A unidirectionally invisible -symmetric complex crystal with arbitrary thickness

Abstract

We introduce a new class of parity-time ()-symmetric complex crystals which are almost transparent and one-way reflectionless over a broad frequency range around the Bragg frequency, i.e., unidirectionally invisible, regardless of the thickness L of the crystal. The -symmetric complex crystal is synthesized by a supersymmetric (SUSY) transformation of a Hermitian square well potential, and exact analytical expressions of transmission and reflection coefficients are given. As L is increased, the transmittance and reflectance from one side remain close to one and zero, respectively, whereas the reflectance from the other side secularly grows like owing to unidirectional Bragg scattering. This is a distinctive feature as compared to the previously studied case of the complex sinusoidal -symmetric potential at the symmetry breaking point, where transparency breaks down as .