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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Four-wave mixing and gain-gratings in laser materials

A. Brignon, Jean‐Pierre Huignard

Published Jan 1, 1996• 0 citations
Publisher

Abstract

Phase conjugal ion by degenerate four-wave mixing (DTVVM) in saturable gain media is a nonlinear process of major interest for applications to dynamic holography and phase-distortion correction of an optical wave propagating in laser media [1,2,3]. The use of laser amplifiers for such operations presents very attractive features including the automatic matching of the nonlinearity with the laser wavelength, a fast response time and a high efficiency of the nonlinear process due to the laser amplification of all interacting beams. This process is based on the possibility of writing dynamic gain gratings when interfering beams are propagating in a laser medium by gain saturation.

DOI
10.1364/cleo_europe.1996.cmk1

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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1994•0 citations
Phase conjugal ion by degenerate four-wave mixing (DTVVM) in saturable gain media is a nonlinear process of major interest for applications to dynamic holography and phase-distortion correction of an optical wave propagating in laser media [1,2,3]. The use of laser amplifiers for such operations presents very attractive features including the automatic matching of the nonlinearity with the laser wavelength, a fast response time and a high efficiency of the nonlinear process due to the laser amplification of all interacting beams. This process is based on the possibility of writing dynamic gain gratings when interfering beams are propagating in a laser medium by gain saturation.
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
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
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.
A presentation is made of recent work in 3-D saturable gain-gratings, produced by spatial hole-burning, as efficient, externally programmable and/or self-adaptive diffractive optical elements for application in gain-media phase conjugators and as a technology for versatile adaptive spatial, spectral, and Q-switching control of high-gain solid-state lasers. Description is to be mainly made of gain-gratings written by spatial hole-burning when coherent beams, at the lasing wavelength, interfere in a gain medium. Such 3-D gain gratings, which have a persistence for the upper-state lifetime of the gain medium, can be considered as volume gain holograms and the application of these adaptive grating devices can be considered as a type of dynamic "gain holography."
Degenerate four-wave mixing (DFWM) interaction in saturable media has received considerable attention because of its potential for application to optical phase conjugation and correction of phase distortions through aberrating media. For this purpose, saturable solid-state materials, operating at the classical wavelength of neodymium lasers near λ0 = 1.06 μm, are of great interest. Here, we present DFWM in a tetravalent chromium-doped gadolinium-scandium-gallium-garnet (Cr4+:GSGG) crystal. Indeed, tetravalent chromium (Cr4+) doped crystals were recently shown to be effective solid-state saturable absorbers for neodymium lasers.1,2 Furthermore, in comparison with traditional saturable absorbers such as dyes in solution, polymeric films, and color-center materials, these crystals exhibit chemical stability, high optical damage threshold, compactness, and would enable operation at high repetition rates.