Normal and antinormal ordering of field operators in quantum optics

The relations between the probability distributionpn_vt of the number of photonsn_vt in a volumeV at timet and the probability distributions P_N(W) and P_A(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn_vt, P_N(W) and P_A(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn_vt, P_N(W) and P_A(W) become equal.