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 fo r which the differential theory of gratings is able to compute the dif fracted field for both TE and TM polarization without numerical instab ilities. The use of a suitable transition matrix (R matrix) then allow s one to analyze the entire stack without encountering the numerical i nstabilities that generally occur with use of the T-transmission matri x, which is well known in stratified media theory. The use of the R-ma trix propagation algorithm provides a breakthrough for grating theoret icians in the sense that it not only permits the study of grating of a rbitrary depth but also eliminates the numerical instabilities that ha ve plagued the differential theory in TM polarization during the past 20 years.