### Abstract

We investigate the polarization switching phenomenon for a one-soliton solution to the Λ-configuration Maxwell-Bloch equations in the case of initial coherence in the material, corresponding to the forbidden transition between the two lower energy levels. We find two polarization states that are stationary. They are not the purely right- and left-circularly polarized solitons, as in the case of zero initial coherence, but rather two mixed, elliptically po- larized, states. These polarization states, of which only one is asymptotically stable, depend on both the initial population levels of the lower states and the coherence value. We also find the existence of superluminal soliton propaga- tion, but through numerical simulations show this solution to be unstable, and therefore likely not realizable physically.

Original language | English (US) |
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Pages (from-to) | 2285-2301 |

Number of pages | 17 |

Journal | Discrete and Continuous Dynamical Systems - Series S |

Volume | 13 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2020 |

### Keywords

- Dressing method
- Maxwell-Bloch equations
- Polarization switching
- Solitons

### ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

*Discrete and Continuous Dynamical Systems - Series S*,

*13*(8), 2285-2301. https://doi.org/10.3934/dcdss.2020189