Surface State Engineering Using Bulk-Band Geometric Phases: Band Inversion and its Observable Implications in One-Dimensional Photonic Crystals

This work comprehensively investigates possibilities of surface states realization in one-dimensional photonic systems that are terminated with 𝜀-negative and 𝜇-negative bandgap materials. We begin by first fathoming the topological properties of photonic band structure and notice that its bulk properties completely characterize the surface phenomena in all the foreseeable cases. This approach is inspired from topologically non-trivial behavior in low-dimensional condensed matter systems and the ensuing emergence of topologically protected edge states in such systems. Specifically, we will be following the setup of Su-Schrieffer-Heeger model and emulate the topological phenomena in one-dimensional photonic systems with a substantial advantage of relatively less demanding fabrication. More importantly, being distributed systems, the photonic crystal realizations in question further enrich the available parameter space and provide application avenues for topological phenomena. For example, unlike the atomic chains, in the case of photonic crystals, we can achieve the band inversion and topological phase transition without altering the arrangement of constituents. Our investigations primarily focus on exploiting this very aspect of higher-order photonic bandgaps and in this process, we experimentally demonstrate that the bulk-band geometric phases offer a deterministic yet customizable route for surface state engineering.