Abstract
In this work we study scattering in a 𝓟𝓣 symmetric periodic optical lattice, when two coherent beams are incident on it from two opposite directions. We focus our attention on both 𝓟𝓣 broken as well as 𝓟𝓣 unbroken phase, with special emphasis on spectral singularity. This is another example of an analytically solvable model, apart from the 𝓟𝓣 symmetric Scarf II potential discussed in ref. Ahmed (Phys. Rev. A 81, 022102 (2014)), which exhibits the phenomenon of Coherent Perfect Absorption (CPA) with lasing, in the domain of broken 𝓟𝓣 symmetry. At the same time, CPA is neither possible for unbroken 𝓟𝓣 symmetry, nor at the transition point.
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