Nonlinear polarizability of a two-isotope active medium in a ring laser in the presence of interisotope resonance photon exchange

The resonance radiation trapping operators are constructed for a two-isotope excited atom ensemble allowing for interisotope resonance photon exchange. The nonlinear polarizability of a ring-laser medium is calculated using the strong collision model and an expression is obtained which relates the exchange parameter with the isotope shift due to the resonance transition and with the trapping parameter. Relationships are derived and analyzed for the nonlinear self-interaction and interaction parameters of the opposite waves under complete exchange conditions by accurately solving a system of kinetic equations.