The finite difference frequency domain method for the eigenanalysis of open periodic structures

The eigenanalysis of periodic stuctures is presented herein by extending our previous two - dimensional curvilinear frequency domain finite difference domain (FDFD) toward the eigenanalysis of open/radiating periodic structures. Initially, the open/radiating structures are simulated using the Perfectly Matched Layer (PML), while later Mur´s Absorbing Boundary Conditions (ABC) will be introduced within the FDFD formulation. In parallel, the periodicity of the structure is accounted through the enforcement of Periodic Boundary conditions (PBC) within the FDFD formulation. The periodicity can be either in one or in two dimensions, while out of plane propagation is assumed along the third dimension with propagation constant different from zero.