Focus wave mode solutions of the inhomogeneous n-dimensional scalar wave equation.

Abstract

In the following focus wave mode solutions of the inhomogeneous n-dimensional scalar wave equation are determined when the source term is of separable type (i.e., separable in the characteristic variables). In this case the n-dimensional inhomogeneous wave equation is transformed into a formally equivalent (n-1)-dimensional inhomogeneous diffusion equation having a complex longitudinal space-time independent variable. The unbounded space propagator of this diffusion equation and the Palmer-Donnelly line source term generalized to n dimensions are used to obtain inhomogeneous wave equation solutions in two, three, and four space dimensions. Localization of these solutions is shown to increase as the dimensionality increases. An infinitely long line source with finite radius is also considered. As the source radius increases past a certain point, the localization and amplitude of the central peak decrease dramatically.