Fourier decomposition of a given amplitude distribution into plane waves and the subsequent superposition of these waves after propagation is a powerful yet simple approach to diffraction problems. Many vector diffraction problems can be formulated in this way, and the classical results are usually the consequence of a stationary-phase approximation to the resulting integrals. For situations in which the approximation does not apply, a factorization technique is developed that substantially reduces the required computational resources. Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.
© 1989 Optical Society of America
Original Manuscript: July 6, 1988
Manuscript Accepted: December 20, 1988
Published: June 1, 1989
M. Mansuripur, "Certain computational aspects of vector diffraction problems," J. Opt. Soc. Am. A 6, 786-805 (1989)