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Journal of the Optical Society of America B

Light waves at the interface of linear and photorefractive media

Ron Daisy, Baruch Fischer

Published Jun 1, 1994• 18 citations
Publisher

Abstract

We study the behavior of light waves at an interface between linear and photorefractive media, where the incident wave propagates from the linear side. We find bistable behavior of the reflection coefficient as a function of the incident angle at incident wave directions in the vicinity of the critical angle for total internal reflection. The analysis is based on approximations in the photorefractive-process equations, for which an analytical plane-wave solution for the boundary problem is found. In this regime an exponentially decaying evanescent field induces a uniform change of the refractive index. The limitation of this solution is also studied by a numerical analysis.

DOI
10.1364/josab.11.001059

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We study the behavior of light waves at an interface between linear and photorefractive media, where the incident wave propagates from the linear side. We find bistable behavior of the reflection coefficient as a function of the incident angle at incident wave directions in the vicinity of the critical angle for total internal reflection. The analysis is based on approximations in the photorefractive-process equations, for which an analytical plane-wave solution for the boundary problem is found. In this regime an exponentially decaying evanescent field induces a uniform change of the refractive index. The limitation of this solution is also studied by a numerical analysis.
The rigorous solution in the plane-wave approximation of the light reflection boundary problem for the interface the isotropic medium - photorefractive crystal with the drift- diffusion nonlinearity mechanism is given. The possibility of the realization of the hysteresis light reflection phenomenon in this case under certain conditions is shown. The analytical expressions describing hysteresis behavior of the reflectivity as a function of the angle of incidence or that of the external electric field strength applied to the crystal are derived. By changing the value and sign of the applied electric field it is possible to transfer system from the total reflection state to the transmission state and vice versa. The obtained results are attractive for the elaboration of the possible devices for laser radiation control and optical information processing.
A rigorous solution is given in the plane-wave approximation for the boundary problem of light reflection from the interface between an isotropic medium and a photorefractive crystal with drift-diffusion nonlinearity. The possibility of realizing hysteresis reflection or optical bistability in the system under certain conditions is shown. Analytical expressions are obtained that describe the hysteresis behavior of reflectivity as a function of the angle of incidence or the strength of a constant external electric field applied to the crystal. The results of the study are of interest for the development of devices controlling laser radiation.
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.