Abstract

While wide-angle algorithms have recently been developed to describe the propagation of highly-divergent beams, only the first non-trivial wide-angle procedure, which is limited to beam half-widths below about 35 — 40°, can be efficiently implemented with standard numerical procedures.[1, 2] To circumvent this limitation, Lanczos recursion[3, 4] may be applied to project the propagation operator at a given cross-section of the refractive index profile onto a restricted subspace comprised of a limited number of Lanczos functions. The resulting matrix is diagonalized in this subspace and the representation of the electric field in the Lanczos basis is propagated through multiplication by the suitably transformed eigenvalues.

© 1992 Optical Society of America