## A unidirectional invisible PT-symmetric complex crystal with arbitrary thickness

Stefano Longhi

We introduce a new class of $$\cal{PT}$$-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 $$\cal{PT}$$-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 ~$$L^2$$ owing to unidirectional Bragg scattering. This is a distinctive feature as compared to the previously studied case of the complex sinusoidal $$\cal{PT}$$-symmetric potential $$V(x)=V_0\exp(−2ik_ox)$$ at the symmetry breaking point, where transparency breaks down as $$L\to\infty$$.

http://arxiv.org/abs/1410.5278
Quantum Physics (quant-ph); Mathematical Physics (math-ph)