Multiscale Analysis of Electrically Tunable Reflection Zeros in Intersubband Polaritonic Metasurfaces
Electrical tuning of intersubband-polaritonic metasurfaces cannot be fully identified from reflectance alone because intensity obscures the complex pole--zero dynamics governing critical coupling. We establish a field-consistent multiscale analysis that connects self-consistent Schr\"odinger--Poisson quantum states, complex rigorous coupled-wave spectra, and constrained one-port temporal coupled-mode theory across 21 electric fields. A single zero-field complex calibration fixes the shared photonic and phase-delay baseline, after which the effective coupling is the only field-dependent fitted parameter. The model reproduces the full-wave spectra with a complex-amplitude RMSE of 0.0255--0.0288 and is independently cross-checked through microscopic residue and overlap calculations. Complex poles describe internal polariton hybridization, whereas reflection zeros expose the external radiative--dissipative balance. The quantum-confined Stark effect drives the lower- and upper-polariton zeros through the real-energy axis in opposite directions, yielding two branch-resolved critical-coupling transitions that agree with direct full-wave cross-checks.