光子晶体薄片中引导共振的广义非厄米特哈密顿量

我们发展了一种针对光子晶体薄片中引导共振的广义非厄米特哈密顿量形式，通过系统化的引导模展开直接从Maxwell方程推导得出。通过对未模式化薄片的完整模式基底对电磁场进行展开，并系统性地消除辐射Fabry--Pérot通道，获得了哈密顿量的算子结构，该结构将引导模耦合和辐射损耗等同对待。 resulting Hamiltonian provides explicit expressions for both dispersive and radiative coupling terms in terms of modal overlap integrals and Fourier components of the permittivity modulation. For specific geometries, the Hamiltonian coefficients can be extracted from full-wave simulations enabling accurate modeling without phenomenological assumptions. As a case study, we investigate hexagonal lattices with both preserved and broken $C_6$ symmetry, demonstrating predictive agreement for complex band structures, near-field distributions, and far-field polarization patterns. In particular, the formalism reproduces symmetry-protected bound states in the continuum (BICs) at the $\Gamma$ point, accidental off-$\Gamma$ BICs near the $\Gamma$ point, and the emergence of chiral exceptional points (EPs). It also captures the tunable behavior of eigenmodes near the $K$ point, including Dirac-point shifts and the emergence of quasi-BICs or bandgap openings, depending on the nature of $C_6$ symmetry breaking. We further demonstrate in the Appendix that the same formalism extends naturally to other symmetry classes, including $C_2$ (1D grating) and $C_4$ (square lattice) photonic crystal slabs. This approach enables predictive and efficient modeling of complex photonic resonances, revealing their topological and symmetry-protected characteristics in non-Hermitian systems.