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Journal of the Optical Society of America B

All-optical switching in a high- Q Fabry–Perot cavity filled with a quadratic material

Giuseppe D’Aguanno, E. Angelillo, C. Sibilia, Michael Scalora, M. Bertolotti

Published Jul 1, 2000• 7 citations

Abstract

A theoretical analysis of the nonlinear quadratic interaction between two monochromatic plane waves at frequencies ω and 2ω in a Fabry–Perot cavity shows that all-optical control of reflectivity and transmissivity of the fundamental beam is possible under suitable conditions. We report all-optical switching of the fundamental beam for cavity lengths that vary from a few micrometers to a few millimeters. Specifically, we show that 100% all-optical switching can occur for a 6-µm cavity when the nonlinear coefficient is not greater than 20 pm/V and the input intensity does not exceed 10 GW/cm2. Our analytical results are obtained without use of the slowly varying envelope approximation and without resort to the undepleted-pump approximation.

DOI: 10.1364/josab.17.001188

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A theoretical analysis of the nonlinear quadratic interaction between two monochromatic plane waves at frequencies ω and 2ω in a Fabry–Perot cavity shows that all-optical control of reflectivity and transmissivity of the fundamental beam is possible under suitable conditions. We report all-optical switching of the fundamental beam for cavity lengths that vary from a few micrometers to a few millimeters. Specifically, we show that 100% all-optical switching can occur for a 6-µm cavity when the nonlinear coefficient is not greater than 20 pm/V and the input intensity does not exceed 10 GW/cm2. Our analytical results are obtained without use of the slowly varying envelope approximation and without resort to the undepleted-pump approximation.

We present a theory of optical bistability for a Fabry-Perot cavity containing a medium with nonlinear refraction but linear absorption with only plane-wave and slowly varying envelope approximations. An analytic expression for the critical intensity Icfor the onset of bistability is derived and used to compare cavity designs. It is shown that 1) the important material parameter for minimum Icis the ration_{2}/\alpha 2) the limit to Icis set by limitations on finesse due to inhomogeneities rather than the absorption itself, and 3) the cavity design which gives lowest Icfor a given finesse is that for which the mirror transmissivity equals the absorption per pass; at high finesse this design leads to a total peak cavity transmission of 1/4 when mirror reflectivities are equal.

In this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip times. The slowing down of the cavity response occurs when the incident intensity is approximately equal to the critical switching intensity. This effect is called critical slowing down. As a result, the response of the cavity is much slower than what could be expected from the steady state analysis. The reflected intensity and the change in round-trip phase have similar dynamic response. In this research, the matlap programs are used to study the switching dynamics of a Fabry-Perot etalon.

The dynamic properties of a Fabry–Perot interferometer filled with a material exhibiting second-order dispersive nonlinearity are studied both theoretically and experimentally. The response of the medium is described by an intensity dependent phase constant as derived from self-action effects. Considering two relaxation times, that of the material and that of the cavity, the basic relations for the stability analysis and for the numerical calculations are obtained. Bistability and self-pulsing effects are predicted. Moreover, the transient behavior is characterized by anomalous switching properties like overshoot and alternate switching. The corresponding experiments performed on a nonlinear transmission line resonator confirm the theoretical results. In a final discussion, the relations to the field of nonlinear optics are outlined.