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Journal of Experimental and Theoretical Physics

Unidirectional two-component optical pulse propagation in an isotropic two-level medium with permanent dipole moment

Alexander A. Zabolotskii

Published May 1, 2008• 6 citations
Publisher

Abstract

The inverse scattering method is used to find the solution in the isotropic limit of the general integrable model of a two-component electromagnetic field interacting with a two-level system. The model describes electromagnetic pulse propagation without invoking the slowly varying envelope approximation and takes into account effects due to a permanent dipole moment.

DOI
10.1134/s1063776108050026

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The inverse scattering method is used to find the solution in the isotropic limit of the general integrable model of a two-component electromagnetic field interacting with a two-level system. The model describes electromagnetic pulse propagation without invoking the slowly varying envelope approximation and takes into account effects due to a permanent dipole moment.
We find a general integrable system of reduced Maxwell-Bloch equations describing the interaction of a two-component electromagnetic field with the dipole transition of a two-level medium. The anisotropy of the anisotropic dipole momentum of the transition as a permanent dipole momentum is taken into account. A solution of the model is found for a particular case by using the inverse scattering transform. The method is based on a solution of the Riemann-Hilbert problem taking into account the symmetry properties of the corresponding fundamental solutions.
Amplification of electromagnetic field pulses approximately one cycle in duration in multilevel media with an effective permanent dipole moment is studied theoretically without application of the approximation of slowly varying envelopes for the case of unidirectional propagation of the radiation. For three-level and quasi-two-level media, it is shown that the set of Maxwell-Schrödinger equations can be reduced to an integrable set of equations for an effective two-level medium. The presence of an (effective) permanent dipole moment of the medium was found to lead to new specific features of the amplification and control of the dynamics of field pulses.
Self-induced transparency is analyzed for optical pulses interacting with a two-level system by solving an integrable system of evolution equations without using the slowly varying envelope approximation. A suitable modification of the inverse scattering method is developed to find soliton solutions. The characteristics of linearly and circularly polarized optical solitons (including those created in a laser) are compared. To assess the scope of the two-level model, the effects due to additional levels are analyzed in the adiabatic approximation. It is shown that these effects violate the integrability of the model and lead to loss of self-induced transparency for pulses with duration comparable to oscillation period. However, self-induced transparency is recovered in the quasi-monochromatic limit. Applications of the results are discussed.
The dynamics of pulses with durations comparable to the inverse transition frequency that propagate in an optical medium is studied in terms of two integrable systems of Maxwell-Bloch equations. The first model describes the field interaction with a nondegenerate medium with a permanent dipole moment and permanent external pumping. A general formula is derived for the N -soliton solution. Particular solutions are used as examples to investigate the effect of permanent dipole moment and pumping on the soliton dynamics. The second model describes the interaction between two-component electric-field pulses and a two-level degenerate medium with permanent upper-level pumping. For different initial magnetic-sublevel populations, soliton solutions are used as examples to show that pumping causes a change in polarization dynamics. A two-soliton solution is used to analyze the interaction of solitons in a two-level medium with external pumping.