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Optics Letters

Efficiency of degenerate four-wave mixing in a two-level saturable absorbing medium

R. J. Knize

Published Oct 1, 1993• 13 citations
Publisher

Abstract

Degenerate four-wave mixing in a two-level saturable absorbing medium is calculated on and off resonance for arbitrary input laser intensities and absorption coefficients. The maximum efficiency occurs at laser intensities higher than saturation in an optically thick medium. On resonance, the maximum efficiency can approach ∼4%, and it can be as large as 25% when the laser is tuned off resonance.

DOI
10.1364/ol.18.001606

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Journal of the Optical Society of America B•Jun 1, 1993•22 citations
Degenerate four-wave mixing in a two-level saturable absorbing medium is calculated on and off resonance for arbitrary input laser intensities and absorption coefficients. The maximum efficiency occurs at laser intensities higher than saturation in an optically thick medium. On resonance, the maximum efficiency can approach ∼4%, and it can be as large as 25% when the laser is tuned off resonance.
A calculation of degenerate four-wave mixing in a homogeneously broadened two-level saturable absorber is presented. An analytical formula for the local electric dipole polarization responsible for degenerate four-wave mixing is derived for arbitrary electric-field strengths. The overall efficiency of the medium is calculated by numerically solving the coupled wave equations with the use of the phase-matching electric dipole polarization. Solutions are presented when the laser is tuned on and off resonance for various input laser intensities and linear absorption coefficients. Optimal conditions for maximum efficiency are discussed.
The phase-conjugate reflectivity attainable by degenerate four-wave mixing in an idealized saturable absorbing medium is calculated for arbitrary values of the laser intensity, laser frequency, and absorption path-length of the nonlinear medium. The influence of pump-wave absorption, including saturation and standing-wave effects, is included in the theory. The treatment is based on an analytic expression for the intensity distribution of the counterpropagating waves. The theoretical predictions differ substantially from those based on theories that ignore pump absorption effects. The results of the present calculation are used to predict the minimum laser intensity, absorption path-length, and detuning required to obtain unit reflectivity and self-oscillation.
A theoretical description for a forward degenerate four-wave mixing process in homogeneously broadened two-level absorbers with arbitrary intensities of all four beams is presented. Assuming no pump absorption and depletion, we obtain an analytical solution of forward degenerate four-wave mixing signal intensity in the limit of the strong pumps and weak probe and signal. In the case of low absorption or large detuning, this solution is shown to become equivalent to that of the phase-conjugate degenerate four-wave mixing derived by Abrams and Lind [Opt. Lett.2, 94 (1978)]. For arbitrary beam intensities and absorption parameters, the signal intensity is numerically calculated by solution of the coupled equations of complex wave amplitudes. Comparing the results of the numerical calculation with those of the analytical solution, we discuss the validity of using the analytical solution in practical experiments and show the saturation behavior that is due to the strong probe beam. The line shapes under the various ratios among the input beams and absorption parameters are also obtained and discussed.
Current experimental studies of degenerate four-wave mixing in saturable absorbers1,2 have shown that the dependence of the reflectivity on the pump intensity exhibits a double maxima. This phenomenon can arise from the fact that the medium approximates a set of four-level quantum systems. We have carried out a detailed analysis of the nonlinear processes of degenerate four-wave mixing in a four-level system. Because resonant saturable absorbers are being considered for systems applications, e.g., optical phase conjugation and wide FOV filters, the results presented are relevant to various optical phase conjugation devices. There are two distinct regimes which are of interest. The first case is when the intramolecular relaxation is very weak or absent. The second is when the intramolecular relaxation is strong. For the weak case the medium behaves like a set of two distinct dipole radiation sources which can generate interference effects.
A theoretical analysis is made of the efficiency of wavefront reversal under conditions of a degenerate form of the four-wave interaction in a resonantly absorbing (amplifying) medium allowing for changes in the pump waves as a result of their natural resonant absorption (amplification). The coefficient of reflection into a reversed wave is obtained as a function of the optical thickness of a layer of the medium, the boundary values of the pump wave intensity, and the shift of the field frequency from the line center. The optimal values of these parameters and the corresponding maximum reflection coefficient are determined.
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.