Spontaneous emission enhancement by rotationally-symmetric optical nanoantennas: impact of radially and axially propagating surface plasmon polaritons.

The excitation and radiation properties of rotationally-symmetric optical nanoantennas are independent of the azimuth angle, which enables great convenience and superior performances in practical applications. However, for rotationally-symmetric nanoantennas, the physical mechanisms behind their resonance properties remain to be clarified. In this paper, firstly, for a simple single-nanocylinder-on-mirror antenna (S-antenna), we establish a first-principles-based semianalytical model of surface plasmon polariton (SPP) by considering an intuitive multiple-scattering process of the radially-propagating gap surface plasmon (RGSP) in the nanogap and the axially-propagating surface plasmon (ASP) on the nanocylinder. The model can comprehensively reproduce all the radiation properties of the S-antenna such as the total and radiative emission rates, SPP excitation rates, and far-field radiation pattern. The model indicates that when the antenna radius is small (respectively, large), the enhancement of spontaneous emission mainly results from the resonance of ASP (respectively, RGSP). To show the wide applicability of the SPP model along with its unveiled decisive role of the RGSP and ASP in the spontaneous emission enhancement for other rotationally-symmetric nanoantennas of cylindrical shapes, we extend the SPP model to a more complex ring-nanocylinder-on-mirror antenna (R-antenna) that supports two ASPs. Moreover, to provide an explicit explanation of the resonance properties of the R-antenna, we further establish a semianalytical model for the resonant modes (called quasinormal modes, QNMs) supported by the R-antenna based on the SPP model, which quantitatively reveals the role of the RGSP and ASP in forming the antenna resonant modes and the resultant enhancement of spontaneous emission.