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

A Formalism Useful to Study Beyond Squeezing in Non-linear Quantum Optics