We have developed a nonlinear differential effective dipole approximation(NDEDA), in an attempt to investigate the effective linear and third-ordernonlinear susceptibility of composite media in which graded sphericalinclusions with weak nonlinearity are randomly embedded in a linear hostmedium. Alternatively, based on a first-principles approach, we derived exactlythe linear local field inside the graded particles having power-law dielectricgradation profiles. As a result, we obtain also the effective linear dielectricconstant and third-order nonlinear susceptibility. Excellent agreement betweenthe two methods is numerically demonstrated. As an application, we apply theNDEDA to investigate the surface plasma resonant effect on the opticalabsorption, optical nonlinearity enhancement, and figure of merit ofmetal-dielectric composites. It is found that the presence of gradation inmetal particles yields a broad resonant band in the optical region, and furtherenhances the figure of merit.
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