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arXiv:physics/0703132 · Applied Physics Letters

Observation of femtojoule optical bistability involving Fano resonances in high-Q∕Vm silicon photonic crystal nanocavities

Xiaodong Yang, Chad A. Husko, Chee Wei Wong, Mingbin Yu, Dim-Lee Kwong

Published Jul 30, 2007• 93 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.2757607

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We observe experimentally optical bistability enhanced through Fano interferences in high-Q localized silicon photonic crystal resonances (Q ~ 30,000 and modal volume ~ 0.98 cubic wavelengths). This phenomenon is analyzed through nonlinear coupled-mode formalism, including the interplay of chi(3) effects such as two-photon absorption and related free-carrier dynamics, and optical Kerr as well as thermal effects and linear losses. Our experimental and theoretical results demonstrate for the first time Fano-resonance based bistable states with switching thresholds of 185 micro-Watt and 4.5 fJ internally stored cavity energy (~ 540 fJ consumed energy) in silicon for scalable optical buffering and logic.
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 demonstrate extremely low-power all-optical bistability by utilizing silicon photonic crystal nanocavities, based on the plasma effect of carriers generated by two-photon absorption. Owing to the high quality factor and the small volume of the nanocavities, the photon density inside the cavity becomes extremely high, which leads to a large reduction in operation power. Optical bistable operation in a single nanocavity permits optical read-write memory operation, which opens the possibility of an integrated optical logic circuit on a single chip, based on photonic crystals. The demonstrated bistable threshold power is 0.4 mW with a set pulse energy of 74 fJ, at a switching speed of <100 ps.
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.