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Soviet Journal of Quantum Electronics

Spatial hysteresis and switching waves in a nonlinear planar waveguide

Vladimir Yu. Bazhenov, M. S. Soskin, V. B. Taranenko

Published Nov 30, 1986• 1 citation
Publisher

Abstract

An experimental investigation was made of the transformation of the intensity profile of a spatially confined light beam reflected from a nonlinear planar waveguide. It was found that when the system exhibited optical bistability, a hysteresis of the intensity profile was observed and it was due to the formation and propagation of a switching wave in the waveguide layer. A hysteresis was also observed when a switching wave crossed the unilluminated part of the waveguide layer.

DOI
10.1070/qe1986v016n11abeh008352

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An experimental investigation was made of the transformation of the intensity profile of a spatially confined light beam reflected from a nonlinear planar waveguide. It was found that when the system exhibited optical bistability, a hysteresis of the intensity profile was observed and it was due to the formation and propagation of a switching wave in the waveguide layer. A hysteresis was also observed when a switching wave crossed the unilluminated part of the waveguide layer.
An experimental investigation was made of the transformation of the intensity profile of a spatially confined light beam transmitted by optical bistable devices based on thin-film semiconductor interferometers formed by vacuum evaporation. A hysteresis of the intensity profile and switching waves was observed: these waves represented the process of consecutive transition from one stable state to another in neighboring zones of the interferometer. An experimental investigation was made of the velocity of switching waves in thin-film interferometers and in a model interferometer with a thermal nonlinearity.
Utilizing prism coupling of an argon laser beam into a nonlinear ZnS waveguide we have observed power-dependent optical bistability. We detuned the incidence angle by several linewidths from the optimal low power efficiency case. At this position we observed switching and hysteresis and verified the hysteresis loop to be bistable. The origin of the bistability we tentatively identified as a combination of intensity-dependent absorption and dispersion. Our conditions for bistability were different from those of W. Lukosz et al. in OPTICAL BISTABILITY III (Springer-Verlag, New York, 1986), p. 109.
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.