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

The coupled-wave method formulated by Moharam and Gaylord [J. Opt. Sec. Am. 73, 451 (1983)] 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 Haggans [J. Opt. Sec. Am. A 10, 1184 (1993)], who made clear that special care must be taken when coupled-wave methods are used for TM polarization. By reformulating the eigenproblem of the coupled-wave method, we provide numerical evidence and argue that highly improved convergence rates similar to the TE polarization case can be obtained. The discussion includes both nonconical and conical mountings.