Light propagation and magnon-photon coupling in optically dispersive magnetic media

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.