Fig. 1. (a) Schematic of our hybrid structure consisting of a silicon nanoring, a silver nanorod, and a silica substrate. Structural parameters are ticked out in the illustration. (b) Field profile of the magnetic-like resonance excited by the MQE (ticked out by a blue dot). (c) Purcell factor (solid line) and the radiation efficiency (pink dashed line) under the excitation of the MQE. The Purcell factors of a single nanoring are illustrated by a blue dashed line. (d) Field profile of the electric-like resonance excited by the EQE (ticked out by a dark red arrow). (e) The Purcell factor (solid line) and the radiation efficiency (pink dashed line) under the excitation of the EQE. The Purcell enhancement of a single nanorod is illustrated by a green dashed line. Cyan arrows depict the electric field around the hybrid structure in (b),(d).

Fig. 2. Variations of the magnetic and electric Purcell enhancement under some structural parameters in the magnetic (electric)-like resonance. Magnetic and electric Purcell factors as a function of (a),(b) gap width g, (c),(d) substrate refractive index n, (e),(f) inner radius of the nanoring r_in, and (g),(h) length of nanorod l_rod.

Fig. 3. Variation of the magnetic and electric Purcell enhancement when the emitter’s position moves. (a)–(c) Magnetic Purcell factors when the MQE moves along the three paths depicted in the insets. The MQE feels the strongest emission enhancement at the inner boundaries. (d)–(f) The electric Purcell factors when the EQE moves along 3 paths depicted in the insets. The peak enhancement appears at the boundary of the nanorod. (g) Illustration of some specific points. The origin is set at the center of the nanoring and on the substrate. Some specific positions are also ticked out by Roman numerals I–V.

Fig. 4. Purcell enhancement, radiation efficiency, and far-field radiation in a 9 × 9 array of hybrid structures. (a),(d) Field profiles of the array excited by the MQE (or EQE) situated at the central cell. (b),(e) Radiation properties including the magnetic (electric) Purcell factors and the radiation efficiency. The right insets give schematics of the 9 × 9 array excited by the MQE or the EQE. (c),(f) The far-field radiation of the array (or the individual structure) excited by the MQE or the EQE. Compared with the individual structure, the far-field radiation exhibits a more directional pattern.