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.