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Journal of the Optical Society of America B

Power transfer by nearly degenerate two-wave mixing in a saturable dye-doped film

Hirofumi Fujiwara, Koji Shio, Shigeki Miyanaga

Published Aug 1, 1991• 13 citations
Publisher

Abstract

We analyze power transfer by nearly degenerate two-wave mixing (TWM) in a saturable absorbing medium by assuming a three-level model for the saturable absorbing medium. The theoretical results are compared with the experimental ones by using an erythrosin-B-doped polymer film as the saturable absorbing medium. Pump-intensity-dependent behavior of the TWM gain that is predicted by the theory was experimentally verified with this dye-doped film. The saturation intensity Is and the detuning parameter δ of erythrosin B were estimated by the comparison of the theory and the experiment: Is ≈ 1.6 W/cm2, δ ≈ 1.1. The theoretical curves calculated from these values are in good agreement with the experimental curves near resonance, whereas they disagree with the experimental results as the laser frequency shifts off resonance.

DOI
10.1364/josab.8.001740

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We analyze power transfer by nearly degenerate two-wave mixing (TWM) in a saturable absorbing medium by assuming a three-level model for the saturable absorbing medium. The theoretical results are compared with the experimental ones by using an erythrosin-B-doped polymer film as the saturable absorbing medium. Pump-intensity-dependent behavior of the TWM gain that is predicted by the theory was experimentally verified with this dye-doped film. The saturation intensity Is and the detuning parameter δ of erythrosin B were estimated by the comparison of the theory and the experiment: Is ≈ 1.6 W/cm2, δ ≈ 1.1. The theoretical curves calculated from these values are in good agreement with the experimental curves near resonance, whereas they disagree with the experimental results as the laser frequency shifts off resonance.
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.
Self-diffraction by nondegenerate two-wave mixing (TWM) in a saturable-dye-doped film is analyzed by means of a model of a three-level system for dyes. The rate equation approximation of a density matrix method leads to the electric polarization for nondegenerate TWM. Under the approximation of a strong pump limit and no pump absorption and depletion, the solution for the self-diffracted probe beam can be analytically obtained. The theoretical predictions are found to be in fair agreement with the experimental results.
Studies on low power optical phase conjugation (OPC) in three saturable dyes, viz., eosin, erythrosin B, and rose bengal, embedded in two polymer films, viz., gelatin and polyvinyl alcohol, are presented. Experiments are performed using the 514.5 nm line of an argon-ion laser. Saturation intensities are determined from the transmission versus intensity plots, and triplet lifetimes are estimated from the phosphorescence decay curves. OPC experiments are performed, and the variation of OPC reflectivity with intensity and absorption length is studied. Experimental results are compared with the theory of degenerate four-wave mixing in absorbing media proposed by R. L. Abrams and R. C. Lind [Opt. Lett. 2(4), 94 (1 978)]. There is fair agreement between the theory and the experimental observations. The limitations in using these films for cw OPC applications are briefly 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.
The properties of polarization-dependent phase-conjugate (PC) reflectivities by degenerate four-wave mixing in saturable-dye-doped films are investigated on the basis of a four-level model including an excited-state absorption. Numerical calculations are carried out by taking account of the effect of molecular orientation as well as of pump propagation under the assumption that optically anisotropic dye molecules are rigidly fixed in a solid matrix without any positional and orientational order, in which a PC wave can be generated even in the case of a probe wave perpendicularly polarized to pump waves. Two cases of the polarization state are employed, where the polarization direction of the probe wave is either parallel or perpendicular to that of the parallel linearly polarized pump waves. Numerically calculating the PC reflectivities as a function of the pump intensity, we show how the polarization properties of the PC-reflectivity curves depend on saturation parameters, and clarify the influences of the molecular orientational and the pump propagation effect. The numerical results are compared with the experimental results obtained by using eosin-Y-doped polyvinyl alcohol films as saturable absorbers.
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.