A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness

Abstract

We introduce a new class of $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetric potential $V(x)=V_0\exp (-2i{k}_{o}x)$ at the symmetry breaking point, where transparency breaks down as $L\to \infty$.

4 figures, to appear in the Journal of Physics A

References in corpus (6)

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• Reciprocal and unidirectional scattering of parity-time symmetric structures
• Scattering by finite periodic $\mathcal{P}\mathcal{T}$-symmetric structures
• Unidirectional Invisibility and PT-Symmetry with Graphene
• Scattering-free pulse propagation through invisible non-Hermitian disorder
• $S$-matrix pole symmetries for non-Hermitian scattering Hamiltonians
• Perturbative Unidirectional Invisibility
• Unidirectional Invisibility and Nonreciprocal Transmission in Two and Three Dimensions
• Broadband and Wide-Angle Invisibility with PT-Symmetric 2D-Weyl Semimetal
• Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering