Modal formulation for index-modulated layers with lateral PMLs

The modal formalism is developed to deal with index-modulated structures ended by anisotropic regions (perfectly matched layers, PML). The method is applicable to scattering problems from dielectric or metallic objects as well as to propagation in planar slab waveguides. The boundaryvalue problem is solved and the dispersion relation inside the PML is derived. The general expression of the eigenvalues equation for an arbitrary number of regions and for both polarization modes is obtained. The modal functions of a layer ended by PMLs are found, and their orthogonality relation is derived. The potential of the method to deal with more general problems is briefly outlined.