DIFFERENTIAL-THEORY OF GRATINGS - EXTENSION TO DEEP GRATINGS OF ARBITRARY PROFILE AND PERMITTIVITY THROUGH THE R-MATRIX PROPAGATION ALGORITHM

The analysis of gratings of arbitrary depth, profile, and permittivity is conducted by cutting the modulated region into different slices for which the differential theory of gratings is able to compute the diffracted field for both TE and TM polarization without numerical instabilities. The use of a suitable transition matrix (R matrix) then allows one to analyze the entire stack without encountering the numerical instabilities that generally occur with use of the T-transmission matrix, which is well known in stratified media theory. The use of the R-matrix propagation algorithm provides a breakthrough for grating theoreticians in the sense that it not only permits the study of grating of arbitrary depth but also eliminates the numerical instabilities that have plagued the differential theory in TM polarization during the past 20 years.