Optically switchable directional invisibility.

It is shown that a scatterer can be designed to be directionally invisible for an incident field composed of a given sum of plane waves. These scatterers are invisible only when all plane waves are present with the given amplitudes and directions of incidence, which suggests a new type of "switchable" invisibility. Such objects could find application in optical devices such as couplers, switches, and optical position sensors. It is also demonstrated that the designed scatterers have balanced gain-loss profiles that are more general than most PT-symmetric objects considered so far.