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, ∣detS∣,
becomes 1, for all positive energies. Next we show that in the parametric
regimes where the PT-symmetry is unbroken, the eigenvalues, s± 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call this property Transparency.Comment: 8 pages no Figure This paper is being withdrawn since we used an
in-appropriate s-matrix for transparency for coherent injection. We will soon
submit our investigation of transparency here and elsewher