The Solution of Waveguides Eigenvalues with Arbitrary Shapes by FD-FD Algorithm in Curvilinear Co-Ordinates

A finite-difference frequency-domain algorithm has been developed in non-orthogonal curvilinear co-ordinates. The full vector Maxwell's equations are discretized on boundary-fitted meshes. Because the algorithm is formulated in a non-orthogonal co-ordinate system, it is not restricted to any a special orthogonal co-ordinate system, and can over the conventional FD-FD algorithm in the orthogonal co-ordinate system. To demonstrate the method, several of the lowest eigenvalues of waveguides with arbitrary cross-section shapes have been computed. The subspace iterative algorithm is used to solve the unsymmetric eigen-equation. Boundary-orthogonal meshes are introduced in order to eliminate the error generated by non-orthogonal meshes on which the boundary conditions for the electromagnetic fields are not satisfied.