Second- and third-harmonic generation in random composites of graded spherical particles

We consider the effective nonlinear susceptibility tensors for second-harmonic generation (SHG) and third-harmonic generation (THG) of nonlinear composite media, in which dilute graded particles with nonvanishing second- and third-order nonlinear susceptibilities are randomly embedded in the dielectric host. With the aid of the nonlinear differential effective dipole approximation, we derive two differential equations for the equivalent nonlinear susceptibilities describing the SHG and THG of the graded particles, which are valid indeed for arbitrary gradation profiles. Accordingly, the effective SHG and THG susceptibilities for the nonlinear composites of graded spherical particles are obtained by using the analytical expressions available in the dilute limit. Numerical results show that the graded profile plays a crucial role in determining the magnitude of effective SHG and THG susceptibilities. Furthermore, the SHG and THG susceptibilities for graded metallic films are exactly derived. The presence of the dielectric gradation is helpful to achieve large enhancement of SHG and THG in the low-frequency region.