EM field analysis of complementary structures

The symmetry of the Maxwell equations is such that, given one electromagnetic field solution, E, H, satisfying electric conductor and (theoretical) magnetic conductor boundary conditions, a second solution, E´, H´, may be constructed. At a waveguide port to a region formed by electric and magnetic conductors, the input impedance of the original waveguide, Z, is related to the input impedance, Z´, of the complementary/dual region as ZZ´ = Z₀². This principle has been applied to relate equivalent circuit parameters for symmetrical obstacles in waveguides (inductive and capacitive windows in rectangular guides). The implications of the symmetry principle are illustrated through a waveguide example constructed for the express purpose of providing computable means for illuminating EM and equivalent network features of complementary structures and, in particular, the self-complementary case.