  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.
