Optical nonlinear response of small metal particles: A self-consistent calculation

We report a self-consistent calculation of the optical nonlinear response of the electrons of a small metal spherical particle. We use the jellium model to describe the metal sphere and work within the random-phase approximation. This calculation allows us to obtain general expressions of the linear polarizability and of the third-order nonlinear source polarization, in a form very similar to those calculated in the local approximation. This model has been applied numerically to the case of a homogeneous response of the electrons and it is shown that screening effects may be important in the nonlinear response of spheres with radii in the range of a few nanometers.