Local Spectrum Representation of Waves in Inhomogeneous Media Using Non-orthogonal Coordinate System

Tilted Gaussian beams which are defined by their initial field distribution over a plane generally inclined to the beam axis, serve as the building blocks for the phase-space beam summation method, hence the importance of obtaining asymptotically exact solutions for these wave objects. By applying a novel non-orthogonal ray-centered coordinate system to the inhomogeneous wave equation and using asymptotic (paraxial) considerations, the wave equation is reduced into a new form of a parabolic wave equation. The characteristics of these wave fields are investigated, as well as the novel wave phenomena associated with them.