Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Conference on Lasers and Electro-Optics

Generalized time-dynamics of saturable gain four-wave mixing applied to adaptive laser resonators

Darren Udaiyan, Graham J. Crofts, Michael J. Damzen

Published Jan 1, 2000• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleo.2000.906855

Related papers

Transient analysis of four-grating copolarized four-wave mixing in saturable gain media with finite probe

K. S. Syed, Graham J. Crofts, Michael J. Damzen

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.

Journal of the Optical Society of America B•Sep 1, 1996•13 citations

Effect of pump beam propagation on transient degenerate four-wave mixing in saturable Nd:YAG amplifiers

A. Brignon, Jean‐Pierre Huignard

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

Transient analysis of degenerate four-wave mixing with orthogonally polarized pump beams in a saturable Nd:YAG amplifier

A. Brignon, Jean‐Pierre Huignard

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.>

IEEE Journal of Quantum Electronics•Jan 1, 1994•29 citations

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

Robert Elsner, Roland Ullmann, Axel Heuer +2 more

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.

Optics Express•Mar 12, 2012•3 citations

Temporal analysis of pulsed phase conjugation in laser amplifiers: application to Nd:YVO_4

A. Brignon

The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.

Journal of the Optical Society of America B•Aug 1, 1996•4 citations

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
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.
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 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
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 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.
The theory of phase conjugation in laser amplifiers by saturable-gain degenerate four-wave mixing with copolarized beams is developed for pulses of arbitrary temporal shape and duration in the limit of a weak signal beam. The influence of the input pulse’s characteristics (energy, temporal pulse shape, duration) on the phase-conjugate reflectivity and on the conjugate pulse shape is analyzed. A sharp instantaneous peak of phase-conjugate reflectivity is predicted at high intensities of the four-wave mixing beams. This effect is experimentally demonstrated at λ0 = 1064 nm in a Nd:YVO4 amplifier pumped by a cw Ti:sapphire laser. A transient peak reflectivity of R ∼ 50% is thus obtained, corresponding to an enhancement of 1.6× compared with the maximum steady-state reflectivity. The experimental results and the theoretical predictions are in good agreement.
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.