Mathematical Models of Diffraction Problems Based on the Discrete Source Method

Abstract

The discrete sources method emerged in the 1980s as an alternative to the method of integral equations has become an effective tool for analyzing problems of diffraction of optical radiation on various physical objects. On the basis of the discrete sources method, a computer technology has been developed and implemented that makes it possible to solve fundamental and application tasks, specifically, to study the scattering properties of coarse atmospheric particles and erythrocytes, to build effective schemes of surface scanners for detecting and recognizing defects in silicon substrates, to measure the potential of interaction of colloidal particles in a solution with the surface of a layered substrate with the simultaneous determination of the distance to the substrate accurate to 1 nm, to develop an optimum design of a near-field microscope based on the effect of total internal reflection of waves, and to investigate the impact of quantum effects on the optical characteristics of nanoplasmonic structures taking into account the manifestation of the nonlocality and occurrence of a longitudinal electric field using the theory of a generalized nonlocal response. All these and other issues related to the use of the discrete sources method are discussed in the proposed review.