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IEEE Journal of Quantum Electronics

Transfer of pump spatial variations to Stokes phase in Raman amplifiers

George Valley

Published Sep 1, 1982• 15 citations
Publisher

Abstract

Many applications of forward Raman amplifiers require that transverse spatial amplitude and phase aberrations in the pump beam not be transferred to the phase of the amplified Stokes signal. Detailed one-dimensional depleted-pump calculation are given for two mechanisms that transfer pump aberrations to the Stokes phase. The first is multilongitudinal mode pump fluctuations that vary faster than the coherence time of the Raman transition. The second is saturated dispersion combined with a detuning either due to Raman operation off of line-center or due to the dynamic Stark effect.

DOI
10.1109/jqe.1982.1071706

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Physical Review A•Jan 1, 1990•1 citation
Many applications of forward Raman amplifiers require that transverse spatial amplitude and phase aberrations in the pump beam not be transferred to the phase of the amplified Stokes signal. Detailed one-dimensional depleted-pump calculation are given for two mechanisms that transfer pump aberrations to the Stokes phase. The first is multilongitudinal mode pump fluctuations that vary faster than the coherence time of the Raman transition. The second is saturated dispersion combined with a detuning either due to Raman operation off of line-center or due to the dynamic Stark effect.
We address the problem of pumping Stokes radiation by broadband incoherent laser beams in contrast to aberrated beams. While for aberrated beams the transversal phase variations in any given plane of reference are constant in time, they will fluctuate in time for incoherent beams. As is well known for Raman scattering by broadband lasers, the frequency mode structure of the amplified Stokes beam will be modified by the pump laser, leading to an increase in temporal correlation between pump and Stokes. For collinear pumping by an incoherent pump this implies that the amplified Stokes beam will also be incoherent, even if seeded initially with a coherent beam. For transversal pumping geometries Stokes beam coherence will be affected by the reduced temporal correlation between the pump fields at different transversal locations. In the case of resonant scattering (linewidth much smaller than mode spacing), we show that the transversal Stokes coherence length is limited by the longitudinal coherence length of the pump. In addition, a reduction in gain occurs. We present analytical and numerical results which indicate corresponding limitations for intermediate scattering (linewidth comparable to mode spacing), which is the case of practical interest in gases.
We have studied the phase pulling and locking of an injected Stokes pulse in a transient Raman amplifier both experimentally and theoretically. In addition, we have investigated the pulse energy statistics and related spatial modes of a high gain amplified Stokes pulse. Experiments reported here show that in the unsaturated case, the phase of the amplified Stokes is pulled almost instantaneously to that of the pump, as soon as integrated gain levels of slightly greater than unity are reached. For higher input seed-Stokes levels, such that the amplified Stokes energy is saturated, the phase locking is completed early, and the phase of the amplified Stokes then follows the phase excursion of the pump. The phase pulling has been modelled theoretically for the specific parameters of our experiment. We have also used the pulse energy statistics to study the seed-Stokes control of a high gain Raman amplifier. For an input seed-Stokes beam to control a transient, high gain Raman amplifier, operated near threshold, it must dominate the self-generated Raman which builds from quantum noise. For a near-unity-Fresnel-number Raman amplifier we have measured the number of input seed-Stokes photons needed to produce an unchanged statistical signature on the amplified Stokes pulse and have found that a surprisingly large number (109) were needed. For a larger Fresnel number Raman amplifier, a near-field camera was used to study the level at which the seed-Stokes pulse controlled the spatial output of the amplifier. Control of the spatial modes seems to have a sharp threshold with input Stokes energy and was fully established with an input of 2x103 photons per mode.
We have studied the transverse modes of a transient stimulated Raman signal generated in unsaturated Raman amplifiers with Fresnel numbers from one to seven, both with and without a seed Stokes pulse. In the absence of a seed Stokes pulse and for a pump Fresnel number greater than 1.5, the spatial intensity pattern of the stimulated Stokes signal is highly variable from shot to shot, reflecting the random nature of the quantum-noise source. However, when a separately generated and sufficiently strong seed Stokes pulse with a Gaussian spatial profile is injected into the amplifier, the spatial mode of the output Stokes beam assumes a smooth Gaussian spatial pattern that is significantly smaller in diameter than either the pump or the seed Stokes beam. This spatial mode control, which is due to the injected Stokes signal, persists down to a level of approximately 300 seed Stokes photons per spatial mode and, surprisingly, is observed to suppress the noise-initiated signal by at least a factor of 10 in the outer regions of the amplified Stokes beam. We have also studied the Stokes pulse-energy statistics over a range of Fresnel numbers. Data taken with systems having Fresnel numbers between 4 and 7 follow the same pattern as the spatial-mode-control results in that the statistical character of the Stokes pulse energies changes rapidly from that characteristic of a quantum-noise-initiated process to one characteristic of a stable source as the level of the injected seed Stokes is increased. However, for interaction regions with Fresnel numbers of 1 or smaller, the Stokes pulse-energy statistics show a gradual change as the level of the seed Stokes signal is increased and do not become stabilized until the seed Stokes is more than 100 times the total level needed to control the spatial character of the output Stokes in the larger-Fresnel-number cases. This slow change in the statistics for the Fresnel 1 system, and the suppression of the quantum-noise-initiated signal in the larger-Fresnel-number systems, is not fully understood at this time.
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.