We present energy coupling (EC) and power coupling (PC) formalisms for analyzing optical instability in coupled microring resonators having instantaneous intensity dependent nonlinear refractive index. Analysis of a chalcogenide double-microring resonator is performed to investigate and compare instability phenomena predicted by both formalisms. It is shown that the EC formalism fails to predict Ikeda instability in the double-microring resonator and generally yields results that drastically deviate from those of the more rigorous PC formalism at high input powers and large phase detunings. We also show that the input threshold powers for reaching self-pulsation and Ikeda instabilities in a double-microring resonator can be minimized by proper selection of the coupling parameters. In particular, self-pulsation can be reached in a chalcogenide double-microring with input powers as low as tens of milliwatts, while the threshold power for Ikeda instability can be reduced by more than 20% compared to the value required in a single microring.
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