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Opto-Electronics Review

Experimental investigation of SRS polarization pulling in depleted pump regime for various pump SOPs

Robert K. Cybulski, Krzysztof Perlicki

Published Feb 18, 2024• 0 citations
Publisher

Abstract

This article presents an experimental investigation of polarization pulling based on stimulated Raman scattering induced by a continuous, fully polarized pump wave in an optical fibre. By means of probe wave states of polarization aggregation, degree of polarization and gain analysis, an assessment of all-optical polarization control, repolarization and amplification in a standard single mode fibre in depleted pump regime is presented. Polarization pulling is proved to be dependent on fibre length, pump power, and pump state of polarization, with respect to pump depletion effect, acting oppositely to the polarization pulling effect. Authors evaluate results aiming to obtain a configuration of stimulated Raman scattering parameters, which allows for the most effective polarization pulling, with respect to statistical stability of the process measured by standard deviation of polarization degree and polarization-dependent gain of the probe wave. The highest polarization attraction efficiency was obtained for 15 km, 0.97 W and the horizontal polarization state of the pump wave.

DOI
10.24425/opelre.2024.149381

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This article presents an experimental investigation of polarization pulling based on stimulated Raman scattering induced by a continuous, fully polarized pump wave in an optical fibre. By means of probe wave states of polarization aggregation, degree of polarization and gain analysis, an assessment of all-optical polarization control, repolarization and amplification in a standard single mode fibre in depleted pump regime is presented. Polarization pulling is proved to be dependent on fibre length, pump power, and pump state of polarization, with respect to pump depletion effect, acting oppositely to the polarization pulling effect. Authors evaluate results aiming to obtain a configuration of stimulated Raman scattering parameters, which allows for the most effective polarization pulling, with respect to statistical stability of the process measured by standard deviation of polarization degree and polarization-dependent gain of the probe wave. The highest polarization attraction efficiency was obtained for 15 km, 0.97 W and the horizontal polarization state of the pump wave.
The polarization-related properties of stimulated Brillouin scattering (SBS) processes in long, randomly birefringent, standard optical fibers are examined. Evolution equations for the pump and signal waves, in the presence of both birefringence and SBS, are provided in Jones and Stokes spaces. It is shown that in the undepleted pump regime, the amplification of the SBS signal wave is equivalent to that of a linear medium with polarization-dependent gain. The process is associated with a pair of orthogonal states of polarizations (SOPs) of the signal wave, which undergo maximum and minimum amplification. In long, standard fibers, the Jones vector of the probe SOP which corresponds to maximum amplification is aligned with the complex conjugate of the pump wave Jones vector. The maximum and minimum SBS gain coefficients in such fibers equal two-thirds and one-third of the gain coefficient that is predicted by scalar theory, respectively. The large differential gain of the SBS process gives rise to an effective pulling of the amplified Stokes probe wave SOP, towards that of maximum amplification. Lastly, Stokes wave pulses that are aligned for maximum and minimum amplification experience different group delays, which manifest as polarization-related distortions in SBS slow light setups.
The depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
The Raman effect is the inelastic scattering of photons by matter. When a monochromatic light beam (pump beam) propagates in an optical fibre, spon- taneous Raman scattering transfers some of the photons to new frequencies. The probability of a photon scattering to a particular frequency shift, depends on that frequency shift, forming a characteristic spectrum. The scattered photons may lose energy (Stokes) or gain energy (anti-Stokes). If the pump beam is linearly polarized, then the polarization of scattered photons may be the same (parallel scattering) or orthogonal (perpendicular scattering). If photons are already present at other frequencies then the probability of scattering to those frequencies is enhanced (stimulated scattering). In this thesis, the equations governing the Raman effect, both in bulk glass and single mode fibre, are restated. The probability of spontaneous scattering (parallel and perpendicular) in an optical fibre has been measured for frequency shifts between 4THz and 58THz. Particular attention has been given to those frequency shifts where the scattering is intrinsically weak. This has identified those frequency shifts where it might be possible to eliminate Raman noise from experiments designed to generate quantum states of light in optical fibres using four wave mixing. From the measured scattering probabilities, the Raman equations can be used to predict the scattering cross-section in bulk glass. The prediction is found to be in reasonable agreement with measurements of the bulk glass cross-section published by other authors. By increasing the pump power, the transition to stimulated scattering has been observed. In the case of Stokes scattering there is reasonable agreement between the Raman equations and experimental observations. In the case of anti-Stokes scattering, and in the limit of very high pump power, behaviour is observed which is not predicted by the Raman equations, indicating that other processes must be included to successfully describe such experiments.
In fiber optical parametric amplifiers (FOPAs), the output states of polarization (SOPs) of both the signal and the idler are affected by the pump SOP through the polarization pulling effect. We proposed a normalized model to characterize the general dynamics of polarization pulling in degenerated pump FOPAs. By using this model, we determined the relationship between the output degree of polarization (DOP) and the gain of the FOPAs over three orders of magnitude changes in polarization-mode dispersion (PMD) coefficient. We demonstrated numerically that when fibers with typical PMD coefficients are used, the output signals of the FOPAs can achieve higher DOP than those of co-propagating fiber Raman amplifiers, which depends on whether the parametric gain is sufficiently large to compensate the PMD-induced phase mismatch. We also found that for FOPAs using different types of fibers with moderate PMD coefficients, this DOP-gain relationship exhibits highly similar behaviors. We thus adopted a set of modified empirical formulas to analyze this relationship. This formula can also describe the relationship between the output DOP and the conversion efficiency of the idler. The results indicate that in all cases studied, FOPAs achieve much stronger polarization pulling to the idlers than the signals.
We proposed a theoretical model to investigate the polarization pulling effect in bi-directionally pumped degenerate Raman assisted fiber optical parameter amplifiers (RA-FOPAs) using randomly birefringent fibers. The contributions of chromatic dispersion, polarization mode dispersion (PMD), Raman gain, and nonlinear effects to the phase matching in RA-FOPAs are investigated. We characterize four different states of polarization pulling in RA-FOPAs. We found that broadband polarization attraction can be obtained in the optimum phase-matching state of the bi-directionally pumped RA-FOPAs when the parametric pump power is chosen to avoid deep saturation of the Raman gain.