Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

• Energy ranges for CC & CPA are obtained explicitly for complex WS potential.
• Analytical conditions for CC and CPA for PT symmetric WS potential are obtained.
• Conditions for left & right CC are shown to be different.
• Conditions for CC & CPA are shown to be that of SS for the time reversed system.
• Our model shows the great flexibility of frequencies for CC & CPA.

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.