Operator of photon density in the phase space

We have analyzed the possibility to describe the evolution of optical fields by means of the operator of photon density (the photon distribution function) in the phase space. Ideologically, our approach is in the course of the Mandel operator procedure. Approximate eigenfunctions and eigenvalues of the coarse-grained distribution function are obtained. It is shown that the evolution of the photon density in the phase space can be described in terms of photon trajectories. These trajectories can be obtained by solving the Newton equations of motion, in which an 'external force' may originate from spatial variations of the refractive index. We believe that this method can be useful for the description of various optical phenomena, including the problem of quasi-one-dimensional light propagation in fibers.