Near-resonant light scattering by a sub-wavelength ensemble of identical atoms

We study theoretically the scattering of light by an ensemble of $N$ resonant atoms in a sub-wavelength volume. We consider the low intensity regime so that each atom responds linearly to the field. While $N$ non-interacting atoms would scatter $N^2$ more than a single atom, we find that $N$ interacting atoms scatter less than a single atom near resonance. In addition, the scattered power presents strong fluctuations, either from one realization to another or when varying the excitation frequency. We analyze this counter-intuitive behavior in terms of collective modes resulting from the light-induced dipole-dipole interactions. We find that for small samples, their properties are governed only by their volume when $N\gtrsim 20$.