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Nonlinearity

Enhancement of optical bistability by periodic layering

Roberto Camassa, M. Gregory Forest, Robert E. Knapp

Published May 1, 1992• 1 citation
Publisher

Abstract

The authors study analytically and numerically the effect of a periodic perturbation in the index of refraction of a nonlinear optical medium. Using a one-dimensional model for monochromatic waves incident on the medium, they find that near resonance between the perturbation and the modulation of the electric field there can be a significant enhancement of optical bistability in the low intensity regime. In particular, they discuss in detail the case of the primary resonance, which is responsible for the most significant effects, and show how one can optimize the bistability curve for the implementation of an optical switch, based on the information provided by the resonance structure.

DOI
10.1088/0951-7715/5/3/006

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The authors study analytically and numerically the effect of a periodic perturbation in the index of refraction of a nonlinear optical medium. Using a one-dimensional model for monochromatic waves incident on the medium, they find that near resonance between the perturbation and the modulation of the electric field there can be a significant enhancement of optical bistability in the low intensity regime. In particular, they discuss in detail the case of the primary resonance, which is responsible for the most significant effects, and show how one can optimize the bistability curve for the implementation of an optical switch, based on the information provided by the resonance structure.
A theoretical demonstration of optical bistability in periodic layered media, particularly in long-period GaAs/AlAs superlattices is presented. The proposed structure consists of a periodic multilayer system, as opposed to previously demonstrated nonlinear bistable devices which employed Fabry-Perot etalons. The optical resonance effect which is essential for bistable devices is, in this case, induced by a refractive index modulation. The nonlinear active medium is distributed in the whole structure rather than placed between the two mirrors of a Fabry-Perot cavity. It is shown by a complete calculation of wave propagation in the periodic nonlinear medium that a multiple valued feature appears in the structure's nonlinear reflectivity spectrum. The input/output characteristics of the structure exhibit bistable hysteresis similar to that of a nonlinear Fabry-Perot etalon.>
Wysin et al1 suggested that the local field enhancement near a metal surface which occurs if surface plasmons are excited in a metal film, can be useful for observing optical bistability arising from the nonlinearity of the Kerr medium. Other geometrical arrangements2 have also been suggested. These studies assume plane waves in the nonlinear medium and use the Fresnel formulae for reflection and refraction from a layered medium but with linear refractive index replaced by the nonlinear refractive index. This assumes that the fields in the medium are homogeneous. However if surface plasmons are excited, then the fields are inhomogeneous and one has the problem of reflection and refraction from an inhomogeneous layered medium. The inhomogeneity is to be determined self consistently. Thus a proper treatment of optical bistability with surface plasmons should use the nonlinear solutions of the wave equation in Kerr medium. This is what we do in this paper.
In the last chapter, we examined the effect of cubic nonlinearity on selfrefraction of an optical beam. We have also seen that the presence of a quadratic nonlinearity can also contribute to change in the profile of a Gaussian beam in a crystal. In this chapter we will see how the effect of nonlinearity, alongwith the proper feedback, can give rise to optical bistability and hysteresis. This is not unexpected as hysteresis and bistability are also observed in nonlinear electronic circuits with feedback, such as in the Schmitt trigger, as well as in hybrid optical devices, such as an acoustooptic device with feedback (Banerjee and Poon, 1991). In what follows, we will examine two different types of optically bistable devices based on optical nonlinearities. The first is a nonlinear ring resonator comprising a two-level gain medium as the nonlinear element. We will treat both absorptive and dispersive bistability. Absorptive bistability is the case when the incident optical frequency is close to or equal to the transition frequency of the atoms from one level to another. In this case, the absorption coefficient becomes a nonlinear function of the incident intensity. On the other hand, if the frequencies are far apart, the medium behaves like a Kerr-type material and the system exhibits what is called dispersive bistability. In this case the material can be modeled by an effective n2 or v (3), meaning that the refractive index becomes a nonlinear function of the optical intensity. The second configurationwewill examine is a linear-nonlinear interface. In this case, the interface provides the feedback due to refractive index mismatch. In fact, the reflection coefficient (as well as the transmission coefficient) is modified due to the nonlinearity, which, as we shall see later, is responsible for demonstrating optical switching and bistability.
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.
Intrinsic optical bistability in the scattering and absorption of light from Rayleigh-particle-sized microparticles having an intensity-dependent refractive index is theoretically investigated. For particles near plasmon resonances optical switching also occurs by sweeping the frequency across the resonance at fixed incident intensity above a certain threshold. Several orders of magnitudes of reduction in the switching intensities are possible near sharp resonances, and an optical transistor mode with a very sizable differential gain can be achieved.
A novel mechanism is proposed for optical bistability by utilizing the effect of interference which occurs when two levels are coupled by a one-photon resonance and by a two-photon resonance. The resulting bistability does not require atomic saturation, so the bistability can be observed at relatively low incident intensities, and the mechanism is essentially Doppler free, since it occurs by a two-photon process involving absorption of counterpropagating beams of the same frequency. A significant feature is that two-photon bistability can be controlled not only by the magnitude of the field of the one-photon resonance but also by its phase, and an oscillation or amplification of the field of the two-photon resonance can be observed under certain conditions by the mechanism of the parametric interaction of the field of the one-photon resonance and the field of the two-photon resonance through a nonlinear medium.