In this work, we study the enhancement of the third-order optical susceptibility, X⁽³⁾_e/X⁽³⁾ in periodic composites, where X⁽³⁾_e is the effective Kerr coefficient of the composite, and X⁽³⁾ is the Kerr coefficient of one of the constituents. The results obtained from the commercial software, TOSCA, is based on the iterative finite element approach. For an array of perfectly conducting spheres in a nonlinear dielectric matrix, we obtain for the first time the critical behavior, X⁽³⁾_e/X⁽³⁾~[delta][delta] ^-1.96, as the upper bound of X⁽³⁾_e enhancement where 2δ is the surface separation between spheres. We found this enhancement behavior to be predictable by the perturbation approximation even when the Kerr susceptibility, X⁽³⁾, of matrix is large....[ Read more ]

In this work, we study the enhancement of the third-order optical susceptibility, X⁽³⁾_e/X⁽³⁾ in periodic composites, where X⁽³⁾_e is the effective Kerr coefficient of the composite, and X⁽³⁾ is the Kerr coefficient of one of the constituents. The results obtained from the commercial software, TOSCA, is based on the iterative finite element approach. For an array of perfectly conducting spheres in a nonlinear dielectric matrix, we obtain for the first time the critical behavior, X⁽³⁾_e/X⁽³⁾~[delta][delta] ^-1.96, as the upper bound of X⁽³⁾_e enhancement where 2δ is the surface separation between spheres. We found this enhancement behavior to be predictable by the perturbation approximation even when the Kerr susceptibility, X⁽³⁾, of matrix is large.

For an array of dielectric spheres embedded in a nonlinear dielectric matrix, it is found that the perturbation approximation can only be valid for small Kerr susceptibility of the matrix. The effects of packing concentration and dielectric constant of the spheres on the validity range are studied. Moreover, the X⁽³⁾_e enhancement of the system of nonlinear spheres embedded in a dielectric matrix is also studied and contrasted with the case where the geometry is the reverse.