  Optical waveguide theory is essential to the development of various optical
devices. Although there are reports on the theory of optical waveguides with
magneto-optical (MO) and magnetoelectric (ME) effects, a comprehensive
theoretical analysis of waveguides considering these two effects has not yet
been published. In this study, the conventional waveguide theory is extended by
considering constitutive relations that account for both MO and ME effects.
Using the extended waveguide theory, the propagation properties are also
analyzed in a medium where metamaterials and magnetic materials are arranged
such that MO and ME effects can be controlled independently. It has been
confirmed that the interaction between MO and ME effects occurs depending on
the arrangement of certain metamaterials and the direction of magnetization.
This suggests a nonreciprocal polarization control that rotates the
polarization in only one direction when propagating in free space and enhances
the nonreciprocal nature of the propagating waves in waveguide propagation.
