  A general formalism is given in quantum optics within a ring cavity, in which
a non-linear material is stored. The method is Feynman graphical one,
expressing the transition amplitude or S-matrix in terms of propagators and
vertices. The propagator includes the additional damping effect via the
non-linear material as well as the reflection and penetration effects by
mirrors. Possible application of this formalism is discussed, in estimating the
averaged number of produced photons, Husimi function, and the observables to
examine beyond the squeezing mechanism of photons.
