Effective nonlinear optical properties of compositionally graded films, in which the volume fraction of nonlinear metal particles varies along the direction perpendicular to the films, are theoretically and numerically investigated. Theoretically, we first adopt effective medium approximation to derive equivalent linear dielectric constant and third-order nonlinear susceptibility in a $z$-slice. Then, the formulas for effective nonlinear optical properties of the graded film are established, if we regard the graded film as a multilayer one. Numerically, random resistor-capacitor networks are used to simulate our system. We find that the surface plasmon resonant bands and the optical nonlinearity enhancement magnitude for compositional graded profile become broader and larger than those in the nongraded case. Moreover, for a graded profile $p\left(z\right)=a{z}^m$, increasing $a$ (or decreasing $m$) is helpful to broaden the resonant bands. To one’s interest, there exist two enhancement peaks in the frequency region $0.4{\omega }_p⩽\omega ⩽0.6{\omega }_p$, which are not predicted by our approximate theory. Otherwise, our theoretical results are found to be in good agreement with numerical simulation data.

• Received 7 July 2005

DOI:https://doi.org/10.1103/PhysRevB.72.214208