Exceptional Light Propagation via Generalized Bulk-Edge Correspondence.

In topological photonics, bulk-edge correspondence is conventionally imported by direct analogy with electronic systems, overlooking the fundamentally distinct space-time symmetries of Maxwell's and Schrödinger's equations. In this work, we challenge this prevailing paradigm by demonstrating that nontrivial bulk topology alone is insufficient to guarantee localized edge states in photonic platforms. Using a Su-Schrieffer-Heeger-inspired photonic crystal, we unveil a generalized bulk-edge correspondence intrinsically shaped by the relativistic nature of electromagnetic waves. This constraint imposes a strict frequency cutoff, a feature fundamentally absent in electronic topological insulators, which enables a new regime of frequency-controlled spatial localization near the cutoff. Furthermore, we demonstrate that this generalized correspondence is polarization-dependent: transverse electric and transverse magnetic edge modes exist in different parameter regimes and exhibit distinct dispersion relations, including different zero-dispersion points. Our framework redefines the theoretical boundaries of topological photonics, unlocking new opportunities for polarization-selective dispersion engineering and robust pulse propagation in topological photonic platforms.