On an equation allowing replacement of a sum by an integral, and its application to some problems in diffraction theory
Abstract
An equation by which readily computable integrals can be introduced to replace sums containing oscillating quantities (with exponential functions of complex argument) and that require cumbersome computational labor is derived. The equation is recommended for application in problems involving diffraction of electromagnetic waves, as in antenna theory, screening, and other areas of electrodynamics. Diffraction of a plane wave on a wire array is analyzed by way of illustration, and computations using the integral are not only more manageable but can be readily applied in arbitrary incidence of the wave on the array (rather than only for normal or inclined incidence under stipulated conditions) of period of the same order as wavelength.
- Publication:
-
Problems of Mathematical Physics
- Pub Date:
- 1976
- Bibcode:
- 1976prmp.book...79K
- Keywords:
-
- Electrodynamics;
- Electromagnetic Radiation;
- Integral Equations;
- Wave Diffraction;
- Antenna Design;
- Electromagnetic Shielding;
- Numerical Integration;
- Sum Rules;
- Communications and Radar