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Physical Review A

Multibistability and self-pulsation in nonlinear high- Q silicon microring resonators considering thermo-optical effect

Libin Zhang, Yonghao Fei, Tongtong Cao, Yanmei Cao, Qingyang Xu, Shaowu Chen

Published May 6, 2013• 61 citations
Publisher

Abstract

Optical bistability (BI) and self-pulsation (SP) in high-$Q$ 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.

DOI
10.1103/physreva.87.053805

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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.
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.
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.
We theoretically analyze and experimentally demonstrate optical bi-stability and multi-stability in an integrated nonlinear high-order microring resonator filter based on high-index contrast doped silica glass. We use a nonlinear model accounting for both the Kerr and thermal effects to analyze the instability behavior of the coupled-resonator based filter. The model also accurately predicts the multi-stable behavior of the filter when the input frequency is slightly detuned. To understand the role of the intracavity power distribution, we investigate the detuning of the individual rings of the filter from the optical response with a pump–probe experiment. Such a measurement is performed scanning the filter with a low-power probe beam tuned a few free spectral ranges away from the resonance where the pump is coupled. A comprehensive understanding of the relationship between the nonlinear behavior and the intracavity power distribution for the high-order microring resonator filter will help the design and implementation of future all-optical switching systems using this type of filter.
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.
Optical bistability is one of the nonlinear properties that produce an essential light control which contributes in various photonics applications such as all-optical switching and optical memory. In this thesis, bistability behavior of optical signals generated in microring resonator (MRR) systems using bright soliton input pulses with 1.55 µm wavelength is studied. The generation of the bistable signals is mathematically analyzed through the transfer matrix analysis and simulated by the MATLAB software version 2014a. The behavior of the propagated input pulses in terms of intensity and phase shift is investigated for different configurations including All-pass MRR, Add-drop MRR and PANDA MRR systems. Three novel Mobius MRR configurations consist of All-pass Mobius MRR, Add-drop Mobius MRR and PANDA Mobius MRR configurations are proposed and the light treatment through Mobius MRR systems is analytically studied and compared with conventional MRR systems. For determining the effect of physical parameters such as ring radius, control power variation and coupling coefficients on the output pulse, the optical hysteresis loops of bistable signals are generated via silicon-on-insulator nonlinear MRR configurations. The analyses of the results are conducted by calculating the output switching power, input threshold power and hysteresis width of bistable loop for radius variation from 1 µm to 6 µm with an increment of 1 µm, change of coupling coefficient from 0.4 to 0.9 with increment of 0.1 and variation of controlled power from 50 mW to 100 mW with increment of 10 mW. It is found that small coupling coefficients enhance the hysteresis width and output switching power of optical bistable loops. The value of output switching power obtained at the output port of Add-drop Mobius MRR is 30.26 mW which is higher than those obtained from All-pass Mobius and PANDA Mobius MRR configurations. The threshold powers of the All-pass Mobius, Add-drop Mobius and PANDA Mobius configurations for on switching operations are obtained as 20.59 mW, 31.39 mW and 25.19 mW respectively. It is found that, optimization of the Mobius MRR system can be conducted by increasing the external radius of Mobius ring waveguide and decreasing the coupling coefficient with implementation of the high control power. In this work, the Mobius configurations are introduced as a convenient compact design to generate optical bistability in comparison with conventional configurations of nonlinear MRR system.
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.