Quantifying the Minimal Stable Footprint of Nanophotonic Inverse Design via Geometric Phase Sensitivity

ABSTRACT Adjoint‐based inverse design enables high‐performance nanophotonic devices but typically operates as a black box regarding design footprint, often resulting in spatially redundant or computationally expensive solutions. Here, we introduce a phase‐analytic framework that characterizes footprint‐dependent behavior in optimized nanophotonic devices by monitoring the “geometric phase sensitivity”—a phase‐delay quantity normalized by the characteristic design width. This metric identifies three sampled regimes—Insufficient, Stable, and Redundant—providing a diagnostic criterion to identify the Minimal Stable Footprint (MSF) under the investigated design constraints. As a proof of concept guided by this framework, we demonstrate an ultra‐compact, 1 × 2 broadband wavelength division multiplexer in an idealized, lossless 2D model. The optimized device separates two 100‐nm‐bandwidth channels (1240–1340 and 1370–1470 nm) with insertion loss below 0.47 dB and undesired‐channel transmission below −12 dB. To test the selected continuous‐permittivity realization, the nanophotonic design is experimentally realized as a scaled microwave analogue using a drilled‐dielectric effective medium. Measurements reproduce the two‐channel response of the selected microwave device. A separate explicit‐hole 3D SOI design yields modal insertion losses of approximately 2.1–2.2 dB at the two center wavelengths.