Adaptive Eigenvector Continuation for Full-Vector Photonic Waveguide Mode Emulation

Photonic waveguide design often requires repeated full-vector Maxwell eigenmode solves over wavelength, geometry, and material parameters.

We present an adaptive eigenvector-continuation framework for accelerating and stabilizing these modal sweeps.

The method constructs a reduced basis from selected full-order modal snapshots, solves projected Maxwell eigenproblems at new query points, reconstructs the modal fields, and monitors accuracy with a full operator residual.

We demonstrate three regimes.

In fixed-geometry wavelength sweeps of a strip waveguide, well-distributed snapshots reproduce the target modal branch with low residual and low effective-index error.

In a multimode ridge waveguide, a shared reduced basis containing several modal families enables robust broadband mode-family tracking and residual-guided adaptive enrichment.

In geometry-dependent width sweeps, the method gives accurate effective-index predictions and high field overlap, but the residual reveals moving-boundary errors caused by non-smooth changes of the discrete operator on a fixed Cartesian grid.

These results show that adaptive eigenvector continuation is an operator-consistent modal emulator and diagnostic tool for photonic waveguide sweeps.