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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Optical bistablity and differential amplification in coupled nonlinear microcavity resonators

Ying Lu, Jianquan Yao, Yizhong Yu, Peng Wang

Published Jan 28, 2005• 0 citations
Publisher

Abstract

We present a theoretical study of optical bistability and differential amplification, arising as a consequence of the nonlinear Kerr effect in mutually coupled nonlinear microcavity resonators. The dependence of the bistability and differential amplification on various parameters of the coupling range and the resonators is investigated. Multiple closely spaced bistability of the internal intensity in the microresonator is found with appropriate parameters. The results may be useful for a complex logic, memory or switch operation system.

DOI
10.1117/12.574961

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We present a theoretical study of optical bistability and differential amplification, arising as a consequence of the nonlinear Kerr effect in mutually coupled nonlinear microcavity resonators. The dependence of the bistability and differential amplification on various parameters of the coupling range and the resonators is investigated. Multiple closely spaced bistability of the internal intensity in the microresonator is found with appropriate parameters. The results may be useful for a complex logic, memory or switch operation system.
Bistability of an optical resonator with distributed Bragg-reflectors is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the Kerr medium (the quadratic electrooptic coefficient n 2 and the length of the Kerr medium l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in the corrugated waveguide Γ). We show that the optical resonator with distributed Bragg-reflectors has a multi-valued transmission characteristic by the Kerr effect. From the numerical calculations, the up-switching and down-switching power intensities of bistable operation are estimated.
Optical Kerr nonlinearity is central to optical bistability in high-Q microcavities. Here, we show that optical Kerr nonlinearities in Fabry Perot resonators can also result in self-focusing effects, that can substantially modify the Q-factors of the resonators. For the studied cavities, up to five-fold increase in Q-factors is predicted, attributed to reduction of sidewall leakage, confirmed via simulations performed on curved cavities. We also show that for high Q-factor cavities, the higher-order Kerr effect can become relevant already at modest input intensities scaling inversely with Q-factor for a particular n2/n4 ratio. We investigate numerically the role of higher-order Kerr effect on optical bistability responses and find that its inclusion can shift the bistability threshold to higher input intensities than predicted by the standard n2-only model.
We analyze theoretically the nonlinear phenomenon of optical bistability inside a ring resonator formed with a silicon-waveguide nanowire and derive an exact parametric relation connecting the output intensity to the input intensity. Our input-output relation accounts for linear losses, the Kerr nonlinearity, two-photon absorption, free-carrier-induced absorption and dispersion, and thermo-optic effects within the resonator. Based on our study, we generalize the standard definition of effective length to allow for all possible losses within a silicon ring resonator. We also present a simplified version of the bistable phenomenon valid for resonators operating in a regime in which losses resulting from two-photon absorption are relatively small. Our analytical results provide clear insight into the physics behind optical bistability and may be useful for designing silicon-based optical memories.