Lop-sided diffraction by absorbing crystals

Diffraction of atoms by a particular absorbing `crystal of light', that has been studied experimentally, is described by the complex potential . The diffracted beam intensities can be calculated exactly, as a function of (dimensionless) potential strength , angle of incidence , and crystal thickness . Only the beams have nonzero intensity; this `lop-sidedness' is a dramatic violation of Friedel's law. The n th beam is strong at Bragg angles , and the peaks get sharper with increasing ; they correspond to degeneracies of the (non-Hermitian) governing matrix. For normal incidence , the are periodic in , and as n increases they approach a self-similar function of .