Abstract
The evolution of the state of polarization (SoP) in a twisted vector optical field (TVOF) with an astigmatic phase in a strongly nonlocal nonlinear medium (SNNM) is investigated. The effect of an astigmatic phase on the propagation dynamics of the twisted scalar optical field (TSOF) and TVOF during propagation in the SNNM leads to reciprocally periodical evolutions of stretch and shrink, accompanied by the reciprocal transformation of the beam shape between an initial circle shape and threadiness distribution. The TSOF and TVOF rotate along the propagation axis if the beams are anisotropic. In particular, the reciprocal conversions between the linear and circular polarizations occur in the TVOF during propagation, which are strongly related to the initial powers, twisting strength coefficients, and initial beam reshapes. The numerical results confirm the analytical predictions by the moment method for the dynamics of the TSOF and TVOF during propagation in a SNNM. The underlying physics for the polarization evolution of a TVOF in a SNNM are discussed in detail.
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