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8 May 2013 Polarization properties of vector solitons generated by modulation instability in circularly birefringent fibers
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Common optical fibers are randomly birefringent, and solitons formatting and traveling in them are randomly polarized. However it is desirable to have solitons with a well-defined polarization. We analyzed the two coupled propagation equations in a circularly birefringent fiber. Our equations include SPM, XPM and the soliton self frequency shift. In a difference of previously published works we consider the polarization dependence of the Raman amplification. We have found that the difference between perpendicular and parallel Raman gain results in energy transform from slow to fast circularly polarized component. We have shown this effect analytically and by a numerical simulation. For analytical consideration we performed a transformation of equations which reduces them to a form of perturbed Manakov task. The perturbation method gives us equations for evolution of the polarization state of pulse which show that in a circularly birefringent fiber the cross–polarization Raman term leads to unidirectional energy transfer from the slow circularly polarized component to the fast one. The magnitude of this effect is determined by the product of birefringence and amplitudes of both polarization components. Thus, solitons with any initial polarization state will eventually evolve stable circularly polarized solitons. We also made numerical analysis of two coupled nonlinear Shrödinger equations using a split-step Fourier method. The parameters of a standard fiber were used with delay between left- and right- circular polarizations of 1 ps/km that corresponds to circular birefringence in a fiber twisted by 6 turns/m. Numerical analysis confirms the analytical approximation. We analyzed also the polarization of solitons generated by modulation instability. We used a 30-ps, 40-W pulse with noise imposed on them at the fiber input. We found that polarization ellipticity of solitons is distributed randomly; however the average polarization ellipticity is closer to the circular than the polarization ellipticity of the input pulse. In experiment we used 220-m SMF-28 fiber twisted by 6 turns/m. The fiber was pumped by 1-ns pulse. We have found that at circular polarization of the input pulse solitons at the fiber output have polarizations close to the circular.
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E. A. Kuzin, A. Flores-Rosas, J. I. Peralta-Hernandez, B. A. Villagomez-Bernabe, B. Ibarra-Escamilla, A. Gonzalez-Garcia, O. Pottiez, and M. Duran-Sanchez "Polarization properties of vector solitons generated by modulation instability in circularly birefringent fibers", Proc. SPIE 8772, Nonlinear Optics and Applications VII, 877218 (8 May 2013);

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