We introduce a unitary operator representing the exponential of the ph
ase difference between two modes of the electromagnetic field. The eig
envalue spectrum has a discrete character that is fully analyzed. We r
elate this operator with a suitable polar decomposition of the Stokes
parameters of the field, obtaining a natural classical limit. The case
s of weakly and highly excited states are considered, discussing to wh
at extent it is possible to talk about the phase for a single-mode fie
ld. This operator is applied to some interesting two-mode fields.