Hamiltonian formulation of self-induced transparency theory without slowly varying envelope approximation

Abstract

It was shown that the propagation of an ultrashort light pulse in resonance absorbing medium under self-induced transparency conditions can be described by the theory which allows Hamiltonian formulation where corresponding Poisson brackets are non-ultralocal and the restrictions of a slowly varying envelope approximation are lifted. By employing the representation of zero curvature, a compact form of fundamental Poisson brackets for a monodromy matrix was found to satisfy the requirements of the generalized Hamiltonian formulation of completely integrable systems. An explicit form of PB amongst monodromy matrix elements, canonical variables of an angle-action type and integrals of motion can then be derived by a standard procedure. Semi-classical quantization of this model can also be done. The model considered extends the list of completely integrable non-ultralocal models.