Adaptive Eigenvector Continuation for Full-Vector Photonic Waveguide Mode Emulation
Abstract
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.
Versions
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BibTeX
@misc{rodiguezguillen2026adaptive,
title = {{Adaptive Eigenvector Continuation for Full-Vector Photonic Waveguide Mode Emulation}},
author = {Daniel Rodíguez-Guillén and Lorena Velázquez-Ibarra},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.30744},
eprint = {2606.30744},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30744},
}
RIS
TY - UNPB
TI - Adaptive Eigenvector Continuation for Full-Vector Photonic Waveguide Mode Emulation
AU - Daniel Rodíguez-Guillén
AU - Lorena Velázquez-Ibarra
PY - 2026
DA - 2026/06/29
PB - arXiv
DO - 10.48550/arxiv.2606.30744
UR - https://arxiv.org/abs/2606.30744
AB - 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.
ER -