Four-wave mixing in fibers with random birefringence

Abstract

Parametric amplification is made possible by four-wave mixing. In low-birefringence fibers the birefringence axes and strength vary randomly with distance. Light-wave propagation in such fibers is governed by the Manakov equation. In this paper the Manakov equation is used to study degenerate and nondegenerate four-wave mixing. The effects of linear and nonlinear wavenumber mismatches, and nonlinear polarization rotation, are included in the analysis. Formulas are derived for the initial quadratic growth of the idler power, and the subsequent exponential growth of the signal and idler powers (which continues until pump depletion occurs). These formulas are valid for arbitrary pump and signal polarizations.

Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime

“…Intra-channel dispersion was also neglected which is a reasonable assumption for a recent experiment [34,38] and a wide variety of related experiments. The case with different polarizations is considered in [35,[39][40][41]. The effect of spontaneous Raman scattering (SRS) is not modeled by Eqs.…”

“…Also it allows for a very broad bandwidth of conversion as well as coupling from the visible to the telecom band and inter-telcom band conversion [26]. The quantum-noise properties of parametric amplification were considered in [35,36] and it has theoretically been shown that BS allows for noiseless QFC [26]. BS has also been shown theoretically to allow HOMinterference between photons of different colors [37,38].…”

Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability [Invited]

“…For example, it has been theoretically predicted that FWM in a highly birefringent optical fiber in the presence of a dual-polarization pump wave may lead to polarization attraction for the Stokes and antiStokes waves both in the normal and in the anomalous dispersion regime [68]. The impact of random birefringence on vector FWM processes in optical fibers was studied by Lin and Agrawal [69,70] and McKinstrie et al [71]. In the anomalous dispersion regime, parametric amplification or induced modulation instability in a low-PMD fiber operating in the Manakov limit leads to polarization attraction of both the signal and the generated idler toward the same SOP of the pump [72].…”

Full and semi-analytic analyses of two-pump parametric amplification with pump depletion

“…It is assumed that the input fields are parallel polarized, but in the case of perpendicular pumps and sidebands, the factor of 2 in the coupling term should be changed to a 1 [16,17].…”