Short note on the dipole approximation for electric field enhancement by small metallic nanoparticles

Widespread numerous applications of electric field enhancement on the surface of nanoparticles are of interest, either in physics, chemistry, or biology. The Lorentz–Mie–Debye rigorous model of the scattering of light by spherical nanoparticles has been known for over a century but is often simplified to its dipole approximation for small particles. Indeed, approximated models are of interest to identify the phenomena involved in the electric field enhancement that is used to improve the signal of surface enhanced raman spectroscopy (SERS) in particular. Using the series expansion of the electric field given by the Lorentz–Mie–Debye theory, we show that an order higher than the dipole approximation is necessary to evaluate the field enhancement, even for small radii.