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Optics Letters

Analytical study of optical bistability in silicon ring resonators

Ivan D. Rukhlenko, Malin Premaratne, Govind Prasad Agrawal

Published Dec 24, 2009• 85 citations
Publisher

Abstract

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.

DOI
10.1364/ol.35.000055

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We present a theoretical model that describes accurately the nonlinear phenomenon of optical bistability in silicon-waveguide resonators but remains amenable to analytical results. Using this model, we derive a transcendental equation governing the intensity of a continuous wave transmitted through a Fabry-Perot resonator formed using a silicon-on-insulator waveguide. This equation reveals a dual role of free carriers in the formation of optical bistability in silicon. First, it shows that free-carrier absorption results in a saturation of the transmitted intensity. Second, the free-carrier dispersion and the thermo-optic effect may introduce phase shifts far exceeding those resulting from the Kerr effect alone, thus enabling one to achieve optical bistability in ultrashort resonators that are only a few micrometers long. Bistability can occur even when waveguide facets are not coated because natural reflectivity of the silicon- r interface can provide sufficient feedback. We find that it is possible to control the input-output characteristics of silicon-based resonators by changing the free-carrier lifetime using a reverse-biased p-n junction. We show theoretically that such a technique is suitable for realization of electronically assisted optical switching at a fixed input power and it may lead to silicon-based, nanometer-size, optical memories.
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We demonstrate optical bistability in a Silicon-On-Insulator two-bus ring resonator with input powers as low as 0.3mW. We evaluate the importance of the different nonlinear contributions and derive time constants for carrier and thermal relaxation effects. In some cases, we also observe pulsation due to interaction between the dominant nonlinear effects. Such a behaviour may be problematic for possible memory and switching operations. Alternatively, it could be used for (tunable) pulse generation.
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