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Physical review. B, Condensed matter

Comment on ‘‘Optical response of nonlinear planar resonators under pulsed-beam excitation’’

Guy Vitrant, Marc Haelterman, R. Reinisch

Published Nov 15, 1993• 5 citations
Publisher

Abstract

In a recent paper [Phys. Rev. B 46, 7632 (1992)], Peschel and Lederer consider a nonlinear planar resonator filled by a negative Kerr medium which is local but not instantaneous. In this Comment, we show that the loops reported by Peschel and Lederer, for large oblique incidence, do not correspond to bistable cycles. Indeed the noninstantaneous response of the nonlinear material and the dynamics of the fields do not lead to the feedback mechanism required for optical bistability.

DOI
10.1103/physrevb.48.15465

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In a recent paper, we proposed a new theoretical model of nonlinear optical cavities1. Our theory, which is valid for both nonlinear (NL) waveguide couplers and NL Fabry-Pérot (FP) with arbitrary angle of incidence, constitutes a unified theory of nonlinear planar resonators. The main advantage of the model is that it greatly simplifies the numerical study of transverse effects in NL resonators and provides a deep understanding of physical phenomena related to Optical Bistability (OB) in such devices. In particular it allowed us to analyse the role of diffraction and the influence of the incident angle on the steady-state NLFP response1,2.

Nonlinear Dynamics in Optical Systems•Jan 1, 1990•1 citation
In a recent paper [Phys. Rev. B 46, 7632 (1992)], Peschel and Lederer consider a nonlinear planar resonator filled by a negative Kerr medium which is local but not instantaneous. In this Comment, we show that the loops reported by Peschel and Lederer, for large oblique incidence, do not correspond to bistable cycles. Indeed the noninstantaneous response of the nonlinear material and the dynamics of the fields do not lead to the feedback mechanism required for optical bistability.
A comprehensive analysis of the interaction of pulsed light beams with nonlinear planar resonators is presented, covering both arbitrary types of nonlinearity and arbitrary states of polarization of the incident field. The characteristic of the optical response is discussed in its dependence on the crucial parameters of the resonator system as well as of the input pulse. Numerical results are given for the transmission response of a multiple-film configuration under oblique incidence, which is endowed with a dynamic, saturable nonlinearity. In particular, conditions for optical bistability to occur are derived.
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.
Using the modal theory the optical response of a non-linear planar resonator illuminated by a genuine two-dimensional, pulsed beam is studied. We consider a defocusing Kerr-like non-linearity appearing well below the fundamental band-gap of direct semiconductors due to two-photon processes. Optical bistability is identified for normal incidence whereas it disappears if the angle of incidence of the input beam becomes comparable to the width of the resonance. No evidence for symmetry breaking could be found, whereas a pronounced beam shaping arises in the high-transmission state.
A unified nonlinear modal theory that is valid not only for waveguide couplers but also for nonlinear Fabry–Perot resonators has recently been proposed. The validity of this new approach is numerically demonstrated by comparison with the well-known bidimensional theory. The unified modal theory appears to be a powerful tool for studying transverse effects in a broad class of nonlinear resonators. It has been used to derive the main characteristics of the stationary behavior of the optical resonators in the case of a local nonlinearity. In particular, the disappearance of optical bistability when the resonator is tilted is predicted. Optical bistability at nearly normal incidence is interpreted by the coupling between two resonantly excited counterpropagating modes that are at the origin of the required transverse feedback.
In a recent paper, we proposed a new theoretical model of nonlinear optical cavities1. Our theory, which is valid for both nonlinear (NL) waveguide couplers and NL Fabry-Pérot (FP) with arbitrary angle of incidence, constitutes a unified theory of nonlinear planar resonators. The main advantage of the model is that it greatly simplifies the numerical study of transverse effects in NL resonators and provides a deep understanding of physical phenomena related to Optical Bistability (OB) in such devices. In particular it allowed us to analyse the role of diffraction and the influence of the incident angle on the steady-state NLFP response1,2.