Control and characterization of nano-structures with the symmetries of light

Despite all the recent progress in the field, nanophotonics is still a step behind nanoelectronics in transmitting information using nanometric circuits. A lot of effort is being put into making very elaborate structures that can guide light and control light-matter interactions at the nano-scale. The field of plasmonics has been especially successful in this. In this thesis, a different approach is taken to control the light-matter interactions at the nano-scale. The approach is based on considering light and sample as a whole system and exploiting its symmetries. Thanks to this new perspective, new phenomena have been unveiled. These new phenomena have been developed theoretically and/or experimentally and are scattered across this thesis. In chapter 2, the theoretical grounds of this thesis are settled. Even though every physicist is familiar with the concept of symmetry, a formalism to systematically describe the symmetries of electromagnetic fields is explained. With this formalism, some wellknown symmetry considerations can be as easily retrieved as some much less intuitive. For example, it can be demonstrated that a linearly polarised Bessel beam is not cylindrically symmetric; whilst a circularly polarised Bessel beam is both cylindrically and dual symmetric. Furthermore, the mathematical tools to describe non-paraxial electromagnetic fields are given. Due to the fact that this work deals with sub-wavelength scatterers, the light-matter interaction cannot usually be described within the paraxial approximation. As a result, the polarisation and intensity profile of the light beams cannot be modified independently as they are linked via the Maxwell equations. Chapters 3, 4 and 5 deepen in the study of Generalized Lorenz-Mie Theory. Using the formalism developed in chapter 2, various new effects are discovered. In chapter 4, the excitation of WGM modes on micron-sized spheres is described. Indeed, using cylindrically symmetric beams, light can be coupled into spherical resonators without the use of evanescent coupling. Furthermore, it is shown that the use of cylindrically symmetric modes also allows for the enhancement of the ripple structure in scattering. Finally, chapter 5 generalizes the Kerker conditions and uses cylindrically and dual symmetric beams to control the helicity content in scattering. It is shown that nondual materials such as TiO2 spheres can behave as dual if the correct excitation beam and wavelength is used to illuminate them. Chapters 6, 7 and 8 are devoted to experiments. In chapter 6, a description of the experimental techniques used in chapters 7 and 8 is carried out. In particular, the basics of Spatial Light Modulators and Computer Generated Holograms are given. Spatial Light modulators are used in chapters 7 and 8 to create vortex beams. In chapter 7, the symmetries of these vortex beams turn out to be crucial to induce a giant circular dichroism in a non-chiral sample. Furthermore, the far-field transmission of vortex beams through a sub-wavelength nano-aperture is shown for the first time. Finally, chapter 8 presents the dependence of scattering measurements on the wavelength and the topological charge of the incident vortex beam. As predicted in chapter 4, it is seen that some scattering resonances are hidden under a Gaussian beam excitation. These resonances can be unveiled when the illumination is a vortex beam. Overall, this work shows a number of new effects (theoretical and/or experimental) produced by the excitation of symmetric structures with symmetric light. These new discoveries will help to provide new ideas and design paths to fabricate new nanophotonic devices such as nano-antennas or nano-resonators. A study of the symmetries of the system should always be kept in mind for any photonic device where the spatial degrees of freedom and the polarisation cannot be decoupled.