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Optics Communications

A symmetry analysis in the mixed grating geometry of degenerate four-wave mixing in saturable-gain media

R. Gutiérrez-Castrejón, K.M. Hung, Trevor J. Hall

Published Jul 1, 1996• 5 citations
Publisher
DOI
10.1016/0030-4018(96)00159-9

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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.

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Four-wave mixing and gain-gratings in laser materials

A. Brignon, Jean‐Pierre Huignard

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.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1996•0 citations
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.
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.
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.