Optical transport of pseudo-random coatings

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Coatings are widely used to improve the optical performance of surfaces exposed in the built environment, technological devices, and consumer goods. In the last decades the improvement of techniques to create structured coatings has hugely increased the range of properties that can be achieved by such systems. Unfortunately, the theoretical techniques to model the complex and often pseudo-random nature of structured coatings are not yet fully adequate. In this thesis I will address this problem. Specifically, I will develop improved techniques that can be used on different kinds of coatings: mesoporous metals, random two-phase structures, heterogeneous matrices and rough surfaces. First, I will consider silver mesoporous sponges. These are both random and isotropic, and are readily synthesized in the laboratory in various physical densities. Therefore they provide a useful platform on which to begin developing computational strategies. I will analyse these structures using an effective medium approximation based on their far-field response. Mesoporous metals offer a very distinct optical response compared to their constitutive bulk metal. In particular, the topology of such structures creates metal systems with low plasmon response but with high conductivity thanks to their percolated metal filaments. These characteristics make them suitable for many applications, for example as highly absorptive optical coatings. Next, I will introduce the concept of anisotropy into the coating structure by analysing columnar morphologies obtained using physical vapour deposition. These kind of coatings offer some degree of order caused by shadowing effects, and a degree of randomness due to the statistical roughening present when depositing such structures. The most important structural dependence is the plane perpendicular to the growth direction, hence in this work I will analyse them as two-dimensional structures. I will obtain the effective permittivity and optimal bounds (which I will call leaf bounds) by expanding the averaged polarization field in a power series on the susceptibility. To do this we developed a method that relies on a Monte Carlo algorithm to efficiently obtain higher orders of this series expansion. Therefore, this new methodology permits the study of higher order micro-structural parameters. In this thesis I will analyse up to fourth order effects. For anisotropic coatings, the depolarization of the Gaussian random fields studied is related to the depolarization factors of an ellipsoid with the same anisotropy. This fact will make it relatively easy to design simple anisotropic structures that are optically equivalent to experimentally measured ones. Coatings of this type are useful for angular, spectral or polarization selectivity. Thirdly, having explored single-material structures that are either random isotropic (sponges) or pseudo-random anisotropic (columnar), I turn to the problem of heterogeneous systems. The prototypical example is a paint-like coating in which some phases are randomly distributed inside a light-absorbing matrix. I will present a generalized four-flux method which is capable of analysing the optical response of realistic heterogeneous matrices. My new methodology is capable of dealing with factors including different size distribution of components, heterogeneous mix of materials, and weak absorption by the matrix (binder). A matrix formalism is developed to extend this method to multi-layer systems. The methodology is applied to the optimization of paints for achieving solar efficiency and I find that multi-layer paints with larger particles in the outer layer offer better performance in the IR. Finally, I use a variation of the C-method to examine the effect of surface roughness on optical properties. Surface roughness is present in any kind of coating, including any of those described above, and, depending on its scale size, the optical response can vary significantly as a function of angle and wavelength. I analyse the angular effects caused by changing the correlation length of a surface profile with a fixed groove depth, i.e. increasing the noise of the surface and the effective slope of the profile to determine the angular dispersion. The effect of roughness on the optical properties is exemplified by showing how it can control the perceived colour of a gold surface. I show that some tuning of optical properties is possible by this means. My findings include that a significant reduction on reflectance with short correlation length, and that angular colour dependence of rough gold profiles shows a blue-white colour for s-polarization and a yellow-reddish colour for p-polarization.
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