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Annual Meeting Optical Society of America

Spatial evolution of beam profiles in an SBS amplifier

Edward John Miller, Mark D. Skeldon, Robert W. Boyd

Published Jan 1, 1987• 2 citations
Publisher

Abstract

We have performed an experimental and theoretical analysis of how a probe beam is modified on propagation through an SBS gain medium for various input beam parameters and total gains through the SBS medium. For the case of an undepleted lowest-order Gaussian pump beam, we found that when the probe spot size is smaller than the pump spot size in the focal region, the input probe profile is essentially preserved during amplification. However, if the probe is larger than the pump, the beam is modified as it propagates through the medium and in the limit of high gain takes on the mode structure of the pump. To model these effects mathematically, we decompose the probe wave into Laguerre-Gaussian modes and solve numerically the equations describing the spatial evolution of the individual modes. The result of the nonlinear coupling is to transfer energy from the pump beam to the probe and to redistribute the energy among the probe modes. In some cases, the transmitted probe shows a pronounced ring structure.

DOI
10.1364/oam.1987.mi13

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We have performed an experimental and theoretical analysis of how a probe beam is modified on propagation through an SBS gain medium for various input beam parameters and total gains through the SBS medium. For the case of an undepleted lowest-order Gaussian pump beam, we found that when the probe spot size is smaller than the pump spot size in the focal region, the input probe profile is essentially preserved during amplification. However, if the probe is larger than the pump, the beam is modified as it propagates through the medium and in the limit of high gain takes on the mode structure of the pump. To model these effects mathematically, we decompose the probe wave into Laguerre-Gaussian modes and solve numerically the equations describing the spatial evolution of the individual modes. The result of the nonlinear coupling is to transfer energy from the pump beam to the probe and to redistribute the energy among the probe modes. In some cases, the transmitted probe shows a pronounced ring structure.
Results of numerical simulation of coaxial propagation of an intense pump beam and a weak probe beam in a three-level medium with different types of energy diagrams in conditions of inversionless amplification are presented. The effect of the beam self-action and diffraction on the spatial and frequency characteristics of the probe wave were studied. These effects, in combination with linear absorption and refraction, give rise to complex spatial profiles of gain along the beam propagation path. The annular structure of the amplified beam and a small asymmetry of its frequency characteristics, resulting from the nontrivial gain profile over the beam cross section, were found and studied.
In a highly nonlinear thin film, the presence of the diffracted beams from the pump-probe-beam-induced refractive-index grating modifies considerably the energy coupling between the pump and the probe beams. Using coupled amplitude and phase equations, the roles of various factors such as phases and phase shifts, phase modulations, pump-beam intensity, intensity ratio, interaction length, and losses in the medium in the multiwave-mixing processes are clearly identified. We also present experimental results on the dependence of the probe gain on the pump-probe-beam ratio, the pump intensity, and on the interaction length, using a nematic liquid-crystal film as the nonlinear medium.
The transmission spectra of inversionless amplification are investigated. Propagation of a weak probe optical beam through a three-level medium pumped with a microwave strong beam is numerically modeled. Three various schemes of transitions under the conditions providing the amplification of the probe field without inversion are taken to calculate the atomic polarization, which enters the paraxial wave equations. Diffraction and self-action ofbeams due to nonlinear absorption and refraction are properly taken into account. These effects together with linear absorption and refraction form a complex distribution of gain across the beams. As a result the amplified beam acquires ring transverse patterns and slight asymmetry in the frequency characteristics.
While the interaction of optical beams in photorefractive crystals can often be accurately described in terms of 1-D plane-wave approximation, 2-D models are sometimes more suitable, as suggested by recent work.1 Here we discuss some aspects of photorefractive interaction of finite size optical beams. We have solved the system of partial differential equations governing two- and four-wave mixing numerically by using iterative procedures. Simulations of beam amplification in two-beam coupling show strong beam deformation even without any spatial information imposed on them. Spatially nonuniform energy transfer is responsible for this effect. The pump beam loses energy during propagation and at the end of its passage through the beam intersection region (which was completely inside the crystal) it is strongly depleted and cannot contribute significantly to beam amplification. As the pump beam crosses through the probe, it amplifies most strongly that side of the probe that it meets first. By the time the pump has reached the far side of the probe, it is strongly depleted and less effective at probe amplification. In the case of phase conjugation through four-wave mixing, we found that the conjugate beam is strongly deformed only when the coupling constant is negative (corresponding to deamplification of the probe input beam). For positive coupling constants the output conjugate beam is a good replica of the input probe beam.
Distortions of the probe beam wavefront due to scattering on the thermal lens, which is induced by a pump light field, are calculated using a non-linear geometrical model. It is shown that when the probe beam light spot is larger than the pump field one, the initial Gaussian distribution of intensities becomes ring shaped. When the probe beam diameter is smaller than the pump field one, the initial Gaussian distribution remains almost Gaussian. The predicted effects are confirmed by a calculation that takes into account the diffraction effects at the far field. Experimental evidence for the effect is shown for the case of light propagation through an ethanol solution of iodine.
The polarization-related properties of stimulated Brillouin scattering (SBS) processes in long, randomly birefringent, standard optical fibers are examined. Evolution equations for the pump and signal waves, in the presence of both birefringence and SBS, are provided in Jones and Stokes spaces. It is shown that in the undepleted pump regime, the amplification of the SBS signal wave is equivalent to that of a linear medium with polarization-dependent gain. The process is associated with a pair of orthogonal states of polarizations (SOPs) of the signal wave, which undergo maximum and minimum amplification. In long, standard fibers, the Jones vector of the probe SOP which corresponds to maximum amplification is aligned with the complex conjugate of the pump wave Jones vector. The maximum and minimum SBS gain coefficients in such fibers equal two-thirds and one-third of the gain coefficient that is predicted by scalar theory, respectively. The large differential gain of the SBS process gives rise to an effective pulling of the amplified Stokes probe wave SOP, towards that of maximum amplification. Lastly, Stokes wave pulses that are aligned for maximum and minimum amplification experience different group delays, which manifest as polarization-related distortions in SBS slow light setups.