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Optics Express

Two-dimensional modeling of transient gain gratings in saturable gain media

Robert Elsner, Roland Ullmann, Axel Heuer, Ralf Menzel, Martin R. Ostermeyer

Published Mar 12, 2012• 3 citations
Publisher

Abstract

A transient two-dimensional model describing degenerate four-wave mixing inside saturable gain media is presented. The new model is compared to existing one-dimensional models with their qualitative results confirmed. Large quantitative differences with respect to peak reflectivity and optimum pump fluence are observed. Furthermore, the influence of the beam focus size, the transverse position and the crossing angle on the reflectivity of the grating is investigated using the improved model. It is demonstrated that the phase conjugate reflectivity depends sensitively on the transverse features of the interacting beams with a transverse shift in the position of the pump beams yielding a threefold improvement in reflectivity.

DOI
10.1364/oe.20.006887

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Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1994•0 citations
A transient two-dimensional model describing degenerate four-wave mixing inside saturable gain media is presented. The new model is compared to existing one-dimensional models with their qualitative results confirmed. Large quantitative differences with respect to peak reflectivity and optimum pump fluence are observed. Furthermore, the influence of the beam focus size, the transverse position and the crossing angle on the reflectivity of the grating is investigated using the improved model. It is demonstrated that the phase conjugate reflectivity depends sensitively on the transverse features of the interacting beams with a transverse shift in the position of the pump beams yielding a threefold improvement in reflectivity.
We model transient copolarized degenerate four-wave mixing in a saturable gain medium, using pulses of duration much shorter than the population lifetime with a finite probe beam. Initially we describe a model to include the simultaneous existence of both the reflection and transmission gratings for arbitrary field strengths. Then we develop a model to include all four possible gratings, including standing-wave gratings between counterpropagating pump beams and the probe and conjugate beams. By use of two expansion methods for the higher-order grating terms it is possible to model regimes in which either one grating is arbitrarily strong or all four gratings are strong. Comparisons are made among models including one, two, and four gratings. Good agreement is found between the theoretical four-grating case and pulsed copolarized degenerate four-wave mixing experiments in laser-pumped Ti:sapphire for a finite probe beam.
Co-polarised degenerate four-wave mixing (DFWM), in which all the four interacting beams have the same direction of polarisation, has been utilised to generate high phase conjugate reflectivities (~ 2500) recently [1]. In the co-polarised geometries six gratings are written in the material in which each beam forms a grating with another beam. Several theoretical models have been used to describe this co-polarised DFWM process in gain media [2]-[3]. However, all of them involve the use of small probe approximation and hence not all gratings are present in these models. Moreover, the effect of pump depletion has been neglected. A novel approach using the underlying symmetry is described recently to solve the co-polarised DFWM problem [4]. This approach allows us to take into account the effect of pump depletion, although the two standing gratings between the pumps and between the probe and the conjugate beams are ignored.
Summary form only given. Gain gratings in laser media have been extensively studied to understand gain four-wave mixing (FWM) as a means of achieving phase conjugation, particularly in the steady-state and highly-transient regimes. We present an analysis of the generalized time regime (including pumping and spontaneous emission) and model the time-dependent evolution of the gain grating from the highly transient to the steady-state for arbitrary beam strength. For the first time to our knowledge, this analysis considers the formation of a combined transmission and reflection gain grating.
Degenerate four-wave mixing with orthogonally polarized pump beams at /spl lambda/=1.06 /spl mu/m in the saturable gain of a flash-lamp-pumped Nd:YAG amplifier is investigated, both experimentally and theoretically, using pulses of duration much less than the population relaxation time. We introduce a new set of coupled-wave equations in this short pulse regime that includes the effect of the four interacting waves and the laser gain experienced by all the beams. The dependence of the efficiency of the process on the small-intensity-gain-length product, beam ratios, and fluences is analyzed. A reflectivity of a weak probe beam of 25 percent and a transmission-gain-grating diffraction efficiency of 32 percent are achieved. Finally, the temporal shape of the conjugate signal is studied for various gain-saturation regimes.>
A transient model of degenerate four-wave mixing in saturable amplifiers is developed for calculation of the phase-conjugate reflectivity in the weak-probe-beam limit. Our model takes into account the laser amplification of all the interacting beams together with the wave-mixing process between the two counterpropagating pump waves. Experimental investigations are made in a flash-lamp-pumped Nd:YAG amplifier with nanosecond pulses at 1.06 microm. A reflectivity of 22% is achieved when all the waves interfere within the laser medium.
Phase distortion correction of an optical wave propagating in laser media is a crucial problem to be taken into account in most of laser systems. For this purpose, phase conjugation through stimulated Brillouin scattering using the master oscillator-power amplification configuration has shown a very good potential to obtain high beam quality in solid-state lasers that operate at variable repetition rates. Another attractive alternative to generate the phase-conjugate wavefronts is to use a four-wave mixing (DFWM) process in the laser amplifier. In this medium, the interference between the interacting beams leads to a spatial modulation of the complex susceptibility of the medium by gain saturation (amplitude gain grating). This all-solid-state solution presents the advantage of suppressing the external nonlinear medium and would realize the required functions in the laser medium itself. Moreover, due to the amplification experienced by all the interacting beams, associated to the resonant nonlinearity of the gain saturation, high reflectivities already have been achieved in Nd:YAG amplifiers using a multipass geometry.1,2