Predicting the dielectric nonlinearity of anisotropic composite materials via tensorial analysis
Journal of Physics: Condensed Matter
The discovery of new materials with peculiar optical properties as well as the prediction of their behaviour given the microstructure is a matter of remarkable interest in the community of material scientists. A complete theory allowing such a prediction is not yet available. We have formulated a theory able to analytically predict the effective second-and third-order nonlinear electrical behaviour of a dilute dispersion of randomly oriented anisotropic nonlinear spheres in a linear host. The
... linear host. The inclusion medium has non-vanishing second-and third-order nonlinear hypersusceptibilities. As a result, the overall composite material is nonlinear but isotropic because of the random orientation of the inclusions. We derive the expressions for the equivalent permittivity and for the Kerr equivalent hypersusceptibility in terms of the characteristic electric tensors describing the electrical behaviour of the spheres. The complete averaging over inclusion positions and orientations led to general results in the dilute limit. We show that these results are consistent with earlier theories and that they provide null second-order hypersusceptibility as expected in a macroscopically isotropic medium. This theory generalizes the well-known Maxwell-Garnett formula and it can be easily specialized to any of the 32 crystallographic symmetry classes. Despite this study assuming static conditions, it can be generalized to the sinusoidal regime, pointing at an interesting way to engineer optically active materials with desired behaviour.