A set of full-matrix recursion formulas for the W→S variant of the <i>S</i>-matrix algorithm is derived, which includes the recent results of some other authors as a subset. In addition, a special type of symmetry that is often found in the structure of coefficient matrices (<i>W</i> matrices) that appear in boundary-matching conditions is identified and fully exploited for the purpose of increasing computation efficiency. Two tables of floating-point operation (flop) counts for both the new W→S variant and the old W→t→S variant of the <i>S</i>-matrix algorithm are given. Comparisons of flop counts show that in performing <i>S</i>-matrix recursions in the absence of the symmetry, it is more efficient to go directly from <i>W</i> matrices to <i>S</i> matrices. In the presence of the symmetry, however, using <i>t</i> matrices is equally and sometimes more advantageous, provided that the symmetry is utilized.
© 2003 Optical Society of America
(000.3870) General : Mathematics
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(050.7330) Diffraction and gratings : Volume gratings
Lifeng Li, "Note on the S-matrix propagation algorithm," J. Opt. Soc. Am. A 20, 655-660 (2003)