Theoretical and computational studies of the scattering of light from randomly rough dielectric surfaces

We are surrounded by light being scattered from surfaces all around us, both natural and man-made. Improving our understanding of exactly how light (and more generally, electromagnetic waves) interacts with and scatters from or through surfaces, such as a solar cell, a telescope mirror, paint or a glass window, is of value and importance to both industry and society as a whole. It gives us a better understanding of the world around us and how we perceive it, and it can also enable us to develop new technologies and improve upon existing ones. This thesis is a collection of work where we have tried to better understand a few of these interactions through the use of theory, experimental results and computer simulations. We have investigated the scattering of polarized light from two-dimensional randomly rough dielectric interfaces, in order to look for scattering patterns of interest in the angular intensity distributions of the diffusely scattered light. The basis for our investigations has been the reduced Rayleigh equations and their numerical solutions. Our overall contribution is towards an increased understanding of diffuse scattering from randomly rough surfaces, especially for three-dimensional systems where we allow for cross-polarized scattering. This can be useful in a wide range of optical systems, since the non-invasive method of surface characterization through the analysis of scattering data is interesting for both industry and research. When light is scattered diffusely in either reflection or transmission from or through a weakly rough interface, two phenomena of interest can be observed in the scattering intensity distributions. These are the Yoneda phenomenon, relatable to the idea of total internal reflection from a planar interface, and the Brewster scattering phenomenon, relatable to the polarizing angle observed for a planar interface. These scattering phenomena have only partially been investigated in the past, and their study has been the core of this thesis. We investigate these phenomena thoroughly through perturbative and non-perturbative numerical and theoretical work, also with the aid of new experimental results. We show, describe, explain and predict the behavior of both phenomena based on a lowest non-zero order perturbative approach, and as such we conclude that they are so-called single-scattering phenomena. We also investigate the physical mechanisms that underpin these phenomena, and attempt to describe them in terms of simple notions such as scalar waves, oscillating and rotating dipoles and geometrical arguments. If you let sunlight reflect from the layer of water vapor hovering some micrometers above the reflective surface of your morning cup of tea, you might observe some colored rings of light when you look into the reflection. These rings are a variety of Selenyi rings, an interesting interference effect that emerges when light is scattered diffusely by thin dielectric films. We investigate this effect thoroughly in this thesis, and describe the Selenyi phenomenon theoretically and numerically. Lastly, when medium interfaces are randomly rough, it is of value if we can infer the statistical properties of the roughness along with the properties of the scattering media based purely on the non-invasive scattering of light. Through the use of numerical phase perturbation theory based on the reduced Rayleigh equations, we investigate the reconstruction of such properties through a minimization method based on the reflected intensity distributions