Edge Modes in Subwavelength Resonators in One Dimension

Abstract. We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyze both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by a finite dimensional eigenvalue problem involving a capacitance matrix. We are able to compute the Hermitian and non-Hermitian Zak phases, showing that the former is quantized and the latter is not. Furthermore, we show the existence of localized edge modes arising from defects in the periodicity in both the Hermitian and non-Hermitian cases. In the non-Hermitian case, we provide a complete characterization of the edge modes.