Two-Dimensional Bragg-Ewald’s Dynamical Diffraction and Spontaneous Gratings

Abstract

About a history of the question. There are two contrast situations in optics: classical diffraction of light, e.g. Bragg-Ewald’s diffraction on space lattice of point dipoles, and laser trapping of microscopic particles or atoms. At the former light fields are subjected to the material distribution, at the latter particles are obeyed to light [1]. Substance and fields are equal in strength, to some extent, when we deal with a stimulated light scattering. As early as 35 years it’s known particular, two-dimensional kind of that phenomenon. Formation of ripples [2], spontaneous gratings (SG) with stimulated Wood’s anomalies [4], laser-induced periodical surface structures [5] is connected with an instability development of a substance in the interference fields, arising due to superposition of the single incident pumping beam with scattered surface modes. SG spatio-temporal structure has been investigated early in the 80-th by Dr. Fritz Keilmann from Max-Plank-Institute in Shtuttgart [2, 3], who, for the first time, observed a dispersive behavior of the ripple period and connected it with an excitement of surface polaritons. Dr. Keilmann pointed out also that “the situation in our case is somewhat different” comparing to Bragg reflection. Detailed theoretical treatments are based on “surface-scattered waves” [4, 6], “radiation remnants” [5], “analytical solution of the diffraction problem under Wood’s anomalies conditions” [7] and others. All models are sufficiently complicated for physical understanding. Despite the broad range of theories, SG display some bright and universal properties, which testify in favour of a possibility to treat a simple and universal mathematical model of the phenomenon.