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Japanese Journal of Applied Physics

Self-Diffraction by Two-Wave Mixing in Organic-Dye-Doped Film

Hirofumi Fujiwara, Koji Shio, Shigeki Miyanaga, Kazuo Nakagawa

Published Jul 1, 1990• 2 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.29.l1235

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In conclusion, the TWM in broad-area semiconductor amplifier in nondegenerate condition is investigated theoretically. The coupled-wave equations are derived and analytical solutions are obtained when the intensity of the pump is much larger than that of the signal, but much less than the saturation intensity of the amplifier. A special case of TWM, degenerate TWM, is investigated experimentally in a GaAlAs broad-area semiconductor amplifier. The experimental results show good agreement with the theory, and the validity of the theory for this experiment is discussed. A diffusion length of 2.0 m is determined from the experiment. The TWM gain in broad-area semiconductor amplifier is calculated as a function of the frequency difference between the pump and the signal based on the data obtained from the degenerate TWM experiment; and the calculated results are discussed based on the different contributions from the refractive index grating and the gain grating to the TWM gain. Depending on and , the TWM gain in semiconductor broad-area amplifier can be positive or negative. The energy exchange between the pump and signal beams occurs when 0.

InTech eBooks•Apr 1, 2010•1 citation
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.
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.
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.
Polarization dependence of phase-conjugate reflectivity by degenerate four-wave mixing is clarified theoretically and experimentally in a saturable-dye-doped polymer film. 1. _INTRODUCTLON A dyedoped film in which optically anisotropic saturable dye molecules are rigidly fixed and are randomly oriented has been used as a nonlinear material which can generate a phase-conjugate (PC) wave by degenerate four-wave mixing13 (DFWM). Such a film can generate a PC wave which has the same polarization state as the probe wave even for a probe wave orthogonally polarized to two pump waves. Tompkin et. al. 4 showed that in such a phase conjugator the nearly perfect vectorial phase conjugation can be obtained at the pump intensity near the saturation intensity of the phase conjugator. In this work following the analysis of Tompkin et. al. 4 closed-form solutions for the PC reflectivities in the dye-doped film are derived for two states of the polarization: the probe wave is polarized parallel and perpendicular to the pump waves. Some experimental results are also demonstrated in an eosin-Y-doped poly-vinyl alcohol (PVA) film and are compared with the theoretical results. 2. POLARIZATION DEPENDENT PC REFLECTIVITIES Dye molecules are modeled as dipoles which are randomly and uniformly oriented and are rigidly fixed in a solid matrix. We assume that each dye molecule has only one component of transition dipole moments at a wavelength considered5. An induced dipole moment of each dye molecule by
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 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.
In conclusion, the TWM in broad-area semiconductor amplifier in nondegenerate condition is investigated theoretically. The coupled-wave equations are derived and analytical solutions are obtained when the intensity of the pump is much larger than that of the signal, but much less than the saturation intensity of the amplifier. A special case of TWM, degenerate TWM, is investigated experimentally in a GaAlAs broad-area semiconductor amplifier. The experimental results show good agreement with the theory, and the validity of the theory for this experiment is discussed. A diffusion length of 2.0 m is determined from the experiment. The TWM gain in broad-area semiconductor amplifier is calculated as a function of the frequency difference between the pump and the signal based on the data obtained from the degenerate TWM experiment; and the calculated results are discussed based on the different contributions from the refractive index grating and the gain grating to the TWM gain. Depending on and , the TWM gain in semiconductor broad-area amplifier can be positive or negative. The energy exchange between the pump and signal beams occurs when 0.