Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system

Unidirectional invisibility of a PT-symmetric optical system is of great interest, but challenging as well since it is infeasible to fulfill it through wide optical frequency ranges in all angular directions. Accordingly we study reflectionless and invisible patterns in the TE and TM modes of an optical slab system consisting of an adjacent or separated pair of balanced gain and loss layers with a gap. We provide a comprehensive study of one of the simplest experimentally accessible examples of a unidirectionally reflectionless and invisible PT-symmetric optical slab system. We obtain the physically optimal conditions for the realization of these phenomena. We derive analytic expressions, and show that only certain gain amounts restricted to take values between certain minimum and maximum values give rise to uni- or bidirectionally invisible configurations. The size of gap decides the measure of reflectionlessness and invisibility parameters, especially on gain value and incident angle.