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Journal of the Optical Society of America B

Optical solitary waves in three-level media: effects of different dipole moments

A. S. Rosenthal, Talal Ghannam

Published Mar 31, 2008• 3 citations
Publisher

Abstract

The exact electric polarization operator of the Maxwell-Bloch equations for a three-level Λ-type system is derived without assuming equality of the transition dipole moments. Numerical solution of the resulting solitary wave equations yields a richer spectrum than found earlier for identical dipole moments [Hioe and Grobe, Phys. Rev. Lett.73, 2559 (1994)]. The two components of the new solitary waves each have a zero-pulse area and take the form of modulated oscillations.

DOI
10.1364/josab.25.000645

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The exact electric polarization operator of the Maxwell-Bloch equations for a three-level Λ-type system is derived without assuming equality of the transition dipole moments. Numerical solution of the resulting solitary wave equations yields a richer spectrum than found earlier for identical dipole moments [Hioe and Grobe, Phys. Rev. Lett.73, 2559 (1994)]. The two components of the new solitary waves each have a zero-pulse area and take the form of modulated oscillations.
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.
An analysis is made of the coherent interaction of a short pulse of polarised electromagnetic radiation with a medium in which the energy levels are degenerate in respect of the angular momentum projection. In the case of the j a = 1 → j b =0 transition it is found, without recourse to the approximation of slowly varying envelopes, that the system of the Maxwell–Bloch equations has an exact solution in the form of a steady-state solitary wave of duration equal to half the period of emission as a result of the investigated atomic transition. A new solution is obtained, in addition to a simple generalisation corresponding to a polarised video pulse. When the populations of the excited states with different projections of the angular momentum are different, the spherical components of the vector representing the electric field intensity do not behave proportionately: if one of them corresponds to a unipolar spike of the electric field, the other component is a variable-sign solitary wave.