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Physical Review E

Dispersive tristability in microring resonators

Yannick Dumeige, Patrice Féron

Published Dec 16, 2005• 41 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.72.066609

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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.
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.
A convenient for practical use new theoretical approach describing a nonlinear frequency response of the multi-resonant nonlinear ring cavities (RC) to an intense monochromatic wave action is developed. The approach closely relates the many-valuednesses of the RC frequency response and the dispersion relation of a waveguide, from which the cavity is produced. Arising of the multistability regime in the nonlinear RC is treated. The threshold and the dynamic range of the bistability and tristability regimes for an optical ring cavity with the Kerr nonlinearity are derived and discussed.
Systems of coupled cavity modes have the potential to provide bright quantum optical states of light in a highly versatile manner. Microring resonators, for instance, are highly scalable candidates for photon sources. Thanks to CMOS fabrication techniques for their small footprint and the relative ease of coupling many such microrings together. However, surface roughness of the waveguides and defects in the coupler geometry routinely induce splitting of the cavity modes due to backscattering and backcoupling. The parasitic back-propagating mode in a microring leads to hybridization of the modes, altering the linear and nonlinear properties of a system of coupled cavity modes and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian nonlinear processes in systems of coupled cavity modes based on an effective field Hamiltonian and a dispersive input–output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via symplectic transformations on the optical modes. We then use this framework to numerically model and explore the problem of backscattering in microring resonators in physically relevant parameter regimes, involving the splitting of various resonances, and we calculate the consequent impurity and heralding efficiency of various heralded photon schemes. We provide a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.