The coordinate-transformation-based differential method of Chandezon et al.
[J. Opt. (Paris) 11, 235 (1980); J. Opt. Soc. Am. 72, 839 (1982)] (the C m
ethod) is one of the simplest and most versatile methods for modeling surfa
ce-relief gratings. However, to date it has been used by only a small numbe
r of people, probably because, traditionally, elementary tensor theory is u
sed to formulate the method. We reformulate the C method without using any
knowledge of tensor, thus, we hope, making the C method more accessible to
optical engineers. (C) 1999 Optical Society of America.