Complex Eigenmodes and Eigenfrequencies in Electromagnetics

A comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures. The per unit length propagation phase shift ( ?)-dependent eigenfrequencies ?(?) are mapped to frequency-dependent constant ?(? 0 ) a variety of Rigorous procedures compute the both uniform and periodic structures, confirmed using full-wave simulations known analytical results. We further present two mapping arbitrary where {?-?} relationship expressed rational polynomial expansions. Consequently, replacing {?, j?} with {? , ?} in relation, characteristic equation formed, which then numerically solved ?, representing physical dispersion relation ? (?) attenuation ?(? structure. procedure demonstrated cases, including an unbounded media, rectangular waveguide, Drude dispersive metamaterial, biased ferrite medium, dielectric stack, waveguide. exact characteristics have been successfully retrieved all cases across passbands stopbands frequency.