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Annual Meeting Optical Society of America

Quantum initiation of stimulated Raman scattering

R. C. Swanson, David C. MacPherson, John L. Carlsten

Published Jan 1, 1988• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oam.1988.fv3

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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.
Results from a study of quantum noise and its macroscopic manifestations in stimulated Raman scattering are presented.Shot to shot fluctuations in quantum noise initiated Stokes spectra are considered.The Stokes spectra were recorded experimentally using a Fabry-Perot interferometer.For comparison, numerically generated Stokes spectra were produced using the semi-classical model of stimulated Raman scattering with a numerically generated "vacuum" input field.The amount of structure on each spectrum was quantified by calculating the spectrum's standard deviation from its mean frequency.It was found that ensembles with the noisy spectra removed had narrower distributions of mean frequencies than ensembles that included noisy spectra.
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.
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 use the dressed-state representation to generate the full quantum-mechanical treatment of stimulated Raman scattering (SRS). Equations of motion and propagation are obtained from the Heisenberg equations of motion in the plane-wave limit and under conditions such that anti-Stokes and higher-order Stokes processes can be neglected. Equations for a stochastic model, based upon antinormal ordering and a quantum-classical correspondence are developed from them, suitable for numerical ensemble calculations for the study of amplified quantum fluctuations and spontaneously generated phase waves and solitons. Several alternative approaches, which have more general validity but present greater difficulty in numerical implementation, are also developed by introduction of quasiprobability functions and their associated Fokker-Planck equations from which corresponding stochastic equations of motion and propagation are derived. The Q representation, whose moments correspond to expectation values of products of antinormally ordered fields, and normally ordered atomic operators yield stochastic equations identical to the equations for the stochastic model developed directly from the Heisenberg equations for the same initial and boundary conditions, giving strong credence to the stochastic model. The Wigner representation, whose moments correspond to expectation values of symmetrically ordered operators, leads to a set of equations that are valid where the stochastic model fails, namely, where conditions are such that quantum fluctuations and nonlinearity are simultaneously important. The stochastic model, which is shown to be, by far, the simplest to implement in numerical calculations, is shown also to be valid for the conditions of SRS.