  Some magnetoelectric multiferroics have a canted spin structure that can be
described by a Dzyaloshinkii-Moriya coupling. We calculate properties and
features expected for surface and bulk magnon polaritons in such media with a
linear magnetoelectric interaction for the case of transverse electric
polarisation. The dielectric polarisation and magnetisation of weak
ferromagnetism are constrained to lie in the plane parallel to the surface. We
examine a geometry with the polarisation oriented in the film plane and present
numerical results for the transverse electric polarisation. Particular
attention is given to non-reciprocal surface modes, which exist in frequency
between two bulk bands, and show how these modes can be modified by external
magnetic field. Results for attenuated total reflection are presented, and
discussed in relation to nonreciprocity. Example results are calculated for the
canted antiferromagnet BaMnF4.
