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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 20 — Jul. 10, 2006
  • pp: 4803–4809

Enhanced R -matrix algorithms for multilayered diffraction gratings

Eng Leong Tan  »View Author Affiliations

Applied Optics, Vol. 45, Issue 20, pp. 4803-4809 (2006)

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I present enhanced R-matrix algorithms for analysis of general multilayered diffraction gratings. The previous R-matrix algorithms are enhanced in three aspects: computational efficiency, numerical stability, and application of half R-matrix in addition to full and quarter R-matrix recursions. On the basis of the eigensolutions of rigorous coupled-wave analysis, the enhanced R-matrix algorithms deal with eigen-submatrices directly and bypass the auxiliary layer R matrix. Such exclusion of a layer matrix leads to improvements in efficiency and algorithm robustness particularly for zero or small layer thickness relative to wavelength. Application of the enhanced algorithms to grating diffraction is exploited especially for the half and quarter R-matrix recursions. Comparison of various R-matrix algorithms via a table of flop counts shows that the enhanced algorithms are more efficient apart from being well conditioned.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings

Original Manuscript: November 28, 2005
Revised Manuscript: February 3, 2006
Manuscript Accepted: February 4, 2006

Eng Leong Tan, "Enhanced R-matrix algorithms for multilayered diffraction gratings," Appl. Opt. 45, 4803-4809 (2006)

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  15. The ill conditioning of Rl does not appear in RCWA only. For example, in the differential method (beyond the present scope), the transfer matrix may be simply approximated from the system matrix as Tl ≈ I + dhLambdal for sufficiently small numerical thickness dl. However, the corresponding Rl at such thickness could be very ill conditioned and inaccurate also.

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