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Optical bistability and soliton switching in an optical ring cavity

Eric Curtis John Oliver

Published Jan 1, 2004• 0 citations
Publisher

Abstract

This thesis presents the theory of the driven optical ring cavity containing a nonlinear material. First, an overview of the history of bistability and spatial solitons in driven nonlinear cavities is outlined. Then, the basic theory of the optical Kerr effect is presented and two of its consequences are outlined: optical bistability and spatial solitons. Within this background, the mirror feedback model is derived from the Maxwell-Bloch equations and considerations of the classical optics of the cavity. This model is analytically shown to exhibit bistability in the plane wave case. The mean-field model is subsequently derived by applying the mean-field limit to the Maxwell-Bloch equations and the cavity optics. In addition, the mean-field model is analytically shown to exhibit bistability in the plane wave case. Numerical simulations are performed on the mean-field model demonstrating the existence of: (i) plane wave bistability, (ii) transverse modulational bistability, (iii) the ability to “switch†between bistable states in both the plane wave and modulated case, (iv) instabilities in the modulated case and (v) the possibility for optimization of the switching process. Finally, an application of bistable driven cavities is explored: an all-optical digital information processor and storage device.

DOI
10.26108/ktaz-tx51

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This thesis presents the theory of the driven optical ring cavity containing a nonlinear material. First, an overview of the history of bistability and spatial solitons in driven nonlinear cavities is outlined. Then, the basic theory of the optical Kerr effect is presented and two of its consequences are outlined: optical bistability and spatial solitons. Within this background, the mirror feedback model is derived from the Maxwell-Bloch equations and considerations of the classical optics of the cavity. This model is analytically shown to exhibit bistability in the plane wave case. The mean-field model is subsequently derived by applying the mean-field limit to the Maxwell-Bloch equations and the cavity optics. In addition, the mean-field model is analytically shown to exhibit bistability in the plane wave case. Numerical simulations are performed on the mean-field model demonstrating the existence of: (i) plane wave bistability, (ii) transverse modulational bistability, (iii) the ability to “switch†between bistable states in both the plane wave and modulated case, (iv) instabilities in the modulated case and (v) the possibility for optimization of the switching process. Finally, an application of bistable driven cavities is explored: an all-optical digital information processor and storage device.
Light propagation in a 2-D array of coupled optical cavities with Kerr nonlinearity driven by a plane holding beam is numerically studied. Optical bistability together with its modulational instability (MI) are investigated, and 2-D discrete cavity solitons are simulated. These simulations revealed the switching on/off of the solitons along with the ability of a proper Gaussian beam (GB) to control their positions. Soliton-soliton and soliton-GB interactions are considered, and finally, all-optical NOR , XNOR, and NAND gates are proposed as realized by this device.
In Chapter 9 we discussed the case of a nonlinear cavity containing an active medium. In this framework, the outstanding phenomenon which arises is laser emission, and we calculated the stationary solutions for the ring laser. In this chapter, instead, we turn our attention to the passive nonlinear cavity and in this framework the outstanding phenomenon is optical bistability , i.e. the existence of two distinct stable stationary states that coexist for the same fixed values of the parameters in play. This phenomenon can arise also in the case of an active system contained in a cavity, as we have already noted in Section 9.1 and as we will discuss further in connection with the laser with injected signal, but it became popular from the studies of nonlinear passive optical cavities in the 1970s and 1980s. In contrast to the laser case, in the passive configuration we use an input coherent field, which is injected into the cavity. We discussed this case in Chapter 8 and derived a general equation for the transmission of the cavity (Eq. (8.23)), which we used for an empty cavity and for a linear cavity in Sections 8.4 and 8.5, respectively. In this chapter we will discuss the full nonlinear configuration. It is customary to identify two extreme cases of optical bistability called absorptive optical bistability and dispersive or refractive optical bistability . In both cases an essential ingredient to obtain the bistable behavior is the feedback action exerted by the mirrors of the cavity. In the purely absorptive configuration, in which there is exact resonance among the frequencies of the input field, of the atoms and of the cavity, the other essential ingredient is the saturable nonlinearity of the absorption. In the dispersive case, instead, the main feature is the nonlinearity of the refractive index. These two cases will be illustrated in Sections 11.1 and 11.2, respectively, both “exactly” and in the low-transmission limit.
We analyze instabilities in mixed absorptive and dispersive optical bistability in the rate-equation approximation and the mean-field and good-cavity limits. Our starting point is a set of multimode equations derived from the Maxwell-Bloch equations for ring-cavity boundary conditions. We obtain analytic expressions for the instability conditions. In a plane-wave analysis, we find that a portion of the lower transmission branch can be unstable in addition to the upper-branch instability found in purely absorptive bistability. Also, a new disconnected region of instability can exist on the upper branch. Our analysis becomes particularly simple for equal and opposite cavity detunings and we explore this case in detail. We extend our treatment to include a Gaussian transverse intensity profile and show that the instabilities remain in the presence of Gaussian averaging. We also show that many of the results obtained in the rate-equation approximation hold when the atomic linewidth and atomic decay rate are of the same order.
The nonlinear phenomenon known as optical bistability, which enables optical systems to maintain two stable output states for a single input, is thoroughly examined in this review article. Through a detailed analysis of two important devices—the Simple Fiber Ring (SFR) resonator and the Nonlinear Optical Loop Mirror (NOLM)—it investigates the basic concepts of optical bistability, namely nonlinearity and feedback. Numerical simulations demonstrating dynamic dynamics and stability conditions bolster a strong theoretical framework. Recent advancements in bistable optical technologies, including developments in epsilon-near-zero materials, silicon photonics, hybrid plasmonic structures, neuromorphic photonics, and AI-driven photonic processors are also discussed. Furthermore, this review highlights emerging applications of optical bistability in optical logic circuits, high-speed communication, and quantum information processing. This review work is a useful tool for researchers and engineers creating next-generation optical systems because it connects theoretical insights with cutting-edge technological developments.
We compare theoretical predictions and experimental data for the multimode instability of optical bistability, which arises from the coherent dynamics of a system of two-level molecules contained in an optical cavity and driven by an external stationary laser field. Considerable insight into this phenomenon is provided by two ``rules of thumb'' that govern the behavior of the self-pulsing frequency, and establish its relation with the Rabi frequency of the intracavity field. We describe in detail the experimental apparatus and the main features of the experimental findings. The theoretical results are based on the Maxwell-Bloch equations for a ring cavity in the plane-wave approximation. Despite the crudeness of this model, the numerical data display a satisfactory qualitative agreement with the experimental results. Additional period-doubling and chaotic phenomena, predicted by the theory and not observed in the experiment, are presumably washed out by the longitudinal and radial variation of the electric field in the cavity.