Highly improved convergence of the coupled-wave method for TM polarization and conical mountings

Several methods exists to analyze grating diffraction problems by solving rigorously Maxwell's In some circumstances, all these methods suffer from some numerical instabilities and difficulties. We focus on a method originally derived from the integral method, namely the coupled-wave method (RCWA) formulated by Moharam and Gaylord1. This method is known to be slowly converging especially for TM polarization of metallic lamellar gratings. The slow convergence-rate has been analyzed in detail by Li and Haggans2. In this paper, we provide numerical evidence that the coupled-wave method is slowly converging for conical mounts of one-dimensional metallic grating. By reformulating the eigenproblem of the coupled-wave method, we provide numerical evidence that highly improved convergence-rates similar to the TE polarization case can be obtained for conical mounts. Of course, this result can be applied to the case of TM polarization for non-conical mounting, which is a particular case of the general conical mounting diffraction problem. We reveal that the origin of the slow convergence in the original RCWA method is not due to the use of Fourier expansions (as was argued by Li and Haggans), but to an inadequate formulation of the eigenproblem.