Fig. 1. (a) Electric field distribution of resonator. (b) Electric field distribution of the slotted resonator.

Fig. 2. Schematic of the optical WGM microdisk resonator with a single slot. ain, the amplitude of input light; aCWout, output amplitude of CW; aCCWout, output amplitude of CCW.

Fig. 3. Schematic representation of Δr(φ), φ, and θ are the polar angle and the angular position of slot, respectively.

Fig. 4. Normalized transmission of the theory model (red solid line) and FEM simulation (blue dash–dot line) with the slot width of 220 nm and the slot angular position of 0°. The close agreement between the theoretical and simulation result is obtained with κ0=1.211×1011  Hz, Γ=1.65κ0, κex=1.78  κ0, γ=2.215κ0, and γc=8.4κ0.

Fig. 5. Simulation results of the normalized transmission without single slot (corresponding parameter in the theoretical model: κ0=1.211×1011  Hz, κex=1.78κ0) and under the difference slot width of 50 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.4κ0, κex=1.78κ0, γ=1.59κ0 and γc=1.4κ0), 100 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.7κ0, κex=1.78κ0, γ=1.74κ0 and γc=3.9κ0) and 200 nm (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=1.4κ0, κex=1.78κ0, γ=2.09κ0 and γc=7.9κ0).

Fig. 6. (a) Normalized detuning frequency as a function of the slot width; the blue solid curve presents the theoretical results, and the red dash curve depicts the simulation results. (b) Normalized linewidth broadening induced by the slot and Q factor of the slotted resonator with different slot widths.

Fig. 7. (a) Normalized transmission in a slotted resonator with the slot width of 150 nm and the slot angular position of 0° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=κ0, κex=1.78κ0, γ=1.89κ0, and γc=6.1κ0), 60° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.85κ0, κex=1.78κ0, γ=1.815κ0, and γc=5.8κ0) and 160° (corresponding parameters in the theoretical model: κ0=1.211×1011  Hz, Γ=0.6κ0, κex=2κ0, γ=1.8κ0, and γc=3.3κ0). (b) Relationship between slot width and normalized detuning frequency with the slot angular position of 0° (green dash line), 60° (blue dash–dot line), and 160° (red solid line).

Fig. 8. Normalized detuning frequency as a function of the slot angular position in a slotted resonator with the slot width of 150 nm. Blue line presents the theory analysis results; red line depicts the FEM simulation results for the case of azimuthal number m=41.