On the quantum statistics of the superposition of coherent and chaotic fields

The generating function, the corresponding integrated intensity distribution, and the photon-counting distribution and its fractional moments are derived for the superposition of coherent and chaotic M-mode fields on the basis of a formalism of arbitrary ordering of field operators in quantum optics. An alternative description is also given based on a recent analysis of the superposition of coherent and chaotic fields in terms of the correlation functions which makes it possible to derive a number of results valid for arbitrary mean occupation numbers per mode from which the model considered follows as a special case. Many earlier results obtained for coherent and chaotic fields and their superposition are included as special cases. The present results generally describe a superposition experiment for an N-mode coherent field (e.g. generated by an N-mode laser operating far above threshold) and an M-mode chaotic field (M>or=N) as well as a field generated by an M-mode laser operating above threshold.