Generalized waveguide theory including electromagnetic duality

ncreasing interest in optical metamaterials, including f or waveguides, has engendered the need for a theoretical framework that explicitly incorporates the electromagnet ic properties of natural materials and metamaterials. Meta - materials expand the parameter space for electromagnetic p henomena such as negative magnetic susceptibility, which can be described by magnetic monopoles on a sufficiently larg elengthscale.Althoughmagneticmonopolesarenot known to exist, they are theoretically permitted and serve a savaluablemathematicaltool. We employ the concept of magnetic monopoles to extend the Dru de-Lorentz model for the electromagnetic re- sponses of the constituent materials. Our extended model, w hich we refer to as the generalized Drude-Lorentz model, underpins all physically accessible values of both the perm ittivity and permeability. Using our generalized Drude- Lorentz model, we construct a generalized waveguide theory that fully respects the duality of electromagnetism. As duality treats electric charge and magnetic monopoles on an equal footing our theory inherently includes ma- terials with positive, negative and zero electric and magne tic susceptibilities. By exploiting the concept of magneti c monopoles our theory can easily treat arbitrary combinatio ns of standard materials and metamaterials for select waveg - uide geometries.