Homogenisation of isotropic, cubically nonlinear, composite mediums by the strong-permittivity-fluctuation theory: Third-order considerations

The third-order strong-permittivity-fluctuation theory (SPFT) is presented for an isotropic, cubically nonlinear, composite medium, under the long-wavelength approximation. The effective permittivity of the homogenised composite medium is thereby estimated. Convergence of the SPFT at the second-order level is demonstrated with respect to both the linear and nonlinear contributions to the effective permittivity. The nonlinear SPFT is found to be relatively insensitive to the choice of covariance function. The manifestation of nonlinearity enhancement is considered up to the level of the third-order SPFT.