We present a new method for the efficient modeling of the conversion of LP modes to vortex modes in gradually twisted highly birefringent fibers, employing the coupled-mode approach in helicoidal coordinates. The method is applicable to a class of highly birefringent fibers with cylindrical cores and stress-applying elements. We analyzed the effects of refractive index contrast, birefringence, and twist rate profile on the quality of the converted vortex beams, including the intensity and polarization distributions, as well as on the crosstalk between different eigenmodes at the output of the twisted fibers. The obtained results prove the possibility of a broadband quasi-adiabatic generation of vortex beams of high purity in gradually twisted highly birefringent fibers a few centimeters long and provide hints for optimization of the conversion process.
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