PT-symmetry and Transparency

It is known that the perfect absorption of two identical waves incident on a complex potential from left and right can occur at a fixed real energy and that the time-reversed setting of this system would act as a laser at threshold at the same energy. Here, we argue and show that PT-symmetric potentials are exceptional in this regard which do not allow Coherent Perfect Absorption without lasing as the modulus of the determinant of the $S$-matrix, $\mathrm{\mid }\det S\mathrm{\mid }$, becomes 1, for all positive energies. Next we show that in the parametric regimes where the PT-symmetry is unbroken, the eigenvalues, $s_{\pm }$ of $S$, can become unitary (uni-modular) for all energies. Then the potential becomes coherent perfect emitter on both sides for any energy of coherent injection. We call this property Transparency.