Hybridized-band parametric oscillations in coupled Kerr microresonators

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.

💡 Research Summary

This paper investigates the emergence and control of hybridized optical parametric oscillations (OPOs) in coupled Kerr microresonator arrays, focusing on a three‑ring silicon nitride platform. By exploiting evanescent coupling, the three identical rings form three super‑modes—symmetric (S), central (C), and anti‑symmetric (AS)—each possessing its own integrated dispersion that is a combination of the bare‑ring group‑velocity dispersion and a wavelength‑dependent coupling function J(μ). The authors classify phase‑matching topologies into three categories: horizontal (Type‑I‑like), where signal and idler reside on the same super‑mode branch and benefit from an effectively anomalous curvature; vertical (Type‑II‑like, Δμ = 0), where signal and idler occupy different branches (S and AS) and phase‑matching is achieved solely by the inter‑band splitting; and diagonal (Type‑II‑like, Δμ ≠ 0), which requires simultaneous compensation of inter‑ and intra‑band dispersion. Closed‑form expressions for the parametric gain are derived, incorporating super‑mode overlap factors Γ and pump‑induced cross‑phase modulation (XPM) shifts.

Experimentally, continuous‑wave pumping is pulsed (250 ns) and amplified to ≈2 W peak power to overcome the moderate Q (≈4 × 10⁵) of the 50 µm radius rings. In the symmetric |ooo| configuration two distinct OPO processes are observed when the C super‑mode is pumped. OPO 1 corresponds to diagonal phase‑matching (AS↔S) with sidebands appearing around μ ≈ ±4, while OPO 2 follows horizontal phase‑matching (AS‑AS) with sidebands near μ ≈ ±21. Measured transmission maps, integrated dispersion curves, and calculated gain spectra show excellent agreement with the analytical model, confirming that the gain maxima are set by the balance of bare‑ring dispersion, coupling J(μ), pump detuning, and XPM‑induced shifts.

To suppress mode competition and achieve a compact, competition‑free oscillation, the authors introduce an asymmetric |oOo| design where the outer rings differ in radius, creating a deliberate dispersion mismatch and an avoided mode crossing (AMX). This engineering yields a single OPO with a 7 GHz (≈0.056 FSR) signal‑idler spacing, well within the bandwidth of standard photodetectors, and eliminates competing comb‑generation channels.

The work provides a scalable analytical framework that requires only knowledge of the coupling topology, the coupling function J(μ), and the individual ring dispersion. Consequently, it can be extended to larger resonator networks for designing tailored nonlinear interactions. The demonstrated ability to engineer specific phase‑matching pathways and to isolate a single OPO has direct implications for coherent photonic computing, neuromorphic architectures, and quantum information processing, where high‑purity squeezed states and multimode entanglement are essential. The paper thus establishes practical design rules for harnessing the rich nonlinear dynamics of coupled‑resonator platforms.