Use of expansion into a spatial spectrum of kotelnikov-shannon sampling functions in the theory of light scattering

• Published in: Journal of modern optics 1997-06, Vol.44 (6), p.1093-1110
• Main Authors: Rysakov, Wladimir, Ston, Marian
• Format: Article
• Language: English
• Subjects: Diffraction and scattering; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Optics; Physics; Wave optics
• ISSN: 0950-0340; 1362-3044
• DOI: 10.1080/09500349708230722

This work offers a new method of finding a solution to a wide class of diffraction problems by the use of an expansion of a radiator distribution in a spectrum of Kotelnikov-Shannon sampling functions. From this point of view, the electromagnetic radiation of a spatially limited object is presented as a finite discrete sum of elementary beams, each of which transfers a certain amount of power. The signal collected by a detector is then the sum of the powers of the elementary beams. Since detectors are quadratic, i.e. they measure light intensity rather than electric field, it is possible from the very beginning to use the power-generating characteristics of beams. This considerably simplifies the solution, since accounting for interference effects is not required. Our method is illustrated by a number of examples. Comparison of our results with the results of standard methods shows that our method accurately predicts the scattered power intercepted by the detector.