Dispersion relation and similarity transform of electromagnetic waveguide

The dispersion relation between the frequency and the propagation constant in a waveguide structure is discussed. Deduced by dimensional analysis, the functional dependency of the geometrical parameters in the dispersion relation is derived. The results inspire the concept of a similarity transform. Applying this transformation together with the two-dimensional finite difference time domain solver, the linear region of the quasi-TEM branch of the dispersion relation can be computed with an enhanced resolution and a reduced computation time.