## Note on the *S*-matrix propagation algorithm

JOSA A, Vol. 20, Issue 4, pp. 655-660 (2003)

http://dx.doi.org/10.1364/JOSAA.20.000655

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### Abstract

A set of full-matrix recursion formulas for the
*S*-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 (*W* 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
*S*-matrix algorithm are given. Comparisons of flop counts show that in performing *S*-matrix recursions in the absence of the symmetry, it is more efficient to go directly from *W* matrices to *S* matrices. In the presence of the symmetry, however, using *t* matrices is equally and sometimes more advantageous, provided that the symmetry is utilized.

© 2003 Optical Society of America

**OCIS Codes**

(000.3870) General : Mathematics

(050.1950) Diffraction and gratings : Diffraction gratings

(050.2770) Diffraction and gratings : Gratings

(050.7330) Diffraction and gratings : Volume gratings

**History**

Original Manuscript: July 19, 2002

Revised Manuscript: November 4, 2002

Manuscript Accepted: November 4, 2002

Published: April 1, 2003

**Citation**

Lifeng Li, "Note on the S-matrix propagation algorithm," J. Opt. Soc. Am. A **20**, 655-660 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-4-655

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### References

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