A systematic approach based on group theory is established to deal with diffraction problems of crossed gratings by exploiting symmetries. With this approach, a problem in an asymmetrical incident mounting can be decomposed into a superposition of several symmetrical basis problems so that the computation efficiency is improved effectively. This methodology offers a convenient and succinct way to treat all possible symmetry cases by following only several mechanical steps instead of intricate mathematical considerations or physical intuition. It is also general, applicable to both scalar-wave and vector-wave problems and in principle can be easily adapted to any numerical method. A numerical example is presented to show its application and effectiveness.
© 2004 Optical Society of America
Original Manuscript: April 25, 2004
Manuscript Accepted: May 18, 2004
Published: October 1, 2004
Benfeng Bai and Lifeng Li, "Reduction of computation time for crossed-grating problems: a group-theoretic approach," J. Opt. Soc. Am. A 21, 1886-1894 (2004)