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Journal of the Optical Society of America B

Quantum statistical properties of stimulated Raman generation

M. G. Raymer

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

Quantum fluctuations of pulse energy and shape are observed when stimulated Raman generation is pumped by temporally smooth or fluctuating laser pulses. In the case of smooth single-mode frequency-doubled Nd:YAG laser pulses, the generated Stokes pulse energy is seen to fluctuate by more than 100%, although the pulses are macroscopic in energy.1

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Quantum statistics of stimulated Raman scattering using a Gaussian-profile pump

S. J. Kuo, Czesław Radzewicz, Michael G. Raymer

An experimental study of stimulated Raman scattering (SRS) has been performed using a subnanosecond pulse to investigate the statistical properties of Stokes light generation.1 There are macroscopic fluctuations of Stokes pulse energy as well as random generation of spatial mode patterns. When the scattering volume has a low Fresnel number, the spatial patterns of the SRS resemble cavity modes. When the Fresnel number is large, there are irregular structures appearing across the Stokes profile in a random fashion. A theoretical study of the spatial and temporal coherence properties of Raman generation using a Gaussian-profile pump pulse has also been carried out. Using a Gaussian-Laguerre mode expansion technique,2 it is found that the higher-order spatial coherence modes1 experience different gain than the lower-order spatial coherence modes, and consequently the temporal coherence associated with each individual spatial coherence mode is different.

Annual Meeting Optical Society of America•Jan 1, 1987•1 citation

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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Ian A. Walmsley

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.

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We calculate the probability distribution P(W) for the energy W of pulses generated by transient stimulated Raman scattering and find that 100% macroscopic fluctuations are predicted. In the limit of large numbers of Stokes photons we find that P(W) is essentially exponential, implying that the most probable value for Stokes pulse energy is near zero. The macroscopic energy fluctuations, whose origin is quantum mechanical, may impose a fundamental limitation on the stability of the Raman generation process.

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Quantum Fluctuations in Picosecond Transient Stimulated Raman Scattering

N. Fabricius, Kurt Nattermann, Dietrich von der Linde

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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Phase Quasi Integral for Stimulated Raman Scattering Initiated by Quantum Fluctuations and Statistics of Soliton-Like Random Pulses in Depleted Pump

S. Ya. Kilin

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].

Nonlinear Dynamics in Optical Systems•Jan 1, 1992•0 citations
Quantum fluctuations of pulse energy and shape are observed when stimulated Raman generation is pumped by temporally smooth or fluctuating laser pulses. In the case of smooth single-mode frequency-doubled Nd:YAG laser pulses, the generated Stokes pulse energy is seen to fluctuate by more than 100%, although the pulses are macroscopic in energy.1
An experimental study of stimulated Raman scattering (SRS) has been performed using a subnanosecond pulse to investigate the statistical properties of Stokes light generation.1 There are macroscopic fluctuations of Stokes pulse energy as well as random generation of spatial mode patterns. When the scattering volume has a low Fresnel number, the spatial patterns of the SRS resemble cavity modes. When the Fresnel number is large, there are irregular structures appearing across the Stokes profile in a random fashion. A theoretical study of the spatial and temporal coherence properties of Raman generation using a Gaussian-profile pump pulse has also been carried out. Using a Gaussian-Laguerre mode expansion technique,2 it is found that the higher-order spatial coherence modes1 experience different gain than the lower-order spatial coherence modes, and consequently the temporal coherence associated with each individual spatial coherence mode is different.
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
We calculate the probability distribution P(W) for the energy W of pulses generated by transient stimulated Raman scattering and find that 100% macroscopic fluctuations are predicted. In the limit of large numbers of Stokes photons we find that P(W) is essentially exponential, implying that the most probable value for Stokes pulse energy is near zero. The macroscopic energy fluctuations, whose origin is quantum mechanical, may impose a fundamental limitation on the stability of the Raman generation process.
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.
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].