TY - JOUR

T1 - Polarization dynamics in a resonant optical medium with initial coherence between degenerate states

AU - Newhall, Katherine A.

AU - Kovačič, Gregor

AU - Gabitov, Ildar

N1 - Funding Information:
2010 Mathematics Subject Classification. 78A40, 78A60, 78M35. Key words and phrases. Maxwell-Bloch equations, dressing method, solitons, polarization switching. The second author is supported by National Science Foundation (NSF) grant number DMS1615859. ∗ Corresponding author: Katherine A. Newhall.

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

KW - Dressing method

KW - Maxwell-Bloch equations

KW - Polarization switching

KW - Solitons

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U2 - 10.3934/dcdss.2020189

DO - 10.3934/dcdss.2020189

M3 - Article

AN - SCOPUS:85085315085

VL - 13

SP - 2285

EP - 2301

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

SN - 1937-1632

IS - 8

ER -