Phase-Invariant Thickness Metrology for Subwavelength Gratings via Zero-Crossing Analysis

Subwavelength gratings (SWGs) exhibit optical responses that are highly sensitive to structural parameters, where the etching depth is a critical parameter determining device performance but remains challenging to characterize accurately. In this work, a robust thickness retrieval method based on Variational mode decomposition (VMD)-assisted zero-crossing phase analysis is proposed. By extracting the oscillatory component containing thickness-dependent phase information from the reflection spectrum and exploiting the phase invariance of zero-crossing positions, the proposed method enables thickness retrieval with reduced sensitivity to spectral intensity distortions. Combined with second-order effective medium theory (EMT) and the Sellmeier dispersion model, the physical thickness is retrieved through nonlinear phase matching. Simulation results demonstrate that the equivalent medium model achieves relative deviations below 0.7%. For SWGs with a nominal etching depth of 3 μm, the proposed method maintains thickness retrieval errors of 0.54–0.66%, with a coefficient of variation (CoV) below 0.03% under 20% Gaussian noise. Furthermore, under severe baseline drift and amplitude modulation, the proposed method achieves a retrieved thickness of 2.982 ± 0.005 μm, significantly outperforming conventional peak-fitting methods. This approach provides an effective solution for high-precision characterization of subwavelength optical structures.