Transparency of the complex PT-symmetric potentials for coherent injection

• Unimodularity of eigenvalues of s-matrix called Transparency.
• Complex PT-symmetric potentials are conditionally transparent for coherent injection.
• Complex PT-symmetric Scarf II potential yields simple analytic results.
• Transparency occurs regardless of the presence of real discrete spectrum.
• Numerically solvable models display qualitatively similar results as Scarf II.

Two port s-matrix for a complex PT-symmetric potential may have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We call this phenomenon transparency which is distinctly different from coherent perfect absorption with or without lasing. Using the versatile PT-symmetric complex Scarf II (scattering) potential, we demonstrate analytically that the transparency can occur regardless of whether PT-symmetry is unbroken or broken or if there are only scattering states. In these three cases, for a given value of the strength of the real part, the strength of the imaginary part |V2||V2| of the potential lies in (0,Vα),(Vα,Vβ)(0,Vα),(Vα,Vβ) and (0,Vβ)(0,Vβ) respectively. Several other numerically solved potentials also support our findings.