Study of the convergence behavior of the vectorial modal method for metallic lamellar gratings

Abstract

This paper studies the convergence behavior of the vectorial modal method (VMM) recently applied to model diffraction from gratings. Results of the VMM are compared with the well established Fourier modal method (FMM) commonly used to analyze interaction of the electromagnetic waves from periodic structures. Numerical simulations carried out for the VMM and FMM demonstrate practically identical convergence of the diffraction efficiencies for the case of incident illumination being TE polarized. However for TM polarization the convergence of VMM is poor as compared to the FMM for metallic gratings. The reason for this is the formulation of the eigenvalue method used to find the fields in the grating region. An alternate formulation of the eigenvalue equation for the VMM for TM polarization is devised which provides the same level of convergence as the FMM. Numerical simulations are carried out to confirm the validity of this formulation.