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Journal of the Optical Society of America B

Control of transverse spatial modes in transient stimulated Raman amplification

Michael D. Duncan, Rita Mahon, Lawrence L. Tankersley, John F. Reintjes

Published Jul 1, 1990• 33 citations
Publisher

Abstract

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.

DOI
10.1364/josab.7.001336

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Control Of Transient Raman Amplifiers

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Imaging and quantum interference in a low light level Raman amplifier

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Physical Review A•Feb 1, 1992•14 citations
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.
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 previously reported experimental results of Raman amplification of a low-light-level seed-Stokes beam in the transient limit.1 Here we present results of measurements which used a 10-nsec seed-injected Nd:YAG laser. The 532-nm frequency-doubled output had a duration of 8.5 ns and was used both to generate a 4.5-ns duration seed-Stokes pulse at 683 nm and to pump the 1-m long Raman amplifier. The seed-Stokes beam was spatially filtered, apertured at the Airy minimum, and collimated before the amplifier at a diameter of 5.2 mm. Likewise, the spatial mode of the pump was optimized to be as smooth as possible and was collimated into the Raman amplifier at a diameter of 3.4 mm. With no seed Stokes incident in the amplifier, random spatial patterns characteristic of the quantum-noise initiated, self­generated Stokes light were observed over a spatially gain-narrowed beam size supporting ~ 12 spatial modes. For the Raman gains of ~105 used in these experiments the number of temporal modes was 1.8. The seed-Stokes light was used to illuminate a bar chart of line-width 0.315 mm, and either a direct image of the bar chart, or its Fourier transform, was amplified in the Raman amplifier. The original bar chart image was then observed using an intensified camera. As the level of seed-Stokes was reduced to that approaching one photon per spatial-temporal mode, we were able to observe intensity modulations approaching 100% within the amplified bar chart images. Modulation levels of a few percent persist out to input levels of ~103 photons per mode. This observation is consistent with an interpretation of interference between electric field of the seed-Stokes beam and the vacuum fluctuations present in the amplifier but is inconsistent with a photon number description where the maximum predicted modulation would be only 50%.
We have carried out an experiment to study the spatial correlation of the Stokes pulses in transient stimulated Raman scattering. The spatial pattern of Stokes pulses is known to fluctuate from shot to shot due to the buildup of the pulses from quantum noise. We have measured a series of spatial profiles of the Stokes intensity for different Fresnel numbers and Raman gains. A correlation area of the Stokes pulses is obtained by calculating the autocorrelation function of an ensemble of the intensity profiles for each set of parameters. The measured results are compared to existing theories.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.
We have investigated the noise characteristics and the low-light-level imaging capabilities of a stimulated Raman amplifier. Diffraction-limited Stokes beams as well as Stokes beams carrying spatial structure have been amplified with a collimated pump with a Fresnel number in the range 3–17. Both direct imaging and Fourier-transform imaging of the Stokes signal through the Raman amplifier were used. Results indicate that approximately 1–4 photons per spatial mode are needed to produce images with a signal-to-noise ratio of 1. Amplification of the Fourier transform of the object effectively provides spatial filtering of the noise and gives the best signal-to-noise ratio at the lowest input levels for our experiments.
We present a measurement of the beam-pointing fluctuations of a transient Raman-amplifier output using an interferometric method and a theoretical treatment of the three-dimensional, spatial propagation of transient stimulated Raman scattering (SRS) including the fluctuations of the Stokes field giving rise to the beam-pointing fluctuations. The theory is based on an effective steady-state model for the transient SRS process. By using nonorthogonal transverse modes to expand the field, we incorporate the effects of excess spontaneous-emission noise associated with gain-guided amplifiers. The agreement of the measurements with the theoretical treatment demonstrates that the beam-pointing jitter is caused by quantum noise. The beam-pointing fluctuations increase as the Fresnel number of the interaction volume increases because more spatial modes are excited.