© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Nonlinear Guided Waves and Their Applications

Nonlinear Prism Coupler with Diffusion

Guy Vitrant, R. Reinisch, Jean-Claude Paumier, Gaetano Assanto, G. I. Stegeman

Published Jan 1, 1989• 0 citations

Abstract

The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first1, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second2, a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approach leads to optical bistability under certain detuning conditions, whereas the second results in switching only. Although it is known that plane wave analyses are inadequate when dealing with linear-nonlinear interfaces, bistability has been observed experimentally with nonlinear prism couplers3. Fundamentally the finite beam theoretical approaches are unable to predict bistability because no longitudinal feedback is included. Recently we showed that when non-locality is introduced into the optically induced refractive index change, longitudinal feedback occurs and bistability is predicted for the growing mode case4. However, the model used for the non-locality was artificial and resulted only in qualitative predictions. In this paper the nonlocality is modelled by the same equation used to describe heat transfer and carrier diffusion, leading to a quantitative estimate of the minimum diffusion length required for bistability.

DOI: 10.1364/nlgwp.1989.fb3

Related papers

Bistability and switching in nonlinear prism coupling

G. I. Stegeman, G. Assanto, Raymond Zanoni +5 more

We demonstrate that when a nonlinear coupler is operated in the switching regime, small amounts of either nonlocality in the optically induced refractive index change or of longitudinal feedback can lead to optical bistability. Outside the switching regime, there is a threshold for the amount of nonlocality or feedback required for bistability. The diverse predictions of previous theoretical formulations are therefore reconciled.

Applied Physics Letters•Mar 14, 1988•71 citations

Demonstration of optical bistability with a nonlinear prism coupler

Guy Vitrant, P. Arlot

A guided wave is launched through a nonlinear prism coupler whose prism-waveguide gap is filled with a liquid crystal. We observed that the intensity of the excited guided wave exhibits optical bistability when the incident intensity is modulated. This result, which is rather surprising when compared to recent theoretical predictions, is shown to arise from a thermal averaging process in the liquid crystal.

Journal of Applied Physics•May 15, 1987•32 citations

Grating Couplers for Kerr-Type Nonlinear Waveguides: A Simplified Theory

R. Reinisch, P. Vincent, M. Nevière +1 more

We consider grating induced optical bistability (OB) arising from the resonant excitation of a given nonlinear guided mode. In that case it can be shown, using the coupled-mode formalismi(1), that in the whole bistable domain : a) the transverse field map of the resonantly excited nonlinear guided mode corresponds to that of the associated linear one which is known. b) the Kerr-type nonlinearity only modifies the longitudinal wavevector component. Thus the rigorous theory of diffraction(2), previously used to study grating-induced plane wave OB(3), can be replaced by a much more simple one which works as follows : i) determine the complex longitudinal wavevector component of the linear leaky guided mode p, βpL, through the solution of the associated linear homogeneous grating problem(2), ii) use the rigorous theory of diffraction in linear optics(2) to determine the in-coupling efficiency, tp, of the incident plane wave, iii) use the coupled-mode formalism to derive the analytical expression(4) of the complex nonlinear longitudinal wavevector component βpNL.

Nonlinear Guided Waves and Their Applications•Jan 1, 1991•0 citations

Demonstration Of Optical Bistability By Resonant Excitation Of Nonlinear Guided Waves

Guy Vitrant, P. Arlot, R. Reinisch

A guided wave is launched through a nonlinear prism coupler whose prism-waveguide gap is filled with a liquid crystal. We observe that the intensity of the guided wave may exhibit optical bistability. Tests are realized which proove that the loops are true bistable cycles and not only hysteresis. The experimental results are in good agreement with plane-wave calculations. The disagreement with finite-width incident beam calculations is explained by a thermal averaging process within the liquid crystal.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 22, 1987•2 citations

Second-harmonic-generation-induced optical bistability in prism or grating couplers

R. Reinisch, E. Popov, M. Nevière

We deal with second-harmonic generation in chi((2)) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in chi((2)) optical resonators.

