Abstract
In this work we study scattering in a đť“źđť“Ł symmetric periodic optical lattice, when two coherent beams are incident on it from two opposite directions. We focus our attention on both đť“źđť“Ł broken as well as đť“źđť“Ł unbroken phase, with special emphasis on spectral singularity. This is another example of an analytically solvable model, apart from the đť“źđť“Ł 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 đť“źđť“Ł symmetry. At the same time, CPA is neither possible for unbroken đť“źđť“Ł symmetry, nor at the transition point.
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