Hamiltonian description of nonlinear propagation in optical fibers

Abstract

Nonlinear propagation in single-mode and multimode fibers in the presence of the optical Kerr effect is described in terms of a number of parameters (four for each propagating mode) which can be interpreted as conjugate variables of a suitable Hamiltonian system. The formal simplicity of this approach, which admittedly furnishes a limited description of nonlinear propagation because of the finiteness of the number of variables employed, is, however, very useful for gaining a straightforward physical insight into the problem. The solution of the pertinent equations, either analytical or numerical, presents a much less formidable task than the solution of the set of nonlinear equations fully describing propagation.