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IEEE Journal of Quantum Electronics

Novel Optical Multibistability and Multistability Characteristics of Coupled Active Microrings

Qiang Zhang, Cui Qin, Kai-Sheng Chen, Meng Xiong, Xinliang Zhang

Published Dec 21, 2012• 7 citations
Publisher

Abstract

We theoretically demonstrate the novel multibistability and multistability features of two coupled active microrings. The continuation method is utilized to solve the parametric nonlinear equations of these two-active-microring systems, and the bifurcation theory is used to investigate the special points, which exist in continuation process. The novel results, which are interpreted by the nonlinear transmission spectrum, arise from gain saturation and the optical field coupling between these two nonlinear rings. Besides the common multibistability, which consists of serial S-shaped hysterical loops, the multibistability, which takes on novel shapes, such as the hat-shaped, knife-shaped, S-shaped butterfly, and inverted double-S-shaped is also demonstrated. The novel multistability includes inverted double-S-shaped tristability, woodpecker-shaped tristability, duke-shaped tristability, grasshopper-shaped tristability, and pseudo-quadristability. The electrical and optical control processes of the stability about these two coupled active microrings are also investigated. Results show that the on–off jumping threshold of this stability can be adjusted via changing the power of the light, which inputs from the add-drop port, and the type of this stability can also be changed by altering the injected current on each active microring.

DOI
10.1109/jqe.2012.2236077

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We theoretically demonstrate the novel multibistability and multistability features of two coupled active microrings. The continuation method is utilized to solve the parametric nonlinear equations of these two-active-microring systems, and the bifurcation theory is used to investigate the special points, which exist in continuation process. The novel results, which are interpreted by the nonlinear transmission spectrum, arise from gain saturation and the optical field coupling between these two nonlinear rings. Besides the common multibistability, which consists of serial S-shaped hysterical loops, the multibistability, which takes on novel shapes, such as the hat-shaped, knife-shaped, S-shaped butterfly, and inverted double-S-shaped is also demonstrated. The novel multistability includes inverted double-S-shaped tristability, woodpecker-shaped tristability, duke-shaped tristability, grasshopper-shaped tristability, and pseudo-quadristability. The electrical and optical control processes of the stability about these two coupled active microrings are also investigated. Results show that the on–off jumping threshold of this stability can be adjusted via changing the power of the light, which inputs from the add-drop port, and the type of this stability can also be changed by altering the injected current on each active microring.
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.
Combining a transfer matrix analysis and slowly varying envelope approximation, we propose a simple method to describe steady states associated with dispersive multistability in coupled microring resonators. This approach allows us to consider nonlinear interactions between independent forward and backward propagative fields. We applied this simple formalism first to decrease the tristability intensity threshold in linearly coupled resonators and second to optically control the tristable behavior in a single microring resonator.
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.
In this work, we study the bistability of an active nonlinear microring resonator and design a flip-flop based on the active microring resonator. In the presence of nonlinear and linear loss, we use Er-doped gain medium in the microring to obtain gain to compensate for the loss of the resonator. Both analytical and numerical methods are used to solve the propagation in the microring with double couplers, and we obtain the hysteresis loops of the microring. The results obtained by the two methods reveal that, in the presence of nonlinearity in microring resonators, the system exhibits bistability, and the gain in the microring leads to a decrease of the bias power when the active microring is taken as a bistable switcher. Basing on the bistability of the microring, we realize a set-reset flip-flop by adding a positive or negative feedback onto the bias. We also find that the duration of the set and reset pulses must exceed the field buildup time of the microring if we want to achieve the switching of the bias signal. In our design, the duration time is about 2 ps.
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.
The theoretical investigation has been performed on the implementation of optical Mobius shape in add-drop microring resonator. The modified add-drop Mobius configuration is used to investigate the optical bistability and the spectral transmission. The optical bright soliton pulse is used as the input source of the resonator system. The pulses propagation of the resonator system is modelled using the iterative programming based on the transfer matrix analysis equations. The enhancement of nonlinear effect of the resonator system is achieved by the add-drop Mobius resonator configuration. The system has been modelled for a variation of coupling coefficient for increase the bistable signal properties. The Add-drop Mobius MRR generated a bistable signal with 6.01 mW hysteresis width, and 9.47 mW output switch power with optimized radius of 5 µm outer and 4.5 m inner ring parts with 50 mW controlled power and input power. Mobius configuration is found as the better shape of resonator cavity that capable of optical switching application.