  Motivated by previous investigations on the radiative effects of the electric
dipoles embedded in structured cavities, localization of electromagnetic waves
in two dimensions is studied {\it ab initio} for a system consisting of many
randomly distributed two dimensional dipoles. A set of self-consistent
equations, incorporating all orders of multiple scattering of the
electromagnetic waves, is derived from first principles and then solved
numerically for the total electromagnetic field. The results show that
spatially localized electromagnetic waves are possible in such a simple but
realistic disordered system. When localization occurs, a coherent behavior
appears and is revealed as a unique property differentiating localization from
either the residual absorption or the attenuation effects.
