Basic properties for cooperative emission of radiation

Basic properties for the emission of radiation are derived from the diagonalization of the matrix (GAMMA/sub i//sub j/), where an element GAMMA/sub i//sub j/ gives the coupling between two atoms i and j via the electromagnetic field. This method gives naturally an estimate of the solid angles in which the radiation can take place. By using these estimates, we discuss whether the emission process can be described by a one- (two-) mode model. As expected, this model fails in the two limiting cases of large and small Fresnel numbers. Also for Fresnel numbers of the order of a few units, it is not obvious whether such a model is valid