Optical theorem for light scattering from a linear atomic chain

Abstract

The radiation pattern of light scattered from a chain of atoms having $J=0$ ground states and $J=1$ excited states is calculated in the weak driving field approximation. It is shown that, in general, for arbitrary orientation of the driving field to the chain axis, it is not possible to treat the atoms in a two-level approximation owing to cooperative effects. In the limit of large detuning, however, all cooperative decay effects can be neglected in calculating the scattered spectrum. Nevertheless, even in this limit, in order to ensure conservation of energy, it is still necessary to include cooperative decay when calculating the energy lost by the driving field. For arbitrary detunings, conservation of energy can be expressed in the form of a generalized optical theorem.