  Achieving strong coupling between light and matter excitations in hybrid
systems is a benchmark for the implementation of quantum technologies. We
recently proposed [arXiv:2110.02984] that strong single-particle coupling
between magnons and light can be realized in a magnetized epsilon-near-zero
(ENZ) medium, in which magneto-optical effects are enhanced. Here we present a
detailed derivation of the magnon-photon coupling Hamiltonian in dispersive
media both for degenerate and non-degenerate optical modes, and show the
enhancement of the coupling near the ENZ frequency. Moreover, we show that the
coupling of magnons to plane-wave non-degenerate Voigt modes vanishes at
specific frequencies due to polarization selection rules tuned by dispersion.
Finally, we present specific results using a Lorentz dispersion model. Our
results pave the way for the design of dispersive optomagnonic systems,
providing a general theoretical framework for describing engineering ENZ-based
optomagnonic systems.
