Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

TE wave reflection from a Kerr medium: spatial dynamics and bistability

Nyamsuren Ochirbat, Ochirbat Guseelee

Published May 8, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1364/opticaopen.31436719.v3

Related papers

TE wave reflection from a Kerr medium: spatial dynamics and bistability

Nyamsuren Ochirbat, Ochirbat Guseelee

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.

•Mar 2, 2026•0 citations

TE wave reflection from a Kerr interface: bistability, critical transitions, and thermodynamic analogies

Nyamsuren Ochirbat, Ochirbat Guseelee

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 interface permittivity ε . For total internal reflection, we obtain the spatial evolution equation for the permittivity, which decays monotonically toward the linear value ε l . The shape of S inc ( ε ) is examined, yielding the condition for a maximum on the evanescent branch: 2 β 2 > ε 1 + ε l , where β is the conserved tangential wavenumber. When this condition holds, an intensity interval ( S c , S max ) exists where three steady states coexist (two evanescent and one propagating), giving rise to optical bistability. The propagating branch exhibits a square-root singularity at ε = β 2 , leading to a non-analytic derivative d S inc / d ε ; the reflectivity slope d R / d S inc remains finite. An alternative representation in terms of the normalized decay constant μ reveals a folded curve, indicating internal bistability within the total internal reflection 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 via waveguide geometry. The two switching thresholds exhibit distinct critical behavior: a first-order jump at S max and a second-order (divergent derivative) transition at S c , the latter suggesting analogies with thermodynamic critical points. A Landau-type expansion of the effective potential is presented heuristically to support this connection. The results may be useful for all-optical switching and sensing applications.

Journal of the Optical Society of America B•Aug 26, 2026•0 citations

Optical bistability with the waveguide mode: the case of a finite-width incident beam

Victor J. Montemayor, Robert T. Deck

We develop an approximate analytical theory for the reflection of a finite-width square-wave light beam at a nonlinear interface and make use of the results to assess the effect of the finiteness of the incident beam on the bistability of the signal reflected from a triple boundary interface under conditions for excitation of a waveguide mode. The nonlinearity of the interface is assumed to result from a substrate medium that has a Kerr-type quadratic dependence on the local electric-field amplitude. Our results indicate that the finiteness of the width of the incident beam substantially reduces the magnitude of the reflectance jump at the bistable switching point in comparison with that predicted by an exact plane-wave theory. Nevertheless, we conclude that a bistable reflectivity should still exist for the geometry that we consider at the switching intensity predicted by the plane-wave theory.

Journal of the Optical Society of America B•Sep 1, 1986•20 citations

Low-threshold bistable reflection assisted by oscillating wave interaction with Kerr nonlinear medium*

Yingcong Zhang, Wenjuan Cai, Xianping Wang +5 more

Owing to the enormously enhanced oscillating wave, a minute variation of the incident light intensity will give rise to a change in the dielectric constant of the Kerr nonlinear medium and lead to a bistable reflection with an ultra-low threshold intensity, which is closely related to the angle of incidence and the thickness of the Kerr nonlinear medium. The criterion for the existence of optical bistability is derived. Our bistability scheme is simple and not limited to the TM-polarization.

Chinese Physics B•Jan 29, 2021•1 citation

Optical bistability in a nonlinear-linear interface with two-wave mixing

Ron Daisy, Baruch Fischer

We introduce a new mechanism for optical bistability at an interface between nonlinear (Kerr or photorefractive) and linear media for a light wave that propagates from the nonlinear side near the critical angle. The origin for this effect is the nonlinear coupling between the incident and reflected (from the interface) waves. We derive the laws of reflectivity and transmissivity and find a bistable behavior as a function of the incident power or the angle.

Optics Letters•Jun 15, 1992•9 citations

Optical bistability at a nonlinear interface

P. W. E. Smith, J.P. Hermann, W. J. Tomlinson +1 more

Under suitable conditions, the boundary between a linear and a nonlinear (Kerr effect) medium should have a reflection coefficient which exhibits hysteresis as a function of optical intensity. We present the first experimental evidence of this effect. Experiments were performed using ∼1-ns ruby laser pulses incident on a glass-CS2 boundary.

Applied Physics Letters•Dec 1, 1979•121 citations
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.
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 interface permittivity ε . For total internal reflection, we obtain the spatial evolution equation for the permittivity, which decays monotonically toward the linear value ε l . The shape of S inc ( ε ) is examined, yielding the condition for a maximum on the evanescent branch: 2 β 2 > ε 1 + ε l , where β is the conserved tangential wavenumber. When this condition holds, an intensity interval ( S c , S max ) exists where three steady states coexist (two evanescent and one propagating), giving rise to optical bistability. The propagating branch exhibits a square-root singularity at ε = β 2 , leading to a non-analytic derivative d S inc / d ε ; the reflectivity slope d R / d S inc remains finite. An alternative representation in terms of the normalized decay constant μ reveals a folded curve, indicating internal bistability within the total internal reflection 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 via waveguide geometry. The two switching thresholds exhibit distinct critical behavior: a first-order jump at S max and a second-order (divergent derivative) transition at S c , the latter suggesting analogies with thermodynamic critical points. A Landau-type expansion of the effective potential is presented heuristically to support this connection. The results may be useful for all-optical switching and sensing applications.
We develop an approximate analytical theory for the reflection of a finite-width square-wave light beam at a nonlinear interface and make use of the results to assess the effect of the finiteness of the incident beam on the bistability of the signal reflected from a triple boundary interface under conditions for excitation of a waveguide mode. The nonlinearity of the interface is assumed to result from a substrate medium that has a Kerr-type quadratic dependence on the local electric-field amplitude. Our results indicate that the finiteness of the width of the incident beam substantially reduces the magnitude of the reflectance jump at the bistable switching point in comparison with that predicted by an exact plane-wave theory. Nevertheless, we conclude that a bistable reflectivity should still exist for the geometry that we consider at the switching intensity predicted by the plane-wave theory.