Transmission, reflection and energy exchanges for waves in finite one-dimensional PT-symmetric periodic structures

Abstract

Time reversibility of waves within a periodic structure constrains their properties but allows both elastic and inelastic scattering. Time reversible elastic scattering leads to Bloch-Floquet waves (BFW) exhibiting passing and stopping bands for an infinite periodic structure, and time reversible inelastic scatterers likewise exhibits passing and stopping bands but only for a particular domain of parameters. Physical realizations of time reversible inelastic scatterers have exploited parity-time (PT) symmetry with two parts, each of which is time irreversible while mirrored such that their PT combination is symmetric. The second propagation domain for inelastic scattering (called “broken” PT-symmetry) is entirely a passing band that transmits and reflects more wave energy than in the input wave. In the “broken” domain for m=2n scatterers, where n is any odd integer, amplification peaks at the same discrete wavenumbers as well-known Bragg reflections. A property of PT-symmetric scatterers at the boundary of its two domains is unidirectional “invisibility” where there are no reflections for one of the two possible incident wave directions. A PT-symmetric periodic structure is shown here to also have bidirectional “invisibility” at certain discrete wavenumbers.