Realization of Jackiw–Rebbi zero-energy modes at photonic crystal domain walls: Emergence of polarization-indiscriminate surface states

Abstract

The Jackiw–Rebbi model is a relativistic quantum model credited with the theoretical predictions of zero-energy bound states and charge fractionalization prior to the discovery of topological insulators and the fractional quantum Hall effect. In this work, we demonstrate a photonic equivalent of the Jackiw–Rebbi model by resorting to photonic crystal band structure engineering. Specifically, our photonic realization employs two spatial inversion symmetric binary photonic crystals exhibiting complementary signs of differential effective mass parameter (δm) for their second bandgaps. Their concatenation manifests a step discontinuity in the spatial profile of the effective mass parameter, forming a domain wall at the photonic crystal interface. Upon analyzing the reflectance spectra of the concatenated photonic crystal structure, we find a midgap surface state localized at this domain wall. Furthermore, much in agreement with the Jackiw–Rebbi zero-energy solution, the materialized photonic surface state also exhibits a zero-energy character in a differential energy space corresponding to the δm parameter, which has been quantified experimentally. Crucially, the conceived zero-energy mode amounts to the observation of a peculiar surface state with polarization-indiscriminate dispersion that can help realize all-angle polarization neutral optics.