Hybridized-band parametric oscillations in coupled Kerr microresonators

TL;DR

This paper presents a comprehensive framework for understanding and controlling hybridized optical parametric oscillations in coupled Kerr microresonators, enabling advanced nonlinear photonic functionalities.

Contribution

It introduces an analytical model for interband parametric gain in coupled resonators and demonstrates design principles for tailored nonlinear dynamics.

Findings

Diverse phase-matching pathways emerge in symmetric configurations.

Analytical expressions for gain maxima are derived.

Asymmetric designs enable operation at 7-GHz spacing without mode competition.

Abstract

Coupled resonators form band-like optical states that support rich nonlinearities beyond what is possible in single resonators. In these systems, four-wave mixing mediates interband coupling, displaying multimode dynamics that span both spatial and spectral degrees of freedom. In this study, we propose a framework describing the onset and control of hybridized optical parametric oscillation in three coupled silicon nitride microring resonators. In a symmetric configuration, we observe the emergence of diverse phase-matching pathways defined by the dispersive band structure. We develop an analytical model that captures the parametric gain of these interband processes and derive closed-form expressions for the dominant gain maxima; the analytical framework itself readily extends to more complex coupled networks. We further report an asymmetric design that co-engineers mode overlap and dispersion to operate on a compact 7-GHz spacing, free from mode competition. Our findings establish design principles for engineering nonlinear dynamics in coupled-resonator platforms, with implications for coherent photonic computing and quantum information processing.