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Optics Letters

Bistable nonspecular reflection at a nonlinear–linear local interface

W. Nasalski

Published Mar 15, 1998• 3 citations
Publisher

Abstract

Nonspecular reflection at a nonlinear-linear dielectric interface with local Kerr nonlinearity is analyzed. The Fresnel reflectivity and the variational solution are explicitly given in a closed form. Bistable switching of the interface is demonstrated by numerical simulations based on the monotonic iteration procedure.
DOI
10.1364/ol.23.000433

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Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text Wojciech Nasalski, "Bistable nonspecular reflection at a nonlinear–linear local interface: errata," Opt. Lett. 24, 184-184 (1999) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

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We analyze transverse-electric (TE) wave reflection at a planar interface between a linear medium and a Kerr nonlinear half-space. Using an amplitude-phase formalism, we derive exact expressions for the reflection coefficient and the incident intensity as functions of the permittivity at the interface. Under total internal reflection, the spatial evolution of the permittivity is described by a first-order differential equation and decays monotonically to the linear value. The incident intensity on the evanescent branch is shown to possess a maximum when 2𝛽2 > 𝜀1 +𝜀𝑙, where 𝛽 is the conserved propagation constant, 𝜀1 the linear permittivity, and 𝜀𝑙 the low-intensity permittivity of the Kerr medium. For intensities between the threshold 𝑆𝑐 and the maximum 𝑆max, three steady states coexist: two evanescent (TIR) solutions (one stable, one unstable) and one propagating solution. The propagating branch rises with an infinite slope at 𝜀 = 𝛽2 (square-root singularity), leading to an ultra-sharp switching transition. The relation between the normalized decay constant 𝜇 and the incident intensity exhibits a folded curve, revealing an “internal” bistability in the TIR regime. Both self-focusing (𝛼 > 0) and self-defocusing (𝛼 < 0) Kerr nonlinearities are treated. The propagation constant 𝛽 appears as a free design parameter, allowing the switching intensity to be tuned through waveguide geometry. These results provide a unified picture of optical bistability at a nonlinear interface, with potential applications in all-optical switching and sensing.
We analyze transverse-electric (TE) wave reflection at a planar interface between a linear medium and a Kerr nonlinear half-space. Using an amplitude-phase formalism, we derive exact expressions for the reflection coefficient and the incident intensity as functions of the permittivity at the interface. Under total internal reflection, the spatial evolution of the permittivity is described by a first-order differential equation and decays monotonically to the linear value. The incident intensity on the evanescent branch is shown to possess a maximum when 2𝛽2 > 𝜀1 +𝜀𝑙, where 𝛽 is the conserved propagation constant, 𝜀1 the linear permittivity, and 𝜀𝑙 the low-intensity permittivity of the Kerr medium. For intensities between the threshold 𝑆𝑐 and the maximum 𝑆max, three steady states coexist: two evanescent (TIR) solutions (one stable, one unstable) and one propagating solution. The propagating branch rises with an infinite slope at 𝜀 = 𝛽2 (square-root singularity), leading to an ultra-sharp switching transition. The relation between the normalized decay constant 𝜇 and the incident intensity exhibits a folded curve, revealing an “internal” bistability in the TIR regime. Both self-focusing (𝛼 > 0) and self-defocusing (𝛼 < 0) Kerr nonlinearities are treated. The propagation constant 𝛽 appears as a free design parameter, allowing the switching intensity to be tuned through waveguide geometry. These results provide a unified picture of optical bistability at a nonlinear interface, with potential applications in all-optical switching and sensing.
The reflection of light at the interface between linear and nonlinear media can provide fundamentally novel nonlinear effects such as nonlinear switching from total internal reflection to partial transmission, bleaching of the interface, and bistability. The nonlinear interface is the simplest switching and bistable optical device. Unlike bistable Fabry-Perot resonators, it allows one to use broadband sources of light and remove resonant restrictions on frequency tuning, and offers potentials to attain high operating speed. Experimental demonstration of those effects shows good agreement with some of the predictions of plane-wave theory. Some of the experimental results as well as computer simulation, however, show a new feature of the phenomenon which requires further exploration.
Both static and dynamic characteristics of light reflected from a specially designed multilayer metal-dielectric structure with Kerr nonlinearity have been studied in this work. Various regimes of nonlinear reflection from the structure have been demonstrated, including bistable switching between low and high reflection states, which occurs at low intensity of the incident light due to a significant enhancement in the optical field in the nonlinear layer under conditions of total internal reflection. This nonlinear structure has been proposed to use as an optically controlled intracavity laser modulator.