THE THIRRING MODEL AS AN APPROXIMATION TO THE THEORY OF 2-PHOTON PROPAGATION

We consider the two-photon propagation process under the two-fold appr oximation that (i) the excitation of the upper level df medium molecul es remains small during the process, (ii) the intensity of one of the two participating electromagnetic waves is always small compared to th at of the other wave. It is then shown that in the limit of the strong dynamical Stark effect the equations describing this process can be r educed to the classical Thirring-model equations. This reduction permi ts one to develop a much simpler theory of wave interaction than was p ossible in the case of the original equations. As an example, the peri odic solutions of two-photon propagation are considered and the Whitha m modulational equations are obtained. The different forms of U-V pair s for the Thirring model are discussed in the appendix. Analogous theo ry can be developed for the stimulated Raman scattering process.