We find the N-photon state emitted by an N-step Dicke model and provid
e a method to construct the field coherence functions based on it. Our
effort is concentrated on the second order coherence, or the one-phot
on density matrix. When expressed in its canonical representation, thi
s matrix gives the photon number occupying each 'pulse eigenmode'. Thi
s number serves as an indicator of the correlation between photons. By
studying the evolution of the one-photon density matrix we can trace
the creation of such correlation during the emission. From the asympto
tic solution we are able to find approximate scaling law relations bet
ween the photon degeneracy in the eigenmodes and the total number of p
hotons involved.