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Modern Physics Letters B

BISTABLE TRANSMITTING NONLINEAR DIRECTIONAL COUPLERS

D. Chevriaux, Рамаз Хомерики, Jérôme J.-P. Leon

Published Apr 30, 2006• 30 citations
Publisher

Abstract

Nonlinearity induced by intensity-dependent refractive indices (Kerr media) can be used as a means to conceive light detectors sensitive to very weak excitation. This property results from the bistability properties of the nonlinear Schrödinger equation submitted to boundary value data on the finite interval. The detector is obtained by coupling two single 1D waveguide to a 2D slab waveguide with adjusted indices. The resulting device then presents unusual light propagation properties and in particular may switch from almost vanishing to intense output under excitation by a weak signal.

DOI
10.1142/s0217984906011190

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Nonlinearity induced by intensity-dependent refractive indices (Kerr media) can be used as a means to conceive light detectors sensitive to very weak excitation. This property results from the bistability properties of the nonlinear Schrödinger equation submitted to boundary value data on the finite interval. The detector is obtained by coupling two single 1D waveguide to a 2D slab waveguide with adjusted indices. The resulting device then presents unusual light propagation properties and in particular may switch from almost vanishing to intense output under excitation by a weak signal.
In our recent research1, it was suggested that counter-propagating laser beams in a Kerr-nonlinear medium can induce intensity-dependent nonreciprocity which consists in different changes of refractive indecies for both of the waves. Under some conditions, this can result in such directionally asymmetrical effects as (i) directional bistability in a nonlinear ring resonator which allows one to switch the direction of propagation of a dominant mode and (ii) enhancement of the Sagnac effect in a rotating ring resonator.
When the output parameter of an optical device could be a multivalued function of the input parameter, this device can be working in an optical bistable status. The most typical optical bistable device is a Fabry–Perot cavity containing a nonlinear optical medium, the refractive index of which depends on the light intensity. Upon the action of an intense input optical beam, the transmitted (or reflected) intensity of this device may exhibit a nonlinear response to the incident light intensity variation and, especially under appropriate working conditions, the characteristic output/input curve may manifest a single (or multiple) hysteresis loop(s). Such type of optical bistable device can be used as an optical differential amplifier, optical switch, optical limiter, optical clipper, optical discriminator, or an optical memory element, depending on the chosen nonlinear medium and operation conditions.
It is known that two-wave coupling in photorefractive crystal may result in an intensity-dependent phase shift as well as energy transfer between the two waves without phase crosstalk. In a sense, this kind of phase shift is similar to the intensity-dependent refractive-index effects in Kerr media. Consequently, optical bistability can be established in an optical cavity with a photorefractive crystal. We formulate the model and get the expected bistable transmission with numerical simulations. Several cases, including that of the codirectional coupling and the contradirectional coupling, are considered. The effects of the photorefractive crystal’s distribution absorption and the spatial phase shift between the index grating and the light interference pattern in the crystal on the nonlinear transmission characteristics have also been studied. It is interesting to note that the output of the pumping wave is dependent on the cavity intensity and thus shows bistable behavior with respect to the cavity input as well.
Nonlinearity-induced nonreciprocity is studied in a system comprising two resonators coupled to a one-dimensional waveguide when the linear system does not exhibit nonreciprocity. The analysis is based on the Hamiltonian of the coupled system and includes the dissipative coupling between the waveguide and resonators, along with the input-output relations. We consider a large number of scenarios which can lead to nonreciprocity. We pay special attention to the case when the linear system does not exhibit nonreciprocal behavior. In this case, we show how very significant nonreciprocal behavior can result from Kerr nonlinearities. We find that the bistability of the nonlinear system can aid in achieving large nonreciprocity. Additionally, we bring out nonreciprocity in the excitation of each resonator, which can be monitored independently. Our results highlight the profound influence of nonlinearity on nonreciprocal behavior, offering an avenue for controlling light propagation in integrated photonic circuits. Nonlinearity-induced nonreciprocity would lead to significant nonreciprocity in quantum fluctuations when our system is treated quantum mechanically. Published by the American Physical Society 2024
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.