Breakdown of bulk-radiation correspondence in radiative photonic lattices

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 noninvasive 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi mathvariant="normal">Γ</a:mi> </a:math> point of the square lattice and the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>K</c:mi> </c:math> 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., inversion symmetry. Besides, net Berry curvature concentration is captured at the valleys of the nonlocal honeycomb lattice, facilitating further exploration on generalized topological phases in photonic lattices beyond the regimes with localized couplings and Hermiticity.