation the Stokes pulse fluctuations are substantially reduced and the Stokes pulse energy is stabilized as a result of damping processes.
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.
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.
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