Homogenisation of linear electromagnetic materials. Theoretical and numerical studies

The calculation of the electromagnetic response of random composite materials is a matter not only of long-standing scientific interest, but also of increasing technological significance. Provided electromagnetic wavelengths are sufficiently long as compared with the length scales of inhomogeneities, composites may be considered as effectively homogeneous and their constitutive properties estimated by means of homogenisation formalisms. The work of this thesis concerns two aspects of homogenisation theory for linear electromagnetic materials. Firstly, the well-established Maxwell Garnett and Bruggeman homogenisation formalisms, along with the recently-developed incremental and differential Maxwell Garnett formalisms, are applied to investigate the constitutive properties of complex composite materials. Two classes of structures are considered: (i) Through a detailed parametric study of a chiroplasma composite, a structure more general than that of the Faraday chiral mediums is revealed; this generalised structure arises when the component phases possess non-spherical topology, (ii) Biaxial composite structures are found to develop whenever the component phases present two noncollinear distinguished axes. Distinguished axes of the component phases arising from both electromagnetic and topological origins are considered for nondissipative dielectric, dissipative dielectric-magnetic and bianisotropic materials. A generalised biaxial structure, for which the principal axes of the real and imaginary parts of the constitutive dyadics do not coincide, is demonstrated. Additionally, orthorhombic biaxial structures are presented which can arise even though the distinguished axes of the component phases are non-orthogonal. Secondly, the strong-property-fluctuation theory (SPFT) is developed for bianisotropic materials, under the bilocal approximation. The SPFT represents a major advance over traditional approaches to homogenisation, such as provided by the Maxwell Garnett and Bruggeman formalisms, by accommodating a more comprehensive description of the distributional statistics of the component phases. In particular, the SPFT takes account of scattering losses and in its zero-order implementation the SPFT reduces to the Bruggeman homogenisation formalism. Detailed numerical studies are presented which highlight the role of the correlation length, as well as the component phase topology and orientation diversity. Also, the choice of covariance function is demonstrated to exert only a secondary influence as compared with the effects of the correlation length. Finally, through calculating the third-order mass operator approximation, the convergence of the bilocally-approximated SPFT is confirmed for isotropic chiral composites as well as for chiroferrites which are both weakly uniaxial and weakly gyrotropic. (author)