Symmetry Properties of Bound States in the Continuum in Hexagonal Lattice Photonic Crystal Slabs
Abstract
Bound states in the continuum (BICs) within photonic crystal (PhC) cavities realise the full confinement of light despite lying within the continuum of radiation modes. While their diverse practical applications has attracted considerable research interest, developing the fundamental understanding of BICs is important for the design of future devices. This paper uses a group theoretical approach to determine the basis functions of the irreducible representations (irreps) of a PhC with the symmetry of the C6v space group, from which the spatial distribution of the electromagnetic fields within the cavity can be determined. Furthermore, the reflection parity of the electric field and a k · p perturbation theory approach are used to determine the far-field polarisation of each irrep. The k · p perturbation explains why the E2 irrep has a topological charge of −2, as well as showing that a topological charge does not necessarily indicate the presence of a BIC. Additionally, it is found that the quality factor of the modes do not necessarily scale as Q ∝ 1/|k|2|q|, but are instead dependent on the coupling to the radiative mode in the k · p perturbation, which is determined from the symmetry of each irrep.
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BibTeX
@misc{jones2026symmetry,
title = {{Symmetry Properties of Bound States in the Continuum in Hexagonal Lattice Photonic Crystal Slabs}},
author = {Rhys Jones and Sang Soon Oh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21727},
eprint = {2609.21727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21727},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Symmetry Properties of Bound States in the Continuum in Hexagonal Lattice Photonic Crystal Slabs
AU - Rhys Jones
AU - Sang Soon Oh
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21727
UR - https://arxiv.org/abs/2609.21727
AB - Bound states in the continuum (BICs) within photonic crystal (PhC) cavities realise the full confinement of light despite lying within the continuum of radiation modes. While their diverse practical applications has attracted considerable research interest, developing the fundamental understanding of BICs is important for the design of future devices. This paper uses a group theoretical approach to determine the basis functions of the irreducible representations (irreps) of a PhC with the symmetry of the C_6v space group, from which the spatial distribution of the electromagnetic fields within the cavity can be determined. Furthermore, the reflection parity of the electric field and a k · p perturbation theory approach are used to determine the far-field polarisation of each irrep. The k · p perturbation explains why the E_2 irrep has a topological charge of −2, as well as showing that a topological charge does not necessarily indicate the presence of a BIC. Additionally, it is found that the quality factor of the modes do not necessarily scale as Q ∝ 1/|k|^2|q|, but are instead dependent on the coupling to the radiative mode in the k · p perturbation, which is determined from the symmetry of each irrep.
ER -