Critical coupling and coherent perfect absorption for ranges of energies   due to a complex gain and loss symmetric system
  We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. 
Mohammad Hasan, Ananya Ghatak and Bhabani Prasad Mandal
quant-ph