Analytical Calculations of Scattering Amplitude of Surface Plasmon Polaritons Excited by a Spherical Nanoantenna

Since surface plasmon polaritons (SPPs) are surface waves, they cannot be excited by an incident plane wave, because free-space photons do not possess a sufficient in-plane momentum. Phase matching between the incident light and SPP can be achieved using a high-refractive-index prism, grating, or nanoantennas. In this work, we found an expression for the amplitude of SPP excited by an arbitrary 3D current distribution placed near a metal interface. The developed method is based on the well-known technique used in waveguide theory that enables finding the amplitudes of waveguide modes excited by the external currents. It reduces the SPP excitation problem to the summation of the set of emitters. As a particular example, we considered a spherical dipole nanoantenna on a metal substrate illuminated by a normally incident plane wave. The analytical calculations were in good agreement with the full-wave numerical simulations.