Splitting scalar fields into a sum of counterpropagating waves leads to formulation of the Helmholtz equation as two coupled parabolic partial differential equations. This rigorous formalism naturally leads to the beam-propagation method (BPM) equation when the backward-propagating field is neglected, but it also permits discussion of various corrections. Two problems specifically are analyzed: wide-angle propagation in near-uniform systems and propagation through lenslike systems, with a strongly discontinuous refractive index. Finally, a BPM modeling is proposed for fiber microlens operation.
© 1993 Optical Society of America
Original Manuscript: November 2, 1992
Revised Manuscript: March 9, 1993
Manuscript Accepted: April 21, 1993
Published: October 1, 1993
Charles Vassallo, "Reformulation for the beam-propagation method," J. Opt. Soc. Am. A 10, 2208-2216 (1993)