Vector Modulation Instability in Highly Birefringent Fibers With Circularly Polarized Eigenmodes

Kinga Zolnacz,Karol Tarnowski,Waclaw Urbanczyk,Krzysztof Poturaj,Maciej Napiorkowski,Pawel Mergo

doi:10.1109/jphot.2021.3053064

Abstract

We report a detailed study of vector modulation instability (VMI) in highly birefringent fibers with circularly polarized modes in the normal dispersion regime. We show that because of suppression of coherent terms, the VMI in circularly birefringent fibers is governed by one set of coupled-mode nonlinear Schrödinger equations regardless of the fiber birefringence. In consequence, the VMI sidebands are polarized linearly and orthogonally to the pump up to the birefringence level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , similarly like in isotropic fibers. For greater birefringence the polarization states of the sidebands become elliptical with opposite handedness while the azimuth angle deviates from orthogonality to the pump. We also point on the dependence of the critical power beyond which the VMI cannot exist upon ellipticity angle θ of the eigenmodes. We show that the critical power gradually increases with the ellipticity angle and for θ > 17.6° the VMI gain is not limited, in contrast to linearly birefringent fibers. Our findings were confirmed experimentally by observation of the isotropic-like VMI in the spun side-hole fiber with nearly circularly polarized eigenmodes, in spite of relatively high birefringence of the order of 2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> .

Highlights

Vector modulation instability (VMI) is a phenomenon of generation of the spectral sidebands occurring in nonlinear birefringent fibers due to cross-phase modulation between orthogonally polarized modes under small phase and amplitude perturbations of the pump [1]
We report a detailed study of vector modulation instability (VMI) in highly birefringent fibers with circularly polarized modes in the normal dispersion regime
We show that the critical power gradually increases with the ellipticity angle and for θ > 17.6° the VMI gain is not limited, in contrast to linearly birefringent fibers

Summary

Introduction

Vector modulation instability (VMI) is a phenomenon of generation of the spectral sidebands occurring in nonlinear birefringent fibers due to cross-phase modulation between orthogonally polarized modes under small phase and amplitude perturbations of the pump [1]. When an elliptically polarized beam is introduced into the isotropic fiber, the amplitude of the sidebands gradually decays with increasing ellipticity and completely vanishes for a circularly polarized pump This fact can be understood by expressing nonlinear propagation equations in circular polarization basis, where only incoherent and cross-phase modulation terms appear [1]. We identify several distinct features of the VMI bands in highly birefringent fibers with circularly polarized eigenmodes These include existence of isotropic-like VMI sidebands (reported earlier for extremely low birefringence of the order of 10−8) up to the group birefringence level of 10−5, which are polarized linearly and orthogonally to the pump. In contrast to linearly birefringent fibers, for ellipticity angle of the eigenmodes |θ | > 17.6°, the VMI gain is not limited and increases with pump power

Circularly and Elliptically Birefringent Fibers

Analysis of the VMI Gain in Circularly Birefringent Fibers

Numerical Analysis of the Polarization Evolution in the VMI Sidebands

Experiment

Conclusion