Periodically loaded waveguide analysis by propagating and evanescent mode superposition

A method to retrieve the eigenvalues of periodically loaded waveguides is presented, where the cumbersome eigenvalue problem is converted into a driven problem type by introducing the wave transfer matrix of a periodic unit cell section. The procedure has already been used before, but we extend the formulation to problems, where only evanescent modes can exist in the homogeneous waveguide. Thus, in order to represent left-handed modes on the loaded waveguide, the superimposed evanescent modes of the homogenous waveguide must transport real power, as known from the tunnelling effect. In conclusion, the periodically loaded waveguide modes are constructed by a series expansion of waveguide modes of the homogeneous waveguide resulting in an eigenvalue problem with very few unknowns. Dispersion results for a corrugated rectangular hollow waveguide are shown and compared to reference results from literature.