Second- and third-harmonic generations in compositionally graded films

We present a theoretical description of the effective nonlinear susceptibilities for second-harmonic generation (SHG) and third-harmonic generation (THG) of compositionally graded films, in which one of the components possesses nonvanishing second- and third-order nonlinear susceptibilities. We first resort to the nonlinear effective medium approximation to obtain the equivalent (local) second- and third-order nonlinear susceptibilities in a z slice. Then, the formulas for effective nonlinear SHG and THG susceptibilities of the graded film are directly established, if we regard the graded film as the limit of a multilayer one. Numerical results show that if the electric field is polarized perpendicular to the plane of layers, both effective SHG and THG susceptibilities for graded profiles are larger than those for nongraded ones. Furthermore, for a given total volume fraction p, the adjustment of compositional gradient results in a large enhancement of effective SHG and THG especially in the high-frequency region. Therefore, the compositionally graded films can be served as a noval candidate material for obtaining the optimal SHG and THG susceptibilities.