Finite element analysis of the waveguide eigenmodes‐a novel method of employing transverse electromagnetic fields

Abstract

There are numerous reports on the numerical analysis of variational expressions for a waveguide with an arbitrary cross section and structure by means of a finite element method. In conventional methods, cumbersome procedures or special programming techniques are required to discriminate the true solution of the guided mode from the spurious solutions. In this paper, a new variational expression for the β propagation constant is derived in which the transverse electromagnetic field components e.t and ht are used as the testing functions. A method is presented for numerical analysis of this new variational expression by means of the finite element method. It is pointed out that the guided mode and the spurious mode can easily and completely be discriminated by only the realistic condition that the propagation constant of the guided mode is real, without resorting to cumbersome procedures or special programming techniques. The new variational expression is well suited for a finite element analysis and resolves difficulties and ambiguities associated with the finite element methods based on the conventional variational expressions.

General gyrotropic finite element formulation with loss

“…In a loss-free medium, Hermitian tensors in which e ij ¼ e n ji and m ij ¼ m n ji can be assumed, where the asterisk ( n ) denotes the complex conjugate. Subsequently, the variational expression in Equation (29) can be simplified to the form obtained in Angkaew et al [25,26].…”

“…However, this only worked for the axially magnetized case. Angkaew et al [25,26] introduced a four transverse-field formulation for an arbitrary direction of applied field for a lossless Hermitian tensor material. This approach is ideal for the gyrotropic waveguide problem as it calculates propagation constant as a function of the waveguide shape, signal frequency, bias field and material properties.…”