Fourier modal method for perturbation analysis of bound states in the continuum

Abstract

Bound states in the continuum (BICs) supported by periodic photonic structures are surrounded by high-Q resonances and serve as centers of polarization vortices in momentum space, making them attractive for a wide range of applications. Recently, a perturbation theory has been formulated for resonant states near BICs, yielding a hierarchy of equations whose solutions directly approximate the resonant states and determine the asymptotic behavior of their Q factors and polarizations. Efficiently solving these equations is therefore essential. Since many studies of BICs concern layered structures, we develop an approach based on the Fourier modal method. Numerical examples confirm the effectiveness of the proposed method and demonstrate its ability to capture higher-order asymptotic scaling. Our work provides a practical tool for the theoretical analysis of BICs and may also facilitate the design of BIC-based photonic devices.

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BibTeX RIS

BibTeX

@misc{zhang2026fourier,
  title = {{Fourier modal method for perturbation analysis of bound states in the continuum}},
  author = {Nan Zhang and Ya Yan Lu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15787},
  eprint = {2609.15787},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15787},
}

RIS

TY  - UNPB
TI  - Fourier modal method for perturbation analysis of bound states in the continuum
AU  - Nan Zhang
AU  - Ya Yan Lu
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15787
UR  - https://arxiv.org/abs/2609.15787
AB  - Bound states in the continuum (BICs) supported by periodic photonic structures are surrounded by high-Q resonances and serve as centers of polarization vortices in momentum space, making them attractive for a wide range of applications. Recently, a perturbation theory has been formulated for resonant states near BICs, yielding a hierarchy of equations whose solutions directly approximate the resonant states and determine the asymptotic behavior of their Q factors and polarizations. Efficiently solving these equations is therefore essential. Since many studies of BICs concern layered structures, we develop an approach based on the Fourier modal method. Numerical examples confirm the effectiveness of the proposed method and demonstrate its ability to capture higher-order asymptotic scaling. Our work provides a practical tool for the theoretical analysis of BICs and may also facilitate the design of BIC-based photonic devices.
ER  -

Abstract

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