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"Non-Lagrangian" Parametric Interaction Of Light Waves

Energy exchange between counter propagating light waves of equal frequency is possible in media with instantaneous and local nonlinear optical response which, however, provides a special form of nonlinearity tensor. The major requirement is that there has to be no Lagrangian describing the light-medium interaction. There is a limited region of the pump wave intensity where the signal wave amplification takes place. The thermal mechanisms of interaction between light waves and liquid crystals provide examples of "non-Lagrangian" nonlinearity.