Traveling wave formalism for the dynamics of optical systems in nonlinear Fabry-Perot cavities

We formulate the dynamics of nonlinear optical Fabry-Perot (FB) cavities
in terms of a model in which only one of the two counter-propagating
electric field envelopes appear. Thus, the model is simpler than the
standard ones but still exact. The field envelope which propagates in
the opposite direction is expressed in a very simple way in terms of the
envelope that appears in the model. Thus we generalize in the simplest
way to the FB case the set of Maxwell-Bloch equations for the ring
cavity. The boundary condition for the field envelope that appears in
the model is a simple periodicity condition. This feature allows for
expanding the variables of the model in terms of traveling waves instead
of standing waves as it is customary, which implies noteworthy
simplifications in the calculations. On the basis of the modal equations
which arise from the model, we discuss the adiabatic elimination of the
atomic variables and of the atomic polarization only.