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Journal of Physics Conference Series

Optical tristability investigation in two coupled ring resonators

Santhad Pithakwongsaporn

Published Sep 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1742-6596/901/1/012107

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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.
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.
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.
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.
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.