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Journal of Lightwave Technology

Optical Bistability Investigation in a Nonlinear Silicon Microring Circuit

Surasak Chiangga, Santhad Pitakwongsaporn, T.D. Frank, Preecha P. Yupapin

Published Jan 30, 2013• 13 citations
Publisher

Abstract

We describe the optical bistability phenomenon in a silicon-on-insulator microring resonators device by using an analytical theory, which includes both linear and nonlinear effects such as two-photon absorption, Kerr effect, free carrier and thermo-optic effect (TOE). We show that the bistable switching threshold and the hysteresis loop width can be tuned by geometrical parameters of the device and by the nonlinear parameters. The accuracy of the analytical approach is verified by comparing the spectrum responds with the predicting data from a commercial finite-difference time-domain software tool, and a very close agreement is found between the two when TOE is incorporated in analytical theory. In addition, our analysis reveals that a new type of hysteresis loop occurs at low input intensity. The mode suppression of the designed device by Vernier effect for tunable filter applications is also briefly discussed.

DOI
10.1109/jlt.2013.2243819

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We describe the optical bistability phenomenon in a silicon-on-insulator microring resonators device by using an analytical theory, which includes both linear and nonlinear effects such as two-photon absorption, Kerr effect, free carrier and thermo-optic effect (TOE). We show that the bistable switching threshold and the hysteresis loop width can be tuned by geometrical parameters of the device and by the nonlinear parameters. The accuracy of the analytical approach is verified by comparing the spectrum responds with the predicting data from a commercial finite-difference time-domain software tool, and a very close agreement is found between the two when TOE is incorporated in analytical theory. In addition, our analysis reveals that a new type of hysteresis loop occurs at low input intensity. The mode suppression of the designed device by Vernier effect for tunable filter applications is also briefly discussed.
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.
Over the past few decades, optical ring resonators have attracted a considerable amount of attention as versatile elements for a wide range of applications ranging from telecommunication and sensing to basic scientific research [1,2]. The silicon-on-insulator (SOI) material system is a mature fabrication technique and provides the ability to implement microring resonators. In addition, the high confinement of light and the large third-order nonlinearity of silicon at wavelengths in the near infrared, typically around 1.4-1.6 µm, can be utilized for a number of applications by microring resonator devices [3,4]. The optical bistability observed in silicon-based microring resonators have been theoretically investigated and numerically simulated through various sophisticated techniques [5-9]. However, only recently unifying analytical theories regarding nonlinear effects of optical bistability in microring resonators in terms of a slowly varying envelope approach have been reported [10,11]. Previously, we analytically described the nonlinear response of microring resonators consisting of an add-drop filter with feedback and showed that Fano lineshapes can be adjusted by the resonator parameters [12]. In this chapter, we extend our work to examine the optical bistabililty in such microring resonators and test the analytical results with those predicted by the OptiFDTD software package.
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.
Optical bistability (BI) and self-pulsation (SP) in high-QQQ silicon microring resonators (MRRs) induced by thermo-optical (TO) effect and other nonlinear effects are theoretically studied with coupled mode theory and linear stability analysis method. It is found that the boundaries for both BI and SP are mainly restricted by two counteracting effects: free carrier dispersion effect and TO effect. If the refractive index changes of a MRR caused by these two effects are on the same order of magnitude, the output power will exhibit much more complicated dependence on the input power and wavelength, namely, input-power-dependent multi-BI and multi-SP regions will exist at certain input wavelength range. The controllability of multi-BI and multi-SP phenomena by the input power and input wavelength could be very useful in all-optical nonlinear devices.
In this work, we experimentally study the optical bistability (BI) behavior in active silicon microring resonators (MRR). A stable hysteresis loop response at the output port is demonstrated at a power level higher than the BI threshold, taking into account the different detuning and free carrier life-times. That hysteresis is observed at low and high BI thresholds, which can be used for all-optical switching and optical routers. The MRR is placed inside a reverse-biased PIN junction and fabricated by CMOS technology. It records a loaded Q-factor, linewidth (3 dB width of the spectrum), and extinction ratio (ER) around105,15.310^{5},15.3105,15.3pm, and 20 dB, respectively.
The microring resonators have potential applications for the photonic integrated circuits. The dynamical phenomena of the two coupled microrings require a simple and efficient numerical formalism for solution of the system. We employ an analytical formula to calculate the optical tristability inside the two coupled microrings that takes into account Kerr nonlinearity and the effect of loss. We also compare the analytical results with the results from 3D finite-difference time-domain simulation. In addition, we show it is possible to obtain configurations which can tune the tristable region. This could be useful for designing optical logic applications.