Fig. 1. Schematic diagram of the model structure and coupling mechanism of the proposed HPM. (a) The schematic diagram of the HPM consists of the MNR and PCNC. (b) Resonance spectra of the MNR and PCNC. (c)–(e) Magnetic field profiles of the resonance modes in the HPM (c), the individual MNR (d), and the individual PCNC (e). (f) The HPM system is modeled as a coupled oscillator, parametrized by a coupling coefficient κ and eigenfrequencies ω₁ and ω₂.

Fig. 2. Mode coupling behavior of the HPM with respect to the coupling gap between the MNR and PCNC. (a) Scattering spectra from the HPM with different coupling gaps. (b) The coupling coefficient κ varies with coupling gaps. The red dots are data obtained from the resonance peaks in scattering spectra, and the blue dots are data calculated by Eq. (4). (c) Fano lineshapes of the resonance peak at different coupling gaps.

Fig. 3. Mode splitting of the HPM when the radius of MNR r is changed gradually. (a) Scattering spectra for r changed from 170 to 405 nm. Δ₁, Δ₂, and Δ₃ represent the mode splitting energies when the MD, MQ, and MO modes of the MNR are coupled with the resonance mode of the PCNC, respectively. (b) Electric field E_y distributions of supermode in the x–z plane with r = 197.5, 290, and 365 nm, respectively.

Fig. 4. Illustration of the energy transfer between the MNR and PCNC with respect to Γ_{S, A}. (a)–(c) Time evolution of the cavity energy in the cases of Γ_S < Γ_A, Γ_S ≈ Γ_A, and Γ_S > Γ_A, respectively. (d) Time evolution of the energy integrated in the MNR and PCNC, respectively. Inset: the electric field distribution of the HPM with time evolution.

Fig. 5. Modulation of far-field radiation of the HPM by modifying the MNR location relative to the PCNC center. (a1)–(a5) Electric field distributions in the x–z plane. (b1)–(b5) Far-field emission patterns in the x–y plane. (c1)–(c5) Far-field emission patterns in the x–z plane.