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arXiv:0808.3963

Comment on 'Evolution of the unidirectional electromagnetic pulses in an anisotropic two-level medium'

N. V. Ustinov

Published Aug 28, 2008• 0 citations
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Abstract

Recently, Zabolotskii [Phys. Rev. E 77, 036603 (2008)] presented the Lax pair for a version of the reduced Maxwell--Bloch equations. This version was derived under considering the unidirectional propagation of a two-component electromagnetic pulse through an anisotropic two-level medium. We demonstrate that his derivation contains essential omission, which led to the wrong version of the reduced Maxwell--Bloch equations. We also point out that the Lax pair for correct version of these equations had been known in the most general anisotropic case.

DOI
10.48550/arxiv.0808.3963

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Recently, Zabolotskii [Phys. Rev. E 77, 036603 (2008)] presented the Lax pair for a version of the reduced Maxwell--Bloch equations. This version was derived under considering the unidirectional propagation of a two-component electromagnetic pulse through an anisotropic two-level medium. We demonstrate that his derivation contains essential omission, which led to the wrong version of the reduced Maxwell--Bloch equations. We also point out that the Lax pair for correct version of these equations had been known in the most general anisotropic case.
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.