Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nonlinear Dynamics in Optical Systems

Dynamics and Transverse Effects in Nonlinear Planar Resonators: A Unified Modal Theory

Marc Haelterman, Guy Vitrant

Published Jan 1, 1990• 1 citation
Publisher

Abstract

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.

DOI
10.1364/nldos.1990.stdopd210

Related papers

Transverse effects in nonlinear planar resonators I Modal theory

Marc Haelterman, Guy Vitrant, R. Reinisch

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.

Journal of the Optical Society of America B•Jul 1, 1990•53 citations

Transverse effects in nonlinear planar resonators II Modal analysis for normal and oblique incidence

Guy Vitrant, Marc Haelterman, R. Reinisch

A unified nonlinear modal theory that is valid not only for waveguide couplers but also for nonlinear Fabry–Perot resonators has recently been proposed. The validity of this new approach is numerically demonstrated by comparison with the well-known bidimensional theory. The unified modal theory appears to be a powerful tool for studying transverse effects in a broad class of nonlinear resonators. It has been used to derive the main characteristics of the stationary behavior of the optical resonators in the case of a local nonlinearity. In particular, the disappearance of optical bistability when the resonator is tilted is predicted. Optical bistability at nearly normal incidence is interpreted by the coupling between two resonantly excited counterpropagating modes that are at the origin of the required transverse feedback.

Journal of the Optical Society of America B•Jul 1, 1990•47 citations

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

Marc Haelterman, Michael D. Tolley, Guy Vitrant

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.

Journal of Applied Physics•Mar 15, 1990•11 citations

Coupled-mode theory of diffraction-induced transverse effects in nonlinear optical resonators

R. Reinisch, Guy Vitrant, Marc Haelterman

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}}$${\mathrm{Ga}}_{\mathit{x}}$As/GaAs with ${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As/AlAs mirrors.

Physical review. B, Condensed matter•Oct 15, 1991•19 citations

Dynamical aspects of polarization induced switching phenomena in diffusively nonlinear Fabry-Perot resonators

Jan Danckaert, Hugo Thienpont A, Irina P. Veretennicoff

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.

Nonlinear Dynamics in Optical Systems•Jan 1, 1992•0 citations

Theory Of Operation Of A Nonlinear Fabry-Perot For Oblique Incidence

Hugo Thienpont A

The steady state operation of a nonlinear Fabry-Perot (NLFP) for oblique incidence is studied. Depending on the values of the angle and the width of the beam, different theoretical models are proposed. They predict important modifications in the bistable behaviour of the device, which also crucially depend on the state of polarisation of the incident beam.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 22, 1987•3 citations
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.
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.
A unified nonlinear modal theory that is valid not only for waveguide couplers but also for nonlinear Fabry–Perot resonators has recently been proposed. The validity of this new approach is numerically demonstrated by comparison with the well-known bidimensional theory. The unified modal theory appears to be a powerful tool for studying transverse effects in a broad class of nonlinear resonators. It has been used to derive the main characteristics of the stationary behavior of the optical resonators in the case of a local nonlinearity. In particular, the disappearance of optical bistability when the resonator is tilted is predicted. Optical bistability at nearly normal incidence is interpreted by the coupling between two resonantly excited counterpropagating modes that are at the origin of the required transverse feedback.
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.
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.