Quantization of polaritons in confined structures

I will describe quantization of exciton-polaritons in confined semiconductor structures, focusing on strong light-matter coupling in dielectric environments. The interplay of confinement and light-matter coupling is analyzed in detail. In the conservative case, we diagonalize the system Hamiltonian via Bogoliubov transformation and show how to find eigenmodes using Maxwell equations coupled to matter resonances. An analogous procedure can be performed in the dissipative case via the so-called third quantization technique. We propose nanostructures in which many-body effects could be observed in realistic conditions.