| Summary: | Multilayer reflectors consisting of 'stacks' of alternating layers of guanine crystals with cytoplasm gaps are present in many different animals including fish and spiders. Common to these reflectors is high birefringence in the guanine crystals and disorder in thickness of the layers in the reflector. The central theme of this thesis is the development of a theoretical framework for understanding the physics of these structures based upon the optics of anisotropic stratified media, and the Anderson localization of light in one dimension. The thesis begins with an investigation of the physical origin of broadband, polarization-insensitive reflectivity from three species of 'silvery' teleost fish: Clupea harengus, Sardina pilchardus and Sprattus sprattus. Reflectance spectrophotometry is used to characterise the spectral, angular and polarization dependence of the reflectivity, and digital holographic microscopy is used to investigate the dielectric properties of the birefringent guanine crystals. It is discovered that there are two 'populations' of guanine crystal present in the fish stratum argenteum that have different alignments of their optic axes in the multilayer structure. An anisotropic model of birefringent-guanine isotropic-cytoplasm reflectors is developed using the 4x4 matrix method and is fitted to the two-crystal system. The model is then used to investigate numerically the production of a non-polarizing reflection, and the proposed camouflage function of the fish reflectors. An explanation for the broadband, polarization-insensitive reflectivity of the two-crystal system in fish reflectors is then developed from the perspective of Anderson localization and the structural property of the localization length. This is achieved by constructing an analytical model of a bio-inspired isotropic-birefringent random stack system. The model system is shown to exhibit the polarization-insensitive localization of light, which is in contrast to isotropic dielectric random stack systems that all have strong polarization-dependence to the localization length. Finally, the application of the theoretical framework of Anderson localization to random stack models of animal multilayer reflector is explored. This includes: a review of the thickness disorder for reflectors in fish, spiders and cephalopods; and investigations of the relationship between thickness disorder, localization length spectra and reflectivity spectra at normal and oblique incidence.
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