Comparison of Finite-Element Method with Variational Analytical Methods for Planar Guiding Structures

An explicit variational principle for the propagation constant of guiding structures is compared to the finite-element method using a functional involved in the explicit variational principle formalism. Values of the propagation constant yielded by the finite-element method are shown to be stationary about the discretized field. Comparative results show how the convergence is influenced by the differing nature of the explicit unknown (field for finite elements, propagation constant for the explicit variational principle).