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
deLorentz model for the electromagnetic re
sponses of the constituent materials. Our extended model, w
hich we refer to as the generalized DrudeLorentz 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.