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Journal of Experimental and Theoretical Physics

Soliton regimes of ultrashort pulse propagation through an array of asymmetric quantum objects

С. В. Сазонов, N. V. Ustinov

Published Oct 1, 2006• 11 citations
Publisher

Abstract

Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.

DOI
10.1134/s1063776106100074

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Nonlinear regimes of two-component ultrashort pulse propagation through an array of anisotropic quantum systems are analyzed theoretically under conditions when the slowly varying envelope approximation is inapplicable. It is shown that if the spectral width of the pulse is much larger than the quantum transition frequency, then the dynamics of its ordinary component can be described by a modified sine-Gordon equation that belongs to the class of integrable models but has never been used in physical applications. It is shown that the extraordinary pulse component responsible for the dynamic Stark shift of the transition frequency is coupled to its ordinary component by an algebraic relation. The soliton solutions to the derived equation are classified. Depending on the pulse duration, the solutions have the form of 2π pulses (kinks and antikinks) or steady traveling 0π pulses having no counterparts in isotropic models (neutral kinks). Interactions between the medium and solitons of different types and soliton collisions are analyzed.
This paper theoretically discusses the propagation of an ultrashort laser pulse consisting of ordinary and extraordinary components in a system of anisotropic quantum centers. The treatment does not use the assumption that the density of quantum centers is small and makes no limitations on the transition dipole moments. It is shown that, if the spectral pulse width is much greater than the frequency of the quantum transitions, the dynamics of its ordinary component obeys a modified sine-Gordon equation that belongs to the class of integrable models. Soliton solutions of the given equation are constructed, and they are classified. Depending on the duration of the soliton, solutions are possible in the form of a 2π pulses (kinks and antikinks) or 0π steady-state traveling pulses (neutral kinks), which have no counterpart in the isotropic case. The behavior of the medium is studied when various types of solitons are transmitted.
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg--de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.
We study theoretically the phenomenon of self-induced transparency for ultrashort pulses (videopulses) propagating in a multilevel quantum medium under conditions in which the method of slowly varying amplitudes and phases breaks down and the pulse spectrum substantially overlaps the quantum transitions. A special class of transitions with one common level is considered. We find that the dynamics of the videopulses in such a medium is described by a double sine-Gordon equation. We establish the conditions under which steady-state traveling 0 π -, 2 π -, and 4 π -videosolitons are formed. It is found that 4 π -videosolitons can propagate both in equilibrium media and in some nonequilibrium media, while 0 π -videosolitons can propagate only in nonequilibrium media. We study amplification processes in highly nonequilibrium systems and show that, depending on the initial state of the medium, 2 π -and qπ -pulses (0< q <1) with increasing amplitudes may be formed. We conclude that the amplification of an ultrashort pulse occurs due to an increase in the photon number density and to an increase in the frequency of each photon. Finally, we study the possibility of an electromagnetic autosoliton being formed in a nonequilibrium dissipative medium.
The propagation of extremely short (without high-frequency filling) pulses and nonresonant envelope solitons in a two-component medium comprising two-level atoms with substantially different quantum transition frequencies was studied. The dynamics of a pulse whose reciprocal time scale lay between these frequencies was shown to be described by the Kosevich-Kovalev equation, the one-way variant of which was the Konno-Kameyama-Sanuki equation. If the transition dipole moments of medium components were equal, the one-way equation became integrable. Soliton and soliton-like solutions to these equations were used to analyze pulse propagation regimes at various two-component medium initial states. The stability of these localized wave formations was analyzed. The possible existence of stable soliton-like pulses propagating in a nonequilibrium medium at group velocities exceeding the velocity of light in vacuum was discussed.
The nonlinear dynamics of a vector two-component optical pulse propagating in quasi-resonance conditions in a medium of nonsymmetric quantum objects is investigated for Stark splitting of quantum energy levels by an external electric field. We consider the case when the ordinary component of the optical pulse induces σ transitions, while the extraordinary component induces the π transition and shifts the frequencies of the allowed transitions due to the dynamic Stark effect. It is found that under Zakharov-Benney resonance conditions, the propagation of the optical pulse is accompanied by generation of an electromagnetic pulse in the terahertz band and is described by the vector generalization of the nonlinear Yajima-Oikawa system. It is shown that this system (as well as its formal generalization with an arbitrary number of optical components) is integrable by the inverse scattering transformation method. The corresponding Darboux transformations are found for obtaining multisoliton solutions. The influence of transverse effects on the propagation of vector solitons is investigated. The conditions under which transverse dynamics leads to self-focusing (defocusing) of solitons are determined.
We consider the propagation of ultrashort optical solitons in media described by a general Hamiltonian of multilevel atoms. Assuming that all transition frequencies of the medium are well below the typical wave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wave approximation and a rigorous application of the reductive perturbation formalism to derive a cumbersome coupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems. The rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation for a special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system of coupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showing the formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalized double-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.