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Optics Letters

Carrier-induced optical bistability in silicon ring resonators

Qianfan Xu, Michal F. Lipson

Published Jan 1, 2006• 244 citations
Publisher

Abstract

We demonstrate optical bistability in a micrometer-sized silicon ring resonator based on the free-carrier dispersion effect in silicon. We measure the transfer function of the resonator showing a hysteresis loop with an input optical power of less than 10 mW. The influence of the thermal optical effect, which is minimized in the experiment by use of nanosecond pulses, is evaluated theoretically. Applications include sequential logic operations for all-optical routing.

DOI
10.1364/ol.31.000341

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We demonstrate optical bistability in a micrometer-sized silicon ring resonator based on the free-carrier dispersion effect in silicon. We measure the transfer function of the resonator showing a hysteresis loop with an input optical power of less than 10 mW. The influence of the thermal optical effect, which is minimized in the experiment by use of nanosecond pulses, is evaluated theoretically. Applications include sequential logic operations for all-optical routing.
We demonstrate low-power thermo-optic-based optical bistability in a free-standing silicon ring resonator. A bistable optical response is achieved at reduced pump powers by thermally isolating the ring resonator from its supporting substrate with an air gap. The conversion efficiency from optical power to temperature change in the silicon core is enhanced. The optical transfer function of the resulting free-standing resonator exhibits a hysteresis loop for 80 microW input optical power. Similar nonthermally isolated resonators at the same detuning do not exhibit a bistable mode for input powers less than 2 mW.
We investigate the significance of secondary effects caused by free carrier accumulation and subsequent heating on the nonlinear behaviour of ultrasmall Silicon-On-Insulator ring resonators. All-optical bistability based on thermal dispersion was experimentally obtained for an input power of only 0.28mW. At higher powers, pulsating behaviour was observed which is problematic for the stability of thermal memory and switching operations. Using free carrier dispersion, we also demonstrate all-optical wavelength conversion with a pulse length of 10 ns, indicating that bitrates of 0.1 Gb/s are feasible. Also here, the presence of unstable pulsations was observed, leading to significant errors in the converted data pattern.
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.
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.