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Optics Express

Quantitative study of birefringence effects in fiber-based orthogonal-pump FWM systems

Hao Liu, Kyle R. H. Bottrill, Valerio Vitali, Austin Taranta, Periklis Petropoulos

Published Jan 25, 2023• 6 citations
Publisher

Abstract

Optical fibers have unwanted residual birefringence due to imperfections in fabrication processes and environmental conditions. This birefringence will randomize the state of polarization of propagating signals and may harm the performance of four-wave mixing based processing devices. Here, we present a quantitative study of the effects of birefringence in orthogonal-pump four-wave mixing systems, and identify different regions of operation of the optical fiber, mainly determined by the relative magnitude between the physical length L and beat length L b . This finding clarifies the characteristics of the complex interplay between birefringence and four-wave mixing and advises appropriate fiber length selection for minimized polarization dependent gain.

DOI
10.1364/oe.480274

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Optical fibers have unwanted residual birefringence due to imperfections in fabrication processes and environmental conditions. This birefringence will randomize the state of polarization of propagating signals and may harm the performance of four-wave mixing based processing devices. Here, we present a quantitative study of the effects of birefringence in orthogonal-pump four-wave mixing systems, and identify different regions of operation of the optical fiber, mainly determined by the relative magnitude between the physical length L and beat length L b . This finding clarifies the characteristics of the complex interplay between birefringence and four-wave mixing and advises appropriate fiber length selection for minimized polarization dependent gain.
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.
We investigate the impact of fiber birefringence and spontaneous Raman scattering on the properties of photon pairs that are generated by the spontaneous four-wave mixing process in birefringent fibers. Starting from the formulation of the theory of four-wave mixing, we show a theoretical model for a generated optical field with the consideration of the Raman scattering and a Gaussian-distributed pump. The theoretical model is then applied for deriving the closed expressions of the photon-pair spectral properties as a function of the fiber birefringence. Also, with the modeled Raman gain, we evaluate the reduction of the pair production rate due to the presence of the Raman effect as well as the contributions of the Raman-scattered photons over a broad wavelength range. The predictions are experimentally verified with a commercial polarization-maintaining fiber.
Polarization analysis of vectorial four-wave mixing (FWM) in birefringent photonic-crystal fibers reveals physically significant tendencies in the behavior of FWM sideband correlations as a function of fiber birefringence, dispersion, and nonlinearity, as well as the pump intensity and bandwidth. Scanning over this parameter space is shown to steer vectorial FWM from largely decoupled sideband generation by individual polarization modes of the pump to FWM scenarios enabling multipartite entanglement generation.
We theoretically and experimentally study changes with pump power in the polarization of an optical signal as it simultaneously experiences Kerr-effect-induced birefringence and four-wave-mixing-based parametric amplification from a copropagating pump in an optical fiber. It is shown that the changes caused by the two nonlinear optical effects are orthogonal to each other in the Stokes space. Results also show that the pump polarization state works as an attractor for signal polarization. The implications of this feature to fiber parametric amplifiers and entangled-photon sources are discussed, and a fiber polarization switch is demonstrated.
Controlling four-wave mixing (FWM) is vital for several applications, including fiber optical communication, optical signal processing, optical amplification, and frequency generation. This paper presents a novel, to our knowledge, approach to control unidirectional FWM in elliptically birefringent fibers. By leveraging the frequency-dependent polarization eigenmodes of these fibers and detuning the optical frequency of one of the pump fields by a few megahertz, we can turn the FWM interaction on and off, thus controlling the generation of signal and idler fields. Moreover, this approach allows us to turn off the FWM interaction at any desired frequency, enabling all-optical switching and narrowband filtering applications.
The noise properties of propagation through optical fiber are of interest in optical communications. In recent years much attention has been focused on reducing the quantum fluctuations in one of two complementary field variables below the limit associated with coherent states. Nonlinear optical processes have played a key role in the realization of such behavior. We numerically investigate the noise properties associated with competing four-wave mixing (FWM) processes in optical fiber from a classical perspective. The nonlinear interaction of two pump waves at frequencies ω1 and ω2, which produce sidebands at 2ω2–ω1 and 2ω1–ω2 by multiple FWM, is considered. By introducing known classical fluctuations at the fiber input, one can trace the evolution of the noise in the different frequency components of the FWM spectrum by generating histograms at different fiber lengths and for different input pump powers and frequency separations. Classical behavior resembling squeezing is observed under appropriate conditions.