Ninth-order effective responses of nonlinear composites in external DC and AC electric fields

The perturbation expansion method, including the third-order potential, is employed to compute the high-order effective nonlinear coefficients of weakly nonlinear dielectric composites. We derive the general formulae for effective nonlinear coefficients up to the ninth order, which include the fifth-order nonlinearity for both DC and AC responses. In addition, the general transformation relations from the effective DC response to effective AC responses up to the ninth harmonic are originally presented in this article. These newly derived formulae are consistent with previously reported work, but are more generally applicable and likely to yield more accurate AC and DC response predictions yet do not require prior knowledge of the fourth-order potential.