BREMMER SERIES, R-MATRIX PROPAGATION ALGORITHM, AND NUMERICAL MODELING OF DIFFRACTION GRATINGS

The connection between the Bremmer (reflection) series method and the R-matrix propagation method for modeling diffraction gratings is revealed. Both methods have been previously demonstrated to be immune from the problem of loss of significant digits caused by the growing and decaying exponential functions. It is mathematically proved that under certain conditions these two methods are formally equivalent. Consequently, the validity of the Bremmer series as a solution of Maxwell's equation to the grating problem is established. Comparisons are also made between the Bremmer series method and the R-matrix propagation method in terms of their physical interpretations, algorithmic structures, numerical stabilities, and ranges of applicability.