Semianalytical model for the enhancement of spontaneous emission by a periodic array of nanowire optical antennas on metallic substrate

We investigate an optical nanoantenna array consisting of a gold substrate, a dielectric nanogap and a periodic array of gold-nanowire antennas with a point emission source in the nanogap. Full-wave numerical results show that this antenna array of nanoparticles on mirror (NPoM) can achieve enhancement factors of total spontaneous emission rate and far-field emission rate of the point source up to 3450.71 and 367.66, respectively, while achieving directional far-field radiation along the direction perpendicular to the substrate. To clarify the underlying physical mechanism of spontaneous emission enhancement and reduce computational amount, by considering an intuitive excitation and multiple-scattering process of surface plasmon polaritons (SPPs), we establish an SPP model for the reciprocal problem of NPoM antenna array under plane-wave excitation based on the reciprocity-theorem method, and establish an SPP model for the original problem of NPoM antenna array under point-source excitation based on the array scanning method (ASM). These semianalytical models can provide comprehensive and quantitative predictions of the spontaneous-emission enhancement properties of the antenna array, including total spontaneous emission rate, far-field emission rate, far-field radiation-intensity angular distribution and so on. By using the phase-matching conditions derived from the models, one can predict the structural parameters when the antenna array resonates and achieves spontaneous-emission enhancement. Compared with the full-wave numerical method, the proposed models can reduce the computation time by several orders of magnitude. The proposed results and models can be used for an efficient design of high modulation-rate, high brightness and large-area directional-radiation light sources based on nanoantenna arrays.