FORMULATION FOR STABLE AND EFFICIENT IMPLEMENTATION OF THE RIGOROUS COUPLED-WAVE ANALYSIS OF BINARY GRATINGS

The rigorous coupled-wave analysis technique for describing the diffra ction of electromagnetic waves by periodic grating structures is revie wed. Formulations for a stable and efficient numerical implementation of the analysis technique are presented for one-dimensional binary gra tings for both TE and TM polarization and for the general case of coni cal diffraction. It is shown that by exploitation of the symmetry of t he diffraction problem a very efficient formulation, with up to an ord er-of-magnitude improvement in the numerical efficiency, is produced. The rigorous coupled-wave analysis is shown to be inherently stable. T he sources of potential numerical problems associated with underflow a nd overflow, inherent in digital calculations, are presented. A formul ation that anticipates and preempts these instability problems is pres ented. The calculated diffraction efficiencies for dielectric gratings are shown to converge to the correct value with an increasing number of space harmonics over a wide range of parameters, including very dee p gratings. The effect of the number of harmonics on the convergence o f the diffraction efficiencies is investigated. More field harmonics a re shown to be required for the convergence of gratings with larger gr ating periods, deeper gratings, TM polarization, and conical diffracti on.