STABLE IMPLEMENTATION OF THE RIGOROUS COUPLED-WAVE ANALYSIS FOR SURFACE-RELIEF GRATINGS - ENHANCED TRANSMITTANCE MATRIX APPROACH

An enhanced, numerically stable transmittance matrix approach is devel oped and is applied to the implementation of the rigorous coupled-wave analysis for surface-relief and multilevel gratings. The enhanced app roach is shown to produce numerically stable results for excessively d eep multilevel surface-relief dielectric gratings. The nature of the n umerical instability for the classic transmission matrix approach in t he presence of evanescent fields is determined. The finite precision o f the numerical representation on digital computers results in insuffi cient accuracy in numerically representing the elements produced by in verting an ill-conditioned transmission matrix. These inaccuracies wil l result in numerical instability in the calculations for successive f ield matching between the layers. The new technique that we present an ticipates and preempts these potential numerical problems. In addition to the full-solution approach whereby all the reflected and the trans mitted amplitudes are calculated, a simpler, more efficient formulatio n is proposed for cases in which only the reflected amplitudes (or the transmitted amplitudes) are required. Incorporating this enhanced app roach into the implementation of the rigorous coupled-wave analysis, w e obtain numerically stable and convergent results for excessively dee p (50 wavelengths), 16-level, asymmetric binary gratings. Calculated r esults are presented for both TE and TM polarization and for conical d iffraction.