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Journal of the Optical Society of America B

Polarization-induced optical switching in a single nonlinear Fabry–Perot resonator

V. Leutheuser, Udo E. Trutschel, F. Lederer

Published Jul 1, 1992• 4 citations
Publisher

Abstract

The transmission characteristic of a single nonlinear Fabry–Perot resonator, illuminated by arbitrary polarized and obliquely incident stationary plane waves, is presented. Using an analytical solution of the nonlinear wave equation, we show that the response characteristic depends strongly on the state of polarization of the input field. This effect is exploited for polarization-induced switching.

DOI
10.1364/josab.9.001145

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Physical review. B, Condensed matter•Oct 15, 1991•19 citations
The transmission characteristic of a single nonlinear Fabry–Perot resonator, illuminated by arbitrary polarized and obliquely incident stationary plane waves, is presented. Using an analytical solution of the nonlinear wave equation, we show that the response characteristic depends strongly on the state of polarization of the input field. This effect is exploited for polarization-induced switching.
The combination of polarization optics and nonlinear optics gives rise to interesting new physical phenomena1. In the work presented here we will focus on planar resonators with a nonlinearity of diffusive nature, such as the nonlinear Fabry-Perot resonator (NLFP). There are two ways to display the role of polarization in the bistable response of such a device. First, in a configuration where the light wave is obliquely incident on the resonator, as the interface's reflectances depend on the polarization state of the incident light. Second, in a configuration where the beam impinges normally on a resonator now filled with an anisotropic material, as a phase shift is induced between the linear Airy resonances of the two polarization eigenmodes. In this paper, two dynamic theories for planar resonators are presented for both configurations mentioned above, for an arbitrary polarization of the incident plane wave.
To merge the fields of polarization and nonlinear optics opens wide perspectives. The present work aims at investigating some of them. It is shown, on one hand, that if a nonlinear Fabry- Perot resonator filled with an optically isotropic material is addressed by an obliquely incident beam, the transmitted irradiance can switch from an up to a down state (or the reverse) if its polarization is properly modulated. If on the other hand the nonlinear cavity is filled with a linearly birefringent material, polarization optical bistability can occur, even at normal incidence. This polarization bistability can arise both by modulating the incident irradiance and by modulating the incident polarization. Optical bistability of the transmitted irradiance can also be induced by the modulation of the polarization of the incident beam. All these features provide new tools for parallel digital optical information processing.
A Fabry-Perot interferometer filled with a medium whose refractive index depends upon intensity has a multiple-valued transmission-vs-intensity characteristic. When the incident light is circularly polarized, and the nonlinearity is only cubic in the fields, Maxwell's equations may be solved exactly for the plane-parallel resonator field in terms of elliptic functions. An accurate approximate analysis is given for more general cases, including resonators with spherical mirrors and finite beams, where self-focusing is important. The theory is developed to yield design information for operation as an optical switch, "transistor," and power limiter.
We develop a one-dimensional theory of diffraction-induced transverse effects in nonlinear Fabry-P\'erot resonators addressed by finite-width incident beams. This is achieved in the framework of the coupled-mode analysis, which takes full advantage of the fact that nonlinear Fabry-P\'erot devices are resonant. As compared with a recently published theory dealing with the same subject [M. Haelterman, Opt. Commun. 75, 165 (1990); M. Haelterman, G. Vitrant, and R. Reinisch, J. Opt. Soc. Am. B 7, 1309 (1990); and G. Vitrant, M. Haelterman, and R. Reinisch, ibid. 7, 1319 (1990)], where the nonlinearity is introduced in an approximate way, the formalism developed here takes the nonlinearity associated with the optical Kerr effect rigorously into account. This feature has an important consequence: It leads to a theory that can be generalized to the TM case and also to anisotropic nonlinear media. The theory presented here is valid for any value of the angle of incidence. Under normal (or quasinormal) incidence, two counterpropagating modes, having the same absolute value of the wave-vector component parallel to the plane of the mirrors, are resonantly (or nearly resonantly) excited, whereas under oblique incidence, only one of these modes is excited.This allows us to point out that the feedback leading to optical bistability occurs along the direction of propagation of these resonantly excited counterpropagating modes of the nonlinear optical resonator. This explains why optical bistability disappears under oblique incidence. Although developed in the case of nonlinear Fabry-P\'erot resonators, this theory applies to a wide range of nonlinear optical resonators such as nonlinear prism couplers, nonlinear grating couplers, nonlinear interference filters, etc. The theory developed here applies whenever the excited electromagnetic field can be accurately described by a single mode or two counterpropagating modes of the nonlinear device. As an example, numerical results are given in the case of a nonlinear multiple-quantum-well Fabry-P\'erot-type structure of ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Gax{\mathrm{Ga}}_{\mathit{x}}Gax​As/GaAs with ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$Gax{\mathrm{Ga}}_{\mathit{x}}Gax​As/AlAs mirrors.