Fig. 1. (a) Schematic of a hybrid system under study. (b) Quantum transition of a MD emitter.

Fig. 2. Extinction spectra of a coupled system in the weak and strong light intensity regimes. (a), (c) The extinction spectra of the individual and coupled ion cluster in the weak (a) and strong (c) light intensity regime. The insets are the population difference spectra of the individual ions and the coupled ions. (b), (d) The extinction spectra of the coupled Si sphere and the hybrid structure in the weak (b) and strong (d) light intensity regime. The insets are the extinction spectra for a wider frequency regime.

Fig. 3. Magnetic polarizabilities αMD, magnetic fields BMD, and magnetic dipole moments mMD for the ionic cluster. (a), (d) The magnetic polarizabilities αMD in the weak and strong light intensity regimes. (b), (e) The magnetic fields BMD in the weak and strong light intensity regimes. (c), (f) The magnetic dipole moments mMD in the weak and strong light intensity regimes.

Fig. 4. Extinction spectra of (a) the ion cluster and (b) the whole system with different light intensities.

Fig. 5. Extinction spectra of the ion cluster and the whole system with varying (a)–(d) the MD matrix element μMD and (e)–(h) the number of ions N. (a), (c) The extinction spectra of the coupled ion cluster in the weak (a) and strong (c) light intensity regime. (b), (d) The extinction spectra of the hybrid structure in the weak (b) and strong (d) light intensity regime. Panels (e)–(h) show the same contents as that in panels (a)–(d), respectively, with varying the N.

Fig. 6. Extinction spectra of the ion cluster and the hybrid structure with different lifetimes T1 and T2 (T1=T2). (a), (c) The extinction spectra of the coupled ion cluster in the weak (a) and strong (c) light intensity regime. (b), (d) The extinction spectra of the hybrid structure in the weak (b) and strong (d) light intensity regime.

Fig. 7. Extinction spectra of the ion cluster and the hybrid structure with different distance d between the ion cluster and the center of the Si sphere. (a) Schematic of a hybrid structure with a distance d. (b), (d) The extinction spectra of the coupled ion cluster in the weak (b) and strong (d) light intensity regime. (c), (e) The extinction spectra of the hybrid structure in the weak (c) and strong (e) light intensity regime.

Fig. 8. Extinction spectra of the GaP-based hybrid structure. (a) Schematic of the system with a GaP sphere. (b), (d) The extinction spectra of the coupled ion cluster in the weak (b) and strong (d) light intensity regime. (c), (e) The extinction spectra of the hybrid structure in the weak (c) and strong (e) light intensity regime.

Fig. 9. Spherical polar coordinates of the Si sphere.

Fig. 10. Magnetic dipole μ exciting a Si sphere.

Fig. 11. FDTD and analysis results of the extinction spectra of the system. (a), (b) The extinction spectra of the magnetic Lorentz sphere and the Si sphere by FDTD simulations. (c), (d) The extinction spectra of the ion cluster and the Si sphere by analytical calculation (I0=104  W/cm2).

Fig. 12. Total magnetic field felt by the ion cluster with different μMD, N, and T2. (a), (b) The magnetic field BMD with different MD matrix element μMD under weak (a) and strong (b) light excitation. (c), (d) The magnetic field BMD with different number of ions N under weak (c) and strong (d) light excitation. (e), (f) The magnetic field BMD with different lifetime T2 (T1) under weak (e) and strong (f) light excitation.