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Cambridge University Press eBooks

Complement 7B: Nonlinear optics in optical Kerr media

G. Grynberg, Alain Aspect, Claude Fabre, Claude N. Cohen-Tannoudji

Published Sep 2, 2010• 0 citations

Abstract

In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.

DOI: 10.1017/cbo9780511778261.036

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Accurate modeling of optical nonlinearities is crucial to describe macroscopic laser propagation in a medium, including sum frequency generation, spectral broadening due to self-phase modulation, various ionization processes and soliton formation. For incident laser light the response of the medium is given by the induced polarization of the microscopic system. The polarization is usually expanded in a Taylor series for the electric field amplitude, which is truncated after the first non-linear term being of third order for isotropic media. A third-order nonlinearity leads to the well-known optical Kerr effect, where the refractive index of the medium becomes intensity dependent via n = n0+ n2I. This leads to an inherent problem when modeling laser propagation in two or more spatial dimensions, linked to the formal divergence (n2> 0) of the refractive index for increasing intensity.

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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.