Interaction of spherical nanoparticles with a highly focused beam of light

The interaction of a highly focused beam of light with spherical nanoparticles is investigated for linear and radial polarizations. An analytical solution is obtained to calculate this interaction. The Richards-Wolf theory is used to express the incident electric field near the focus of an aplanatic lens. The incident beam is expressed as an integral where the integrand is separated into transverse-electric (TE) and transverse-magnetic (TM) waves. The interaction of each TE and TM wave with a spherical nanoparticle is calculated using the Mie theory. The resulting analytical solution is then obtained by integrating the scattered waves over the entire angular spectrum. A finite element method solution is also obtained for comparison.