Mirror and cavity formations by chains of collectively radiating atoms

We search for mirror and cavity-like features of a linear chain of atoms in which one of the atoms is specially chosen as a probe atom that is initially prepared in its excited state or is continuously driven by a laser field. Short chains are considered, composed of only three and five atoms. The analysis demonstrate the importance of the inter atomic dipole-dipole interaction which may lead to a collective ordering of the emission along some specific directions. We examine the conditions under which the radiative modes available for the emission are only those contained inside a cone centered about the inter atomic axis. Particular interest is in achieving the one-way emission along the inter atomic axis, either into left (backward) or right (forward) direction, which is referred to as a mirror-like behavior of the atomic chain. A direction dependent quantity called the directivity function, which determines how effective the system is in concentrating the radiation into a given direction, is introduced. We show that the function depends crucially on the distance between the atoms and find that there is a threshold for the inter atomic distances above which a strongly directional emission can be achieved. The one-sided emission as a manifestation of the mirror-like behavior and a highly focused emission along the inter atomic axis as a characteristic of a single-mode cavity are demonstrated to occur in the stationary field. Below the threshold the directivity function is spherically symmetric. However, we find that the population can be trapped in one of the atoms, and sometimes in all atoms indicating that at these small distances the system decays to a state for which there are no radiative modes available for emission.