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Journal of the Optical Society of America B

Transient phase conjugation by degenerate four-wave mixing in saturable dyes

H. Fujiwara, K. Nakagawa

Published Feb 1, 1987• 39 citations
Publisher

Abstract

Transient phase conjugation by degenerate four-wave mixing in saturable dyes is investigated theoretically and experimentally. Two special cases are examined: (1) the case in which two pump waves and a probe wave are simultaneously turned on and (2) the case in which the pump waves are turned on well before the incidence of the probe wave. For case (1) a peak appears in the transient reflectivity for high pump intensity, while for case (2) the reflectivity increases monotonically with time up to the steady-state value irrespective of the value of the pump intensity.

DOI
10.1364/josab.4.000121

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Annual Meeting Optical Society of America•Jan 1, 1989•0 citations
Transient phase conjugation by degenerate four-wave mixing in saturable dyes is investigated theoretically and experimentally. Two special cases are examined: (1) the case in which two pump waves and a probe wave are simultaneously turned on and (2) the case in which the pump waves are turned on well before the incidence of the probe wave. For case (1) a peak appears in the transient reflectivity for high pump intensity, while for case (2) the reflectivity increases monotonically with time up to the steady-state value irrespective of the value of the pump intensity.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.
Phase conjugation by degenerate four-wave mixing in a saturable absorbing medium with a relatively long-lived excited state is analyzed; the analytical results are compared with experimental results. We propose a four-level model and take into account the effects of both excited-state absorption and pump propagation to explain the experimental results, which could not be explained by the models proposed previously. The numerical result predicts that the value of the phase-conjugate reflectivity as a function of the pump intensity is maximum at a certain absorbance (as absorbance increases) that is dependent on the cross section of the excited-state absorption. The present analysis explains most observations in the experiment, which was performed with a saturable-dye-doped polymer film as the saturable absorbing medium.
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.
We have derived an analytic expression for the intensity distribution of two counterpropagating waves of arbitrary input intensity in a saturable absorber. We use this distribution to extend the theory of degenerate four-wave mixing to include the effects of pump wave absorption. In particular, the spatial variation of the nonlinear absorption and coupling constants that appear in the coupled-amplitude equations for the probe and the signal (i.e., conjugate) waves are determined. These coupled-amplitude equations are solved numerically in a noniterative manner, leading to a prediction for the phase-conjugate reflectivity. The nature of the predictions differs qualitatively from those1,2 derived from theories that ignore pumpwave absorption, especially for the case of off-line-center excitation. At large values of the input pump intensities, the phase conjugate reflectivity can be larger than that predicted by theories that ignore pump-wave absorption.
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.
Rigidly held molecules display nonlinear optical properties which differ substantially from the properties of isotropic absorbers.1 In particular, the absorption of a collection of randomly oriented, rigidly held molecules saturates differently for different polarization states. We show that the polarization properties of degenerate four-wave mixing in such a medium are dramatically modified by this polarization-dependent saturation. We predict theoretically that for linearly polarized pump waves and for an input intensity near the saturation intensity, degenerate four-wave mixing in this material system can lead directly to vector phase conjugation; that is, to the simultaneous reversal of the optical wavefront and conjugation of the polarization state of the incident optical field.2 We confirm these theoretical predictions through phase conjugation experiments using fluorescein doped boric acid glass as the material system, and we find that degenerate four-wave mixing leads to nearly perfect vector phase conjugation when pumped by linearly polarized pump waves for field strengths near the saturation intensity.