Analytical solutions to light scattering by plasmonic nanoparticles with nearly spherical shape and nonlocal effect

We derive analytical solutions for the scattering of electromagnetic waves by a nanoparticle with nearly spherical shape and nonlocal dielectric function by using an extended Mie scattering theory with additional boundary conditions. A perturbation method is used to treat the correction due to deviation from the spherical shape. A surface characteristic function is introduced to describe the non-spherical surface profile of the nanoparticle, and it plays an important role in our analytical formulation. Complex surface plasmon modes are obtained. It is found that not only the transverse but also the longitudinal surface plasmon modes of the nanoparticle are excited due to the nonlocal effect. Our analytical formulation provides an alternative method for investigating the optical behaviors of the surface plasmon of nanoparticles with nearly spherical shape and nonlocal effect.