A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness

TL;DR

This paper presents a new class of PT-symmetric complex crystals that are nearly transparent and reflectionless from one side over a broad frequency range, regardless of the crystal's thickness, using supersymmetric transformation techniques.

Contribution

It introduces a novel unidirectionally invisible PT-symmetric complex crystal with arbitrary thickness, derived via supersymmetric transformation, and provides exact analytical expressions for its transmission and reflection properties.

Findings

Near-perfect transmission from one side over broad frequencies

Reflection from the other side grows quadratically with thickness

Transparency persists regardless of crystal thickness

Abstract

We introduce a new class of $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric complex crystal is synthesized by a supersymmetric transformation of an 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 $ \sim L^2$ owing to unidirectional Bragg scattering. This is a distinctive feature as compared to the previously studied case of the complex sinusoidal $\mathcal{PT}$-symmetric potential $V(x)=V_0 \exp(-2i k_ox)$ at the symmetry breaking point, where transparency breaks down as $L \rightarrow \infty$.