Derivation of a generalized double-sine-Gordon equation describing ultrashort-soliton propagation in optical media composed of multilevel atoms

摘要

We consider the propagation of ultrashort optical solitons in media described by a general Hamiltoniannof multilevel atoms. Assuming that all transition frequencies of the medium are well below the typicalnwave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wavenapproximation and a rigorous application of the reductive perturbation formalism to derive a cumbersomencoupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems.nThe rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation forna special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system ofncoupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showingnthe formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalizedndouble-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.