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Topical Meeting on Optical Bistability (OB)

Overview of Optical Instabilities

Luigi Lugiato

Published Jan 1, 1988• 0 citations
Publisher

Abstract

The last decade witnessed a remarkable research activity, both theoretical and experimental, on the unstable phenomena which arise in optical systems. The development of the theory of optical bistability in the seventies played a major role in stimulating the interest in this subject. Most of this research concerned the onset of spontaneous oscillations and/or chaotic behaviour, and I will review some general theoretical results and few experiments that confirm them.

DOI
10.1364/obi.1988.wc.1

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The last decade witnessed a remarkable research activity, both theoretical and experimental, on the unstable phenomena which arise in optical systems. The development of the theory of optical bistability in the seventies played a major role in stimulating the interest in this subject. Most of this research concerned the onset of spontaneous oscillations and/or chaotic behaviour, and I will review some general theoretical results and few experiments that confirm them.
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The subject of spontaneous pulsations in Optical Bistability has stimulated considerable interest following its prediction by Bonifacio, and Lugiato1 in the framework of the plane-wave, ring cavity model and the realization by McCall2 of an electro-optical converter of cw coherent light into pulsed radiation. In a subsequent important development Ikeda3 showed that, in the dispersive case, the Bonifacio-Lugiato instability leads to chaotic behavior (optical turbulence). This was later observed in a hybrid device by Gibbs, et al4.
Abstract The theoretical description of radiation − matter interactions in terms of master equations can be approximated by a semi-classical theory when quantum fluctuations are small. This approach, the exact definition of which will emerge later, has been enormously influential in understanding instabilities and chaos in quantum optics. Although much of the theory (and experiment) has been done only in the last few years, there were already indications in the early experiments on ruby lasers of ‘spiky’ behaviour. Instabilities are often due to competition between different modes which are coupled together non-linearly. Consequently we will first describe qualitatively the modes that are important when we deal with optical systems in Fabry-Perot or ring cavities.
Although the discovery of oscillatory instabilities (both single-mode and multimode) in free-running lasers was achieved in the 1960s, investigations on oscillatory instabilities in optical bistability did not take place until the 1970s and 1980s. The first section of this chapter does not deal with oscillatory instabilities, but instead concerns an interesting dynamical phenomenon in optical bistability that arises when the input field approaches a boundary of the bistable domain, and is called critical slowing down . This has been investigated both theoretically and experimentally. The remainder of this chapter is entirely devoted to oscillatory instabilities, following a historical order. With an inverse approach with respect to the laser case, we discuss multimode instabilities first. In Section 24.2.1 we start with the description of the instability which arises under exactly resonant conditions. While this is the counterpart in optical bistability of the resonant multimode laser instability discussed in Section 22.5, a striking difference from the laser case is that in the passive configuration there is no corresponding single-mode instability. This difference disappears, however, when we consider the generalization of the multimode instability of optical bistability to the detuned configuration. Finally we show that in the detuned case it has been possible to achieve a convincing experimental observation of the multimode instability in a long microwave cavity. After some relevant miscellaneous considerations in Section 24.2.2, in Section 24.2.3 we address the subject of the multimode Ikeda instability which leads to period doubling and chaos and aroused a lot of interest in optical chaos. We emphasize also the intrinsic connections with the standard multimode instability discussed in Section 24.2.1, showing, in particular, that the Ikeda instability requires conditions far from the low-transmission limit, i.e. that ∝L is not small. In Section 24.3 we discuss single-mode instabilities in optical bistability. In Section 24.3.1 we illustrate a configuration for the single-mode instability that includes also the Gaussian shape of the electric field in the beam section, and leads to periodic, close-to-sinusoidal self-pulsations.