  We have developed a nonlinear differential effective dipole approximation
(NDEDA), in an attempt to investigate the effective linear and third-order
nonlinear susceptibility of composite media in which graded spherical
inclusions with weak nonlinearity are randomly embedded in a linear host
medium. Alternatively, based on a first-principles approach, we derived exactly
the linear local field inside the graded particles having power-law dielectric
gradation profiles. As a result, we obtain also the effective linear dielectric
constant and third-order nonlinear susceptibility. Excellent agreement between
the two methods is numerically demonstrated. As an application, we apply the
NDEDA to investigate the surface plasma resonant effect on the optical
absorption, optical nonlinearity enhancement, and figure of merit of
metal-dielectric composites. It is found that the presence of gradation in
metal particles yields a broad resonant band in the optical region, and further
enhances the figure of merit.
