Breakdown of Bulk-Radiation Correspondence in Radiative Photonic Lattices

TL;DR

The paper develops a non-Hermitian, long-range coupling model for radiative photonic lattices to define and compare bulk Berry curvature $B^b$ with the far-field radiation Berry curvature $B^f$, revealing that the bulk–radiation correspondence is not universal and depends on the specific Bloch states and symmetry. By analyzing minimal models for the square lattice at $\Gamma$ and the honeycomb lattice at $K$, it shows that BICs generically disrupt the correspondence, while non-BIC bands can preserve it under near-symmetric conditions; complex couplings can also yield net Berry curvature concentrations at valley points. The work demonstrates that radiative leakage and dimensional mismatch distort the bulk information carried by leaky modes, but certain symmetry regimes and lattice geometries (e.g., nonlocal honeycomb) can still exhibit meaningful correspondences, suggesting new avenues for generalized topological photonics beyond Hermitian, locally-coupled regimes. The results are supported by Maxwell-solver validations and propose experimental probes via far-field polarization textures and wavepacket dynamics to test the correspondence in realistic structures.

Abstract

The topological characteristics of energy bands in crystalline systems are encapsulated in the Berry curvature of the bulk Bloch states. In photonic crystal slabs, far-field emission from guided resonances naturally provides a non-invasive way to probe the embedded wavefunctions, raising the question of how the information carried by escaping photons relates to the band topology. We develop a non-Hermitian model to describe the guided and leaky modes of photonic crystal slabs with long-range couplings and non-local responses. Within this framework, radiation Berry curvature is defined from the far-field polarization and compared to the conventional bulk Berry curvature of the crystal Bloch modes. We investigate this bulk-radiation correspondence in the vicinity of the $Γ$-point of the square lattice and the $K$-point of the honeycomb lattice. The results show that the comparability between the bulk topology and the radiation topology is not universal; the validity is contingent upon the specific bulk Bloch states. Notably, the correspondence completely breaks down surrounding the far-field singularities, while it can hold in smooth regions under special symmetry conditions, e.g., rotational symmetry. Besides, net Berry curvature concentration is captured at the valleys of the non-local honeycomb lattice, facilitating further exploration on generalized topological phases in photonic lattices beyond the regimes with localized couplings and Hermiticity.

Figures (9)

• Figure 1: The geometric representation of the basis sets $\mathbf{k_{m,n}}$ and $\mathbf{E_{m,n}}$, the wavevector $\mathbf{k}$ of guided resonances and far-field electric field components $\mathbf{E}$ are resulted from their linear combinations.
• Figure 2: Bulk-radiation correspondence for $u_{x}=0.041, u_{y}=0.04, v=0.02, \gamma_{r}=0.002$, representing the quasi-symmetric case. Slightly rotational symmetry breaking is introduced here to avoid the degeneracies, which can cause the failure of the adopted algorithm fukui2005chern. The stars indicate BIC modes. (a-b) Real and imaginary parts of the energy spectrum, with curves of the same color symbolizing the same bands. (c-f) Bulk Berry curvature for bands 1-4, respectively. (g-j). Radiation Berry curvature for bands 1-4, respectively.
• Figure 3: Bulk-radiation correspondence for $u_{x}=0.04, u_{y}=0.1, v=0.02, \gamma_{r}=0.002$, representing the asymmetric case. The stars indicate BIC modes. (a-b) Real and imaginary parts of the energy spectrum, with curves of the same color symbolizing the same bands. (c-f) Bulk Berry curvature for bands 1-4, respectively. (g-j). Radiation Berry curvature for bands 1-4, respectively.
• Figure 4: Bulk-radiation correspondence for $u=0.01+0.00001i, \gamma_{r}=0.002$, representing the quasi-symmetric case. Slightly rotational symmetry breaking is introduced here to avoid the degeneracies, which can cause the failure of the adopted algorithm fukui2005chern. The star indicates a BIC mode. (a-b) Real and imaginary parts of the energy spectrum, with curves of the same color symbolizing the same bands. (c-e) Bulk Berry curvature for bands 1-3, respectively. (f-h) Radiation Berry curvature for bands 1-3, respectively.
• Figure 5: Bulk-radiation correspondence for $u=0.01+0.001i, \gamma_{r}=0.002$, representing a regime of weak asymmetry. The stars indicate BIC modes. (a-b) Real and imaginary parts of the energy spectrum, with curves of the same color symbolizing the same bands. (c-e) Bulk Berry curvature for bands 1-3, respectively. (f-h) Radiation Berry curvature for bands 1-3, respectively.