The Modal Method

The modal method (MM) is a family of mode expansion techniques for the frequency domain developed over the past three decades. These techniques were initially developed as a grating theory under the names of rigorously coupled waveguide analysis (RCWA) and Fourier modal method (FMM) to study diffraction of periodic structures. Subsequently, a mode expansion technique was used to analyse rotationally symmetric structures including vertical-cavity surface-emitting lasers (VCSELs) and micropillar cavities under the name eigenmode expansion technique (EET). The conceptual differences between the individual methods are small and are related to the symmetries and the boundary conditions of the geometry under study as well as to the technique used to compute the modes. The starting point for the MM is the determination of eigenmodes that serve as a basis set for the expansion of the optical field. To define these, the relative permittivity profile is sliced into layers having translational symmetry along the z axis.