Dipolar Emitter Systems: Transition Between a Discrete and Continuous Formalism

Collective light-scattering phenomena, initially investigated within dense atomic gases, have recently been explored in sub-wavelength structured arrays of atoms. Similar effects have been observed within semiconductor monolayers, such as TMDCs, where incident light is scattered collectively by excitons. This study investigates the transition from discrete array arrangements to continuous emitter distributions. A band-structure theory for two-dimensional materials is presented, effectively capturing the system's optical properties and illuminating the significance of their dipole-dipole interactions. Leveraging the continuous nature of semiconductors, a wide variety of periodic structures offer highly adjustable optical properties. These properties hold promise for applications in light storage and manipulation within solid-state platforms.