Localized PT-symmetric directionally invisible scatterers

We demonstrate how to create localized PT-symmetric directionally invisible scatterers directly from a governing wave equation. Moreover, we can construct general non-PT-symmetric objects which exhibit directional invisibility, though such an effect is typically associated with PT-symmetric objects. Whereas previously the determining condition for an optical PT-symmetric device was a PT-symmetric complex refractive index, we show that a broader condition, requiring only the scattering potential to be PT-symmetric, leads to the same behavior. This enables the construction of PT-symmetric objects without a PT-symmetric complex refractive index, effectively doubling the number of possible invisible objects. Consequently, the set of gain-loss invisible objects is much broader than previously realized, and several examples are shown.