Light transport in exotic complex media: from fractal resonances to ultrawhite anisotropic random network

In this work we investigated light matter interaction in two systems presenting peculiar structural properties with strong impact on the light propagation mechanism. This the- sis approached two different classes of intriguing disordered materials that, due to the exotic structural properties, exhibit unique optical properties. The first one is an ideal 2D fractal disordered system with strongly resonant scatterers, while the second one is a biological anisotropic network embedded inside the scale of a white beetle. In the case of the fractals, to push further our understanding of the optical behavior of a scale-invariant system we performed a study of light propagation in 2D fractal distributed point scatterer systems, investigating the electromagnetic field resonances, approach that allowed to ana- lyze important coherent optical phenomena in the field of random media optics. A modal analysis has been performed, computing the solution of Maxwell equations in the single scattering approximation and obtaining the spatial and spectral distributions of electric field modes supported by the systems. Approximating the system scattering centers to point-dipoles, we retrieved quantitative results which validity is extended to any optical system with strongly resonant scatterers. An analysis of the modes size supported by this dipole ensemble has been performed in homogeneous disordered systems, heterogeneous disordered systems and scale-invariant systems generated through the Soneira-Peeble al- gorithm, an algorithm designed for the purpose to generate fractal point-distributions with tunable fractal dimension. Comparing the results of this statistical study in the three different types of disorder, it has been possible to conclude that, contrary to the homogeneous and the heterogeneous disorder media, the fractal system presents config- urations where the geometric self-similarity affects the mode size statistics, generating a coexistence of a wide range of mode sizes. In the second part we investigated the striking optical properties of the white beetle Chyphochilus. The back of this animal is covered by scales hosting a dense, random anisotropic network made of chitin. Despite the low refractive index and the low thickness of the system, the network displays incredibly high brightness and whiteness, feature denoting a high scattering strength reached thorough a smart arrangement of the scattering centers. We investigated the structural feature behind this optical behavior, looking for unveiling through experimental measurements and numerical modeling the strategy behind this smart optimization. A detailed analysis of the structural anisotropy in the random network of the Chyphochilus scale has been performed experimentally proving that anisotropic light transport occurs inside the scale. At the same time, a modeling of the system morphology has been done to attempt both to replicate the system scattering properties and to perform a study of the impact of the degree of anisotropy in disorder network in general. It has been shown how, with a ran- dom walk based simple algorithm, it is possible to obtain simulated network displaying brightness and whiteness comparable to the beetle ones. Moreover, from light transport calculations on the network with tunable structural parameters, a clear dependence of the reflectivity by the scattering properties has been established, demonstrating how the degree of anisotropy, independently from the system filling fraction and the filament packing, produces an increase of the out-of-plane scattering strength. This work does not represent only a progress in our knowledge of light transport in fractals and anisotropic strongly scattering media but it gives more insight also in the study in disorder media in general, attempting to simulate and replicate their behavior. This thesis, at its end, presents a deep investigation of non conventional disordered materials both from the theoretical and experimental point of view showing how it possible to enrich and more deeply understand with different approaches the exotic world of disordered media.