Lopsided diffractions of distinct symmetries in two-dimensional non-Hermitian optical gratings

Fraunhofer light diffraction across a thin two-dimensional lattice of cold atoms subject to transverse hybrid modulations of two standing-wave crossed pump fields is seen to yield lopsided patterns of various degrees of symmetry. We show that one can fully restrain the diffraction of a weak incident probe to two diagonal or adjacent quadrants or even just to a single quadrant, depending on the phases of two standing-wave pumps and on the probe detuning. Different diffraction symmetries with respect to the axes or diagonals of the diffraction plane quadrants are interpreted here in terms of different out-of-phase interplay of absorption and dispersion periodic distributions, resulting from different combinations of Hermitian, PT-symmetric, and non-Hermitian modulations.