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Chinese Physics B

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

Yingcong Zhang, Wenjuan Cai, Xianping Wang, Wen Yuan, Cheng Yin, Jun Li, Haimei Luo, Ming-huang Sang

Published Jan 29, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1674-1056/abe118

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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.
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.
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.
In this study, we investigate the optical bistability and multistability in a pure single Kerr nonlinear layer of dielectric material using the Maxwell-Duffing approach. We employ the Duffing anharmonic oscillator as an alternative constitutive relation to express the electric field as a nonlinear function of the induced polarization. Utilizing both the electromagnetic wave equation and the Duffing constitutive relation, we obtain a nonlinear polarization equation propagates through the nonlinear layer under the slowly varying envelope approximation. With the application of boundary conditions at both interfaces, expressions for the incident, reflected, and transmitted intensities of the light wave are obtained as nonlinear functions of the polarization and other controlling parameters. For realistic input parameters, our numerical results demonstrated the existence of an intrinsic optical bistability (IOB) in a pure single dielectric layer. Furthermore, the threshold value of the observed IOB depends essentially on the value Eth, i.e., the minimum value required to invoke the third-order nonlinearity inside the material. For operating frequency near the sharp resonance region, Eth was found to be ≈105 V/cm; this is equivalent to a threshold value of the optical intensity ≈1010 W/cm2. With the developments in THz sources, it is nowadays possible to observe this IOB experimentally by tuning the operating frequency near the sharp resonance region of the material. Steps to get the threshold value of Eth are also advised.
Optical bistability based on surface plasmon polaritons in the Kretschmann configuration involving a Kerr nonlinear medium is described by analytical solutions. The conditions of forming the optical bistability with different parameters are explored. The resonant angle of surface plasmon polaritons varying with the incident light intensity also generates the phenomenon of bistability. The system could form optical bistability with the special thickness of the metal film and incident angle. This kind of system has potential application in all-optical networks.