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Journal of Applied Physics

Transverse effects in optical bistability with the nonlinear Fabry–Pérot étalon: A new theoretical approach

Marc Haelterman, Michael D. Tolley, Guy Vitrant

Published Mar 15, 1990• 11 citations
Publisher

Abstract

On the basis of a plane-wave analysis we develop an original one-dimensional model for the nonlinear Fabry–Pérot étalon. This model facilitates numerical analysis and physical interpretations. We discuss the role of diffraction and the influence of the incident angle on bistability. A preliminary numerical study of the model is proposed.

DOI
10.1063/1.345436

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On the basis of a pole analysis, we derive a simple and powerful model of the nonlinear Fabry–Perot resonator. Our theory extends the modal approach, which was already developed for the nonlinear prism coupler, to the Fabry–Perot resonator for any angle of incidence. The main advantage of the modal approach is that it greatly simplifies the numerical study of transverse effects and provides a deep understanding of physical phenomena related to optical bistability. By means of a simple analysis of the equations, our model permits us to discuss the role of diffraction and the influence of the incident angle on the nonlinear Fabry–Perot behavior.

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Journal of the Optical Society of America B•Jan 1, 1990•14 citations
On the basis of a plane-wave analysis we develop an original one-dimensional model for the nonlinear Fabry–Pérot étalon. This model facilitates numerical analysis and physical interpretations. We discuss the role of diffraction and the influence of the incident angle on bistability. A preliminary numerical study of the model is proposed.
On the basis of a pole analysis, we derive a simple and powerful model of the nonlinear Fabry–Perot resonator. Our theory extends the modal approach, which was already developed for the nonlinear prism coupler, to the Fabry–Perot resonator for any angle of incidence. The main advantage of the modal approach is that it greatly simplifies the numerical study of transverse effects and provides a deep understanding of physical phenomena related to optical bistability. By means of a simple analysis of the equations, our model permits us to discuss the role of diffraction and the influence of the incident angle on the nonlinear Fabry–Perot behavior.
In a recent paper, we proposed a new theoretical model of nonlinear optical cavities1. Our theory, which is valid for both nonlinear (NL) waveguide couplers and NL Fabry-Pérot (FP) with arbitrary angle of incidence, constitutes a unified theory of nonlinear planar resonators. The main advantage of the model is that it greatly simplifies the numerical study of transverse effects in NL resonators and provides a deep understanding of physical phenomena related to Optical Bistability (OB) in such devices. In particular it allowed us to analyse the role of diffraction and the influence of the incident angle on the steady-state NLFP response1,2.
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.