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Journal of Optics A Pure and Applied Optics

Optical bistability and Fano-like resonance transmission in a ring cavity-coupled Michelson interferometer

Li Li, Xinlu Zhang, Lixue Chen

Published Jun 3, 2008• 7 citations
Publisher

Abstract

This paper presents theoretical investigations on a new ring cavity-coupled scheme of a Michelson interferometer with a linear loop mirror, which has the attraction of low loss and high stability due to the closed geometry. The optical transmission response is modeled using a scattering matrix approach and analytical expressions are derived. This single ring cavity-coupled system exhibits optical Fano resonance features and significantly enhances the switching sensitivity to the cavity detuning required for a large ON/OFF contrast ratio. The evolution of Fano-like interference and the effect of ring cavity confinement on the Fano-like resonance are studied numerically. Furthermore, optical bistability and multi-bistability are demonstrated by introducing Kerr nonlinearity inside the ring cavity. The shape and polarity of hysteresis loops are easily controllable by adjusting the phase compensation of the direct channel, while the switching thresholds are affected remarkably by the linear phase shift of the ring cavity. The simple structure of the single cavity-coupled interferometer will be important for practical applications in optical sensors, all-optical switches and logic function elements.

DOI
10.1088/1464-4258/10/7/075305

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This paper presents theoretical investigations on a new ring cavity-coupled scheme of a Michelson interferometer with a linear loop mirror, which has the attraction of low loss and high stability due to the closed geometry. The optical transmission response is modeled using a scattering matrix approach and analytical expressions are derived. This single ring cavity-coupled system exhibits optical Fano resonance features and significantly enhances the switching sensitivity to the cavity detuning required for a large ON/OFF contrast ratio. The evolution of Fano-like interference and the effect of ring cavity confinement on the Fano-like resonance are studied numerically. Furthermore, optical bistability and multi-bistability are demonstrated by introducing Kerr nonlinearity inside the ring cavity. The shape and polarity of hysteresis loops are easily controllable by adjusting the phase compensation of the direct channel, while the switching thresholds are affected remarkably by the linear phase shift of the ring cavity. The simple structure of the single cavity-coupled interferometer will be important for practical applications in optical sensors, all-optical switches and logic function elements.
The reflectivity of a single-channel waveguide mode upon resonantly coupling to a Kerr-active nonlinear resonant cavity is calculated analytically, including the effects of two-photon absorption. The resonant reflectivity takes the form of a Fano resonance because the solution includes linear reflections from perturbations downstream of the localized cavity. Instead of using a Hamiltonian formulation of the scattering problem, an intuitive set of basis states is used to expand the Green's function of the electric field wave equation. All resulting overlap functions describing the linear coupling between guided and localized states, and the nonlinear renormalization of the material's refractive index, are in terms of well-defined physical quantities. Although derived in the context of photonic crystal-based waveguides and cavities, the treatment is valid for any low-loss waveguide-resonator geometry that satisfies specific weak coupling criteria. For a cavity consisting of Al0.18Ga0.82As, hosting a localized mode at 1.55 microm with a Q of 4000 and a mode volume of 0.055 microm(3), we predict the onset of bistable reflection at incident powers of approximately 40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources.
We theoretically analyse the optical and optomechanical nonlinearity present in a hybrid system consisting of a quantum dot(QD) coupled to an optomechanical cavity in the presence of a nonlinear Kerr medium, and show that this hybrid system can be used as an all optical switch. A high degree of control and tunability via the QD-cavity coupling strength, the Kerr and the optomechanical nonlinearity over the bistable behaviour shown by the mean intracavity optical field and the power transmission of the weak probe field can be achieved.The results obtained in this investigation has the potential to be used for designing efficient all-optical switch and high sensitive sensors for use in Telecom systems.
In this paper we demonstrate the dynamic simulation of light traveling in a nonlinear fiber optic ring resonator (FORR) with a single coupler. The mathematical relations describing the nonlinear characteristics of the FORR are derived from light transmission theory in linear optical systems. Optical nonlinear phenomena such as bifurcation and chaos are investigated for optical bistability and the Ikeda instability. It is found that for the Ikeda instability of light inside a FORR, the ring-cavity lifetime is much longer than the Kerr-effect response time of the fiber ring. Transmission curves of bistability and instability are shown as a function of the coupler insertion losses (γ) and the coupling coefficients (κ).
In this study, we theoretically investigate the optical bistability (OB) in hybrid triple-cavity optomechanical systems (OMSs) composed of three coupled cavities (two optical cavities and one optomechanical cavity) in the presence of semiconductor quantum dot molecules and a Kerr medium with a Kerr coefficient of χ when the optomechanical cavity is driven by a pump laser with frequency ωp and the amplitude Ep, which results in optical pressure on the movable mirror of the OMS. The dynamical equations of motion for this triple-cavity hybrid system in the steady state limit are solved using the Heisenberg-Langevin equations to achieve OB. We have demonstrated that it is possible to adjust both the width of the hysteresis loop and the switching threshold by controlling the Kerr coefficient . t is found that by properly tuning the physical parameters, the bistable thresholds of the system can be switched on and switched off, which is useful for designing and optimizing sensitive all-optical switching .
The authors observe experimentally optical bistability enhanced through Fano interferences in high-Q localized silicon photonic crystal resonances (Q∼30000 and modal volume ∼0.98 cubic wavelengths). This phenomenon is analyzed through nonlinear coupled-mode formalism, including the interplay of χ(3) effects such as two-photon absorption and related free-carrier dynamics, and optical Kerr as well as thermal effects and linear losses. Experimental and theoretical results demonstrate Fano resonance based bistable states with switching thresholds of 185μW and 4.5fJ internally stored cavity energy (∼540fJ consumed energy) in silicon for scalable optical buffering and logic.
We analyze the resonant linear and nonlinear transmission through a photonic crystal waveguide side-coupled to a Kerr-nonlinear photonic crystal resonator. First, we extend the standard coupled-mode theory analysis to photonic crystal structures and obtain explicit analytical expressions for the bistability thresholds and transmission coefficients which provide the basis for a detailed understanding of the possibilities associated with these structures. Next, we discuss limitations of standard coupled-mode theory and present an alternative analytical approach based on the effective discrete equations derived using a Green's function method. We find that the discrete nature of the photonic crystal waveguides allows a geometry-driven enhancement of nonlinear effects by shifting the resonator location relative to the waveguide, thus providing an additional control of resonant waveguide transmission and Fano resonances. We further demonstrate that this enhancement may result in the lowering of the bistability threshold and switching power of nonlinear devices by several orders of magnitude. Finally, we show that employing such enhancements is of paramount importance for the design of all-optical devices based on slow-light photonic crystal waveguides.