Reformulation of the Fourier modal method with adaptive spatial resolution: application to multilevel profiles

Abstract

Formulation of the Fourier modal method for multilevel structures with spatially adaptive resolution is presented, using a slightly reformulated representation for the spatial coordinates. Projections to Fourier base in boundary value problem are used allowing extensions to multilayer profiles with differently placed transitions. We evade the eigenvalue problem in homogeneous regions demanded in the original formulation of the Fourier modal method with adaptive spatial resolution.