Critically coupled zeroth-order resonance for ultrathin nonlinear photonics
Ultrathin active materials are essential for compact nonlinear and quantum photonic devices, yet no general principle exists to link their optical constants to the cavity designs required for simultaneous field buildup and reflection suppression. Consequently, achieving extreme optical confinement currently relies on trial-and-error optimization for every new material. Here, we establish a design rule for metal-backed cavities that maximizes light-matter interaction by ensuring the simultaneous satisfaction of zeroth-order resonance and critical coupling. We derive a closed-form analytical condition that partitions the (n, k) plane into critically coupled, over-coupled, and under-coupled regimes, each mapping to a specific minimal architecture. The critical curve admits a three-layer open cavity, the over-coupled region a closed cavity with a semi-transparent top mirror, and the under-coupled region a spacer-assisted geometry. For low-loss materials, the closed cavity spatially separates dissipation from field accumulation, allowing the quality factor to be controlled by the external mirror rather than intrinsic medium absorption. We validate this framework with 3R-MoS2, demonstrating a second-harmonic enhancement of 1.19 x 10^5 relative to a monolayer, accompanied by the near-complete suppression of reflected pump waves. These results provide a universal framework for efficient light-matter interaction in ultrathin nonlinear and quantum photonics.