Polaritonic modes in a dense cloud of cold atoms

We analyze resonant light scattering by a cloud of cold atoms with randomly distributed positions in a regime where resonant dipole-dipole interactions between scatterers cannot be neglected. Using a microscopic approach we calculate numerically the collective eigenmodes of the cloud for many realizations. It is found that there always exists a small number of polaritonic modes. Using a macroscopic approach, we show that the atomic cloud is equivalent to a homogeneous particle with an effective permittivity and that there is a one-to-one correspondence between the microscopic polaritonic modes and the modes of the homogeneous particle.