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Acta Physica Polonica A

Time Delay in Thin Dielectric Slabs with Saturable Nonlinearity

Petra P. Beličev, I. Ilić, J. Radovanović, V. Milanović, Ljupčo R. Hadžievski

Published Apr 1, 2009• 3 citations
Publisher

Abstract

Time delays for an intense transverse electric wave propagating through a slab with saturable nonlinearity are investigated.The nonlinearity is assumed in a form of the Vinetskii-Kukhtarev model, which is relevant for the slabs made of nonlinear photorefractive crystals, such as GaAs and LiNbO3, which feature a saturable nonlinearity.The expressions for the group delay and the dwell time are derived and the relation between them is studied.It is shown that the difference between them has three different contributions.The first one corresponds to the self-interference associated with the dispersion of the medium surrounding the slab.The other two appear due to the nonlinearity of the slab and oblique incidence of the transverse electric wave.All the results are compared with the case of dielectric slabs with cubic (Kerr) nonlinearity.

DOI
10.12693/aphyspola.115.834

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Time delays for an intense transverse electric wave propagating through a slab with saturable nonlinearity are investigated.The nonlinearity is assumed in a form of the Vinetskii-Kukhtarev model, which is relevant for the slabs made of nonlinear photorefractive crystals, such as GaAs and LiNbO3, which feature a saturable nonlinearity.The expressions for the group delay and the dwell time are derived and the relation between them is studied.It is shown that the difference between them has three different contributions.The first one corresponds to the self-interference associated with the dispersion of the medium surrounding the slab.The other two appear due to the nonlinearity of the slab and oblique incidence of the transverse electric wave.All the results are compared with the case of dielectric slabs with cubic (Kerr) nonlinearity.
Group delay for a reflected light pulse from a weakly absorbing dielectric slab is theoretically investigated, and large negative group delay is found for weak absorption near a resonance of the slab (Re(kd)=mpiRe(kd)=m\\piRe(kd)=mpi). The group delays for both the reflected and transmitted pulses will be saturated with the increase of the absorption.
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 show theoretically that, based on the dispersive phase coupling effect during the wave mixing process, both slow and fast light can be achieved in GaAs–AlGaAs photorefractive multiple quantum wells (PRMQWs) films applied with a transverse direct-current electric field. The general formula for the group velocity of the diffracted beams in the Raman–Nath regime during the wave mixing process in a nonlinear thin film is derived and is then applied to the case of the PRMQWs films in the transverse geometry. The simulation results in the transverse-geometry PRMQWs films show that the group velocity and bandwidth of slow light can be on the order of centimeter per second and 100 kHz, respectively. The extremely low group velocity and the relatively broad bandwidth are mainly originated from the strong quadratic electro-optic effect and the fast response rate of the PRMQWs films, respectively. Our results show that the delay-bandwidth product of slow light can be significantly improved in PRMQWs films as compared to the reported results in other photorefractive materials.
A theoretical analysis on wave propagation and optical properties of slabs with light-induced free charge carriers within a Fabry-Pérot framework is presented. The key of the analysis is to attack the wave propagation problem in terms of the time-averaged Poynting vector modulus within the medium through an alternative approach. This fact allows coupling the microscopic (free charge rate) and macroscopic (electromagnetic field evolution) equations self-consistently by means of the nonlinear permittivity and conductivity, which, in turn, depend on the time-averaged Poynting vector modulus. Thereby, the transmittance, reflectance, and absorptive power are derived as functions of the pump intensity and medium thickness. Bistable behavior is found at relatively high excitation intensity for positive values of the nonlinear permittivity coefficient. The bistability enhances for increasing values of such coefficient and weakens for increasing values of nonlinear photoconductivity coefficient. On the contrary, for negative nonlinear permittivity coefficient, bistability does not appear possessing these media mirrorlike behavior. Some possible applications are suggested.