Numerical study of polarization evolution governed by linear birefringence, twist-induced circular birefringence and nonlinear birefringence in a single-mode optical fiber

Abstract This tutorial presents a numerical analysis of continuous wave and ultrashort pulse evolution through a twisted single-mode optical fiber, modeled by the nonlinear Schrödinger equation. In this model, the polarization evolutions of the continuous wave and the pulse profile are studied by the changes in ellipticity and ellipse rotation, which are driven by the inherent linear birefringence of the optical fiber, the induced nonlinear birefringence due to the centrosymmetric response of the fiber and the induced circular birefringence due to a uniform twist applied along the fiber. In particular, the role of each birefringence effect is studied in detail. As a result, it is pointed out that a large uniform twist rate allows viewing the optical fiber as an isotropic waveguide that preserves ellipticity. On the other hand, a saturable absorber mechanism based on a linear polarizer and the ellipse rotation in a twisted fiber, which introduces a nonlinear transmission characteristic that is part of the principles of operation of the mode-locked fiber lasers, is analyzed in order to illustrate the applicability of this numerical study.