Eigenstates and temporal dynamics in cavity optomagnonics

Many studies of magnon-photon coupling are performed in the frequency domain for microwave photons. In this work, we present analytical results of eigenfrequency, eigenstates, and temporal dynamics for the coupling between ferromagnetic magnon and visible photon. In contrast to microwave photons, optical photons can be coupled with magnon in a dispersive interaction which produces both level repulsion and attraction by varying the magnon-photon frequency detuning. At resonance, the hybridized states are of linear polarization and circular polarization for level repulsion and level attraction respectively. As the detuning increases, the polarizations of level repulsion remain linear but those of level attraction vary from elliptical to linear polarizations. The temporal dynamics of level repulsion presents the beat-like behavior. The level attraction presents monotonous decay in the weak coupling regime but gives rise to instability in the strong coupling regime due to the magnon amplification. As the detuning is large, both magnon and photon amplitudes present a synchronizing oscillation. Our results are important for exploring the temporal evolution of magnon-photon coupling in the range of optical frequency and designing magnon-based timing devices.