AN EWALD TRANSFORMATION OF FREQUENCY-DOMAIN INTEGRAL FORMULATIONS

Ewald's method is extended to frequency domain integral formulations for fields governed by the Helmholtz equation. For formulations in Cartesian coordinates, it is shown how frequency dependent potential integrals can be resolved into superpositions of short-range, standing wave fields plus radiated fields having low-pass spectral amplitudes. The radiated component is shown to be a spectrum of plane waves given by the Fourier transform of a source density transform, spectral Green's function, and low-pass filter function. This low-pass, spatial filtering property of fields from extended sources dominates far-field behavior in Ewald's framework. Localized or concentrated representations are realized through a careful selection of Ewald's splitting parameter.