Numerical techniques for the eigenanalysis of arbitrary curved and open waveguiding structures.

A review of our research effort on the eigenanalysis of open and curved waveguiding structures is presented herein. A hybrid finite element in conjunction with a cylindrical harmonics expansion is established for the analysis of open waveguides. The transparency of the fictitious circular contour truncating the finite element mesh is ensured by enforcing the field continuity conditions according to a vector Dirichlet-to-Newmann mapping. The eigenanalysis of curved waveguides is confronted by a finite difference frequency domain method in orthogonal curvilinear coordinates. The latter eliminates the usually encountered stair case effects by making the grid conformal to the material boundaries. Additionally it supports multi-coordinate systems and inhomogeneous grids enabling fine mesh around current carrying conductors and coarse mesh in the area of low field variations. These features offer high accuracy with minimum computer resources. Finally, both methods are validated against published analytical, numerical and experimental results.