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Journal of the Optical Society of America B

Two-wave mixing by phase and absorption gratings in saturable absorbers

S. A. Boothroyd, Jacek Chrostowski, Maurice S. O'Sullivan

Published Apr 1, 1989• 40 citations
Publisher

Abstract

Two-wave mixing (TWM) by means of moving phase and absorption gratings is reported for acridine-doped glass and ruby. A measurement method is described that enables TWM from the phase and absorption gratings to be determined independently, leading to a value for the ratio of the real part of the nonlinear index n2 to the imaginary part that is independent of beam intensity profiles or overlap conditions. An anomalous TWM response was observed from the absorption grating in ruby.

DOI
10.1364/josab.6.000766

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Optics Letters•Jun 15, 2004•37 citations
Two-wave mixing (TWM) by means of moving phase and absorption gratings is reported for acridine-doped glass and ruby. A measurement method is described that enables TWM from the phase and absorption gratings to be determined independently, leading to a value for the ratio of the real part of the nonlinear index n2 to the imaginary part that is independent of beam intensity profiles or overlap conditions. An anomalous TWM response was observed from the absorption grating in ruby.
The ratio of the imaginary to the real part of the complex nonlinear refractive index has been measured by two-wave mixing in acridine orange doped fluorophosphate glass, fluorescein doped boric acid glass, and ruby at argon-ion wavelengths. A new and simple two-wave mixing measurement is described in which one of the beams contributing to a stationary interference pattern in the nonlinear absorber is subject to a phase transient. This results in a variation of the energy coupling between the beams from which the phase of the nonlinear index and also the sign of its real and imaginary parts can be determined. A simple theory based on homogeneously broadened absorption agrees with the phase of the nonlinear index in acridine, but not in fluorescein where excited state absorption is determined to be greater than absorption from the ground state. These results are compared with new nondegenerate two-wave mixing measurements in which the contribution from the phase and absorption gratings can be determined independently.1 Comparison of results from the two approaches enables the contribution of excited state absorption to the two-wave mixing to be qualified.
A general theory of two-wave mixing (TWM) in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of TWM are derived based on Maxwell's wave equation. The coupled-wave equations can be decoupled as coupled equations for the intensity and coupled equations for the phase of both beams, and these two sets of coupled equations can be solved analytically by using average total intensity in the medium instead of using the total intensity. Compared with the previous theory of TWM, the theory presented here is more general, and the applications of the theory to photorefractive materials, Kerr media, and semiconductor broad-area amplifiers are described.
The solution of the nondegenerate two-wave-mixing problem in an absorptive Kerr medium including the contribution from nonlinear absorption is obtained for the first time to our knowledge. This solution enables us to analyze the influence of nonlinear absorption on the two-wave-mixing gain and account for previously unexplained results reported for ruby and Cr3+:YAlO3. The effect of nonlinear absorption of a pump beam on the gain of a probe beam is shown to be minimized when incident intensities of the interacting beams are equal. The intensity dependence of the two-wave-mixing gain for dispersive (ruby and Cr3+:YAlO3) media and the gain measurements for absorptive (fluorescein-doped glass) media are also in agreement with the new theory.
We present experimental results of two-wave mixing in single-mode Er-doped optical fibers for which dynamic Bragg reflectance gratings are formed as a result of saturation of fiber-optic absorption (i.e., by means of the effect of spatial hole burning). The gratings are probed by the same recording waves at lambda approximately = 1549 nm and are detected as periodic changes of the intensity of light reflected from a Sagnac interferometer (with a piece of the doped fiber included) observed when periodic phase modulation is induced in one of the waves. Both rectangular and sinusoidal modulation were used, which permitted evaluation of the grating recording time (tau(g) approximately = 3 ms for OFS-Fitel EDF-HG980 fiber) and the grating amplitude, which proved to be approximately 6-7 times lower than expected from measurements of saturation of fiber-optic absorption by one wave only.