Coherence theory of laser resonator modes

An analysis of transverse laser resonator modes is presented, based on a recently developed coherence theory in the space-frequency domain. The modes are introduced by means of solutions of an integral equation that expresses a steady-state condition for a second-order correlation function of the field across a mirror of the laser cavity. All solutions of this integral equation are found to be expressible as quadratic forms involving the Fox-Li modes of the conventional theory. If there is no degeneracy, each mode is shown to be necessarily completely spatially coherent, at each frequency, within the framework of second-order correlation theory. It is also shown that, if several transverse modes are excited, the output cannot be completely spatially coherent.