  We present a robust technique for computationally studying surface polariton
modes in hybrid materials. We use a semi-classical model that allows us to
understand the physics behind the interactions between collective excitations
of the hybrid system and develop a scattering and transfer matrix method that
imposes the proper boundary conditions to solve Maxwell equations and derive a
general equation describing the surface polariton in a heterostructure
consisting of N constituent materials. We apply this method to a test structure
composed of a topological insulator (TI) and an antiferromagnetic material
(AFM) to study the resulting surface Dirac plasmon-phonon-magnon polariton
(DPPMP). We find that interactions between the excitations of the two
constituents result in the formation of hybridized modes and the emergence of
avoided-crossing points in the dispersion relations for the DPPMP. For the
specific case of a Bi2Se3 TI material, the polariton branch with low frequency
below 2 THz redshifts upon increasing the thickness of TI thin film, which
leads to an upper bound on the thickness of the TI layer that will allow an
observable signature of strong coupling and the emergence of hybridized states.
We also find that the strength of the coupling between the TI and the AFM,
which is parameterized by the amplitude of the avoided-crossing splitting
between the two polariton branches at the magnon resonance frequency, depends
on the magnitude of the magnetic dipole and the line width of the magnon in the
AFM material as well as on the Fermi energy of Dirac plasmon in the TI.
Finally, we predict that materials with extremely high quality, i.e. low
scattering loss rate, are essential to achieve an experimentally-observable
strong coupling between a TI and AFM.
