Cubic-nonlinearity enhancement via homogenization of a composite material containing truncated spheroidal particles with distributions of shapes

Closed-form expressions were derived for depolarization dyadics relevant to electrically small particles immersed in a cubically nonlinear uniaxial dielectric ambient medium. The particles considered were spheroids, hemispheroids, doubly truncated spheroids, and singly truncated spheres. These depolarization dyadics were implemented within the Bruggeman homogenization formalism to predict the linear and nonlinear constitutive parameters of a homogenized composite material (HCM) composed of a randomly distributed mixture of oriented particles with a distribution of shapes. Numerical simulations were performed to investigate (i) the influence of particle shape and distribution of shapes upon the constitutive parameters of the HCM and (ii) the degree of cubic nonlinearity exhibited by the HCM relative to that exhibited by the component materials. In general, the enhancement in the degree of cubic nonlinearity due to homogenization was found to increase as the diversity of particle shapes increased and also as the contrast between the linear parts of the permittivity scalars for the component materials increased. Greater degrees of cubic-nonlinearity enhancement arose for truncated spheroidal particles, as compared to spheroidal particles. Also, the manner in which the shapes of the component particles were distributed influenced the degree of loss exhibited by the HCM as well as its anisotropy.