Abstract
In order to reduce our general quantum description of light propagation to the standard one we use a method of introducing new variables of the counter-propagating waves (CPW variables). We discuss the effect of the dispersion for Stokes and anti-Stokes modes for chosen relations among some parameters. If we neglect the dispersion in this nonlinear process, no coupling to the wave going in the opposite direction giving rise to a nonlinear reflection of light can take place in this case. The photon space and time dependent modal annihilation and creation operators and the other corresponding quantities remain always dependent only on one of two new CPW variables. We can employ the approach of the standard propagation and relate space and time simply by the velocity of propagation.
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