The present work is concerned with applying a ray-centered non-orthogonal coordinate system which is a priori matched to linearly-phased localized aperture field distributions. The resulting beam-waveobjects serve as the building blocks for beam-type spectral expansions of aperture fields in 2D inhomogeneous media that are characterized by a generic wave-velocity profile. By applying a rigorous paraxial-asymptotic analysis, a novel parabolic wave equation is obtained and termed “Non-orthogonal domain parabolic equation”—NoDope. Tilted Gaussian beams, which are exact solutions to this equation, match Gaussian aperture distributions over a plane that is tilted with respect to the beam-axes initial directions. A numerical example, which demonstrates the enhanced accuracy of the tilted Gaussian beams over the conventional ones, is presented as well.
© 2010 Optical Society of America
Fourier Optics and Signal Processing
Original Manuscript: April 26, 2010
Revised Manuscript: June 11, 2010
Manuscript Accepted: June 16, 2010
Published: July 22, 2010
Yakir Hadad and Timor Melamed, "Tilted Gaussian beam propagation in inhomogeneous media," J. Opt. Soc. Am. A 27, 1840-1850 (2010)