Optics Letters•Apr 15, 1995•23 citations

Nonlinear Prism Coupler: Approximate Theory and Comparison With Rigorous Analysis

Sergey A. Darmanyan, E. Popov, M. Nevière

A prism coupler filled with nonlinear Kerr-like material is studied theoretically. A simple, approximate analysis is developed to predict its behavior in both linear and nonlinear optics. In a wide range of incident amplitude magnitude, optical bistability and multistability are found. As far as field map not undergo drastic change, the simpler approximate theory is able to quantitatively analyze both prism couplers and waveguide in nonlinear optics and to study such effects as nonlinear phase shift, existence of nonlinear asymmetric modes in symmetric environments, bi-and multistability. The predictions of the analytical theory are compared with the results obtained via numerical integration of Maxwell equations and they agree quite well.

Journal of Electromagnetic Waves and Applications•Jan 1, 2000•2 citations

The salient question which arises when light is coupled via a grating or a prism into a waveguide exhibiting an intensity-dependent refractive index is whether switching occurs with or without bistability under appropriate detuning conditions. There are two prevailing theories. In the first1, a plane wave input is assumed leading to a uniform optically induced index change in the coupling region. In the second2, a finite width incident beam is assumed and the growth of the guided field under the coupler leads to an index change proportional to the local guided wave intensity. The first approach leads to optical bistability under certain detuning conditions, whereas the second results in switching only. Although it is known that plane wave analyses are inadequate when dealing with linear-nonlinear interfaces, bistability has been observed experimentally with nonlinear prism couplers3. Fundamentally the finite beam theoretical approaches are unable to predict bistability because no longitudinal feedback is included. Recently we showed that when non-locality is introduced into the optically induced refractive index change, longitudinal feedback occurs and bistability is predicted for the growing mode case4. However, the model used for the non-locality was artificial and resulted only in qualitative predictions. In this paper the nonlocality is modelled by the same equation used to describe heat transfer and carrier diffusion, leading to a quantitative estimate of the minimum diffusion length required for bistability.

We consider grating induced optical bistability (OB) arising from the resonant excitation of a given nonlinear guided mode. In that case it can be shown, using the coupled-mode formalismi(1), that in the whole bistable domain : a) the transverse field map of the resonantly excited nonlinear guided mode corresponds to that of the associated linear one which is known. b) the Kerr-type nonlinearity only modifies the longitudinal wavevector component. Thus the rigorous theory of diffraction(2), previously used to study grating-induced plane wave OB(3), can be replaced by a much more simple one which works as follows : i) determine the complex longitudinal wavevector component of the linear leaky guided mode p, βpL, through the solution of the associated linear homogeneous grating problem(2), ii) use the rigorous theory of diffraction in linear optics(2) to determine the in-coupling efficiency, tp, of the incident plane wave, iii) use the coupled-mode formalism to derive the analytical expression(4) of the complex nonlinear longitudinal wavevector component βpNL.

A guided wave is launched through a nonlinear prism coupler whose prism-waveguide gap is filled with a liquid crystal. We observe that the intensity of the guided wave may exhibit optical bistability. Tests are realized which proove that the loops are true bistable cycles and not only hysteresis. The experimental results are in good agreement with plane-wave calculations. The disagreement with finite-width incident beam calculations is explained by a thermal averaging process within the liquid crystal.

We deal with second-harmonic generation in chi((2)) nonlinear-optical resonators such as prism or grating couplers. The theoretical study is performed within the framework of a recently developed coupled-mode analysis leading to a set of equations governing the amplitudes of pump and second-harmonic frequency fields. We predict analytically that second-harmonic generation in prism or grating couplers may lead to optical bistability. We believe this to be the first demonstration of such an effect in chi((2)) optical resonators.

A prism coupler filled with nonlinear Kerr-like material is studied theoretically. A simple, approximate analysis is developed to predict its behavior in both linear and nonlinear optics. In a wide range of incident amplitude magnitude, optical bistability and multistability are found. As far as field map not undergo drastic change, the simpler approximate theory is able to quantitatively analyze both prism couplers and waveguide in nonlinear optics and to study such effects as nonlinear phase shift, existence of nonlinear asymmetric modes in symmetric environments, bi-and multistability. The predictions of the analytical theory are compared with the results obtained via numerical integration of Maxwell equations and they agree quite well.