On the Simulation of Electromagnetic Wave Scattering by Periodic and Randomly Rough Layered Structures based on the Reduced Rayleigh Equations: Theory, numerical analysis and applications

Abstract

A great number of natural phenomena that we observe, as well as numerous man-made objects we use in our everyday life, are made possible thanks to the interaction between light and matter. In particular, when light is interacting with a surface between two homogeneous media, light may be scattered either diffusely or with specific diffraction properties depending on the level of roughness and geometrical structure of the surface. From one extreme to the other, a perfectly smooth surface will reflect a laser beam only along the specular direction according to the well known Snell-Descartes law of reflection. If the surface is a grating and possesses periodic undulations whose period is of the order of a few wavelength, the laser beam will be diffracted into a set of well defined directions. Now if the undulations on the surface are random and do not exhibit any periodicity, and the level of roughness is comparable to the wavelength, the laser beam will be scattered broadly and become diffuse.

The present thesis deals with the scattering of light by structured and randomly rough surfaces. The study is carried out within the theoretical framework of the so-called reduced Rayleigh equations. This framework is particularly well adapted to the study of weakly rough surfaces and allows for simple approximations which are easy to implement, fast to compute and can give physical insights into some phenomena observed in the diffusely scattered light.

Two such phenomena, the Yoneda ring phenomenon and the Brewster scattering phenomenon, have been observed experimentally and numerically for decades but were lacking clear physical explanations. The work presented in this thesis shed new light on these effects and provides a clear physical interpretation. The Yoneda ring is a ring of enhanced intensity in the diffusely scattered light observed in the medium of highest refractive index. The Brewster scattering phenomenon is the observation of minima, or near zero, of intensity in the diffuse scattered light for polarized light. The proposed theory explains these two phenomena respectively in terms of coupled progressive-evanescent modes and in terms of the dipole radiation from the microscopic scatterers in the materials (atoms, molecules). In the latter, the fundamental role of Snell-conjugate waves is discussed and a simple but powerful geometrical interpretation is presented. Two new phenomena were also predicted by the theory for light scattering under total internal reflection: (i) what we have called the s-black-out phenomenon for which the diffusely scattered light is purely p-polarized independently of the scattering direction, and which occurs exactly at the critical incidence for total internal reflection and is associated with the alignment of the elementary oscillating dipoles along the axis normal to the average surface plane; (ii) a linearly to circularly polarized Brewster scattering effect for incidences beyond the total internal reflection incidence which was shown to be caused by a regime in which dipoles in the materials are no longer oscillating but rotating.

After the study of the scattering by a single rough surface, the scattering by a film whose interfaces are rough was analyzed. In particular, we have been interested in a case where the film thickness is of the order of a few wavelength such that interference rings in the diffuse scattered light, known as Selényi rings, could be observed. We have demonstrated theoretically that, in a single scattering regime, the cross-correlation between the two-rough surfaces of the dielectric film induces a selective intensity enhancement and attenuation of the Selényi rings. This is a clear example of correlation induced interference, an effect of fundamental interest here, but which may be useful for surface characterization and for the design of disordered optical material by engineering correlation.

Finally, we have demonstrated a powerful technique for parameter retrieval, or inverse scattering of surfaces, based on the reduced Rayleigh equations. The method was applied successfully to a plasmonic photonic surface based on experimental Mueller matrix ellipsometry measurements, with a demonstrated accuracy of a couple of nanometers and a speed-up factor of a hundred compared with the use of a commercial the finite element software. The method based on the reduced Rayleigh equations has, however, a limited range of validity