Derivation of a coupled system of Korteweg–de Vries equations describing ultrashort soliton propagation in quadratic media by using a general Hamiltonian for multilevel atoms

摘要

We consider the propagation of ultrashort solitons in noncentrosymmetric quadratically nonlinear optical media described by a general Hamiltonian of multilevel atoms. We use a long-wave approximation to derive a coupled system of Korteweg–de Vries equations describing ultrashort soliton evolution in such materials. This model was derived by using a rigorous application of the reductive perturbation formalism (multiscale analysis). The study of linear eigenpolarizations in the degenerate case and the corresponding formation of half-cycle solitons from few-cycle-pulse inputs are also presented.