A general formulation of focus wave modes

Abstract

A general formulation is given for electromagnetic pulses which remain localized in a multidimensional space, and which propagate at the speed of light without dispersing (focus wave modes). It is shown that such modes necessarily have infinite electromagnetic energy in the source-free, three-dimensional space. Finite-energy focus wave modes cannot exist without sources. A set of complete focus wave modes with Hermite–Gaussian transverse variation is derived. The relation of focus wave modes to the solutions of the paraxial wave equation is established.