Light-matter interaction in photonic metasurfaces

In the present work, we discuss the properties of the complex (i.e., including real and imaginary part of the eigenvalues) eigenmodes in dielectric photonic metasurfaces. These structures are usually composed of a multi-layered waveguide core with a generic in- plane periodic patterning. The presence of active materials, i.e. materials sustaining excitonic resonances, can result in the so-called radiation-matter strong-coupling regime. This phenomenon manifests itself with the formation of the elementary excitations called exciton-polaritons, for brevity only polaritons. The study of these elementary excitations is motivated from either an application point of view, or a fundamental interest. Indeed, these elementary excitations in solids can serve as a platform for the study of various exotic states of matter. For example, polaritons can display superfluid behaviour and undergo Bose-Einstein condensation at relatively high temperature. On the other hand, one of the final goals of this research field is to replace electrons with photons and polaritons as information carriers in circuits. In this thesis, we ultimately studied the dispersions, losses, symmetry and topological properties of either photons or polaritons in the aforementioned metamaterials. The control over these quantities are essentials for any targeted application. Throughout the thesis, several algorithms have been used to investigate the physics of the elementary excitations in metasurfaces, such as the guided mode expansion, the scattering matrix (or rigorous coupled wave analysis) and the finite-difference time-domain methods. Most of the theoretical predictions presented in this thesis are validated by experimental measurements. As the main original contribution, we extended the quantum theory of light-matter coupling to metasurfaces coupled with an arbitrary number of active layers. Thanks to the newly introduced theory, it is possible to take into account either classical active multi quantum well systems, or two dimensional semiconductor materials and perovskite layers coupled with the photonic modes. We compared the results of the generalised theory with semi classical results, and experiments. In each case, we obtained a good agreement for both the real dispersions of the polaritonic modes and the losses. In addition, we studied the symmetry and topological properties of bound states in the continuum (BICs). The BIC is a peculiar type of solution of the wave equation, in this case Maxwell equations, that is perfectly confined despite the fact it lives in a continuum of radiative solutions. Among its exotic properties, we can identify its singularity in the far-field emission pattern, resulting in a polarisation of electromagnetic radiation. We demonstrated that this topological singularity can be transferred to BIC coupled to excitons, namely polaritonic-BIC (pol-BIC). Finally, we studied a platform where the non-linear polariton-polariton scattering processes create a trap for the pol-BIC leading to Bose-Einstein phase transition with extremely low condensation threshold.