We use supersymmetry transformations to design transparent and one-way reflectionless (thus unidirectionally invisible) complex optical crystals with balanced gain and loss profiles. The scattering coefficients are investigated using a transfer matrix approach. It is shown that the amount of reflection from the left can be made arbitrarily close to zero whereas the reflection from the right is enhanced arbitrarily (or vice versa).

• Received 20 January 2014

DOI:https://doi.org/10.1103/PhysRevA.89.032116