Collective polaritonic modes in an array of two-level quantum emitters coupled to an optical nanofiber

In this paper we develop a microscopic analysis of the light scattering on a periodic two-level atomic array coupled to an optical nanofiber. We extend the scattering matrix approach for two-level system interaction with nanofiber fundamental guided mode HE11, which allows us to model the scattering spectra. We support these results by considering the dispersion of the polaritonic states formed by the superposition of the fundamental mode of light HE11 and the atomic chain states. To illustrate our approach we start by considering a simple model of light scattering over an atomic array in free space. We discuss Bragg diffraction in the atomic array and show that the scattering spectrum is defined by the nonsymmetric coupling of a two-level system with nanofiber and vacuum modes. The proposed method allows consideration of two-level system interactions with a full account of dipole-dipole interactions via both near fields and long-range interaction owing to nanofiber mode coupling.