Impact of modulation instability on distributed optical fiber sensors

Modulation instability (MI) as the main limit to the sensing distance of distributed fiber sensors is thoroughly investigated in this thesis in order to obtain a model for predicting its characteristics and alleviating its effects. Starting from Maxwell's equations in optical fibers, the nonlinear Schrödinger equation (NLSE) describing the propagation of wave envelope in nonlinear dispersive media is derived. As the main tool for analyzing modulation instability, the NLSE is numerically evaluated using the split-step Fourier method and its analytical closed-form solutions such as solitons are utilized to validate the numerical algorithms. As the direct consequence of the NLSE, self-phase modulation is utilized to measure the nonlinear coefficient of optical fibers via a self-aligned interferometer. The modulation instability gain is obtained by applying a linear stability analysis to the NLSE assuming a white background noise as the seeding for the nonlinear interaction. The MI gain spectrum is expressed by hyperbolic functions for lossless fibers and by Bessel functions with complex orders for fibers with attenuation. An approximate gain spectrum is presented for lossy fibers based on the gain in lossless optical fibers. The accuracy of the analytical results and approximate formulas is evaluated by performing Monte Carlo simulations on the NLSE. The impact of background noise on the onset and evolution of modulation instability is analytically investigated and experimentally demonstrated. Power depletion due to the nonlinear process of modulation instability is modeled by integrating its gain spectrum using Laplace's method. Based on that, a critical power for MI is proposed by introducing the notion of depletion ratio. The model is verified by numerical simulation and experimental measurement. An optimal input power for distributed fiber sensors is proposed to maximize the output optical power and thus, the far end signal-to-noise ratio. Furthermore, the recurrence phenomenon of Fermi-Pasta-Ulam is experimentally observed and numerically simulated, validating the utilized numerical techniques. A standard Brillouin optical time-domain analyser serves as the experimental test bench for the proposed model. As the physical phenomenon behind the experiment, stimulated Brillouin scattering is described based on a pump-probe interaction mechanism through an acoustic wave. A 25 km single-mode fiber is employed as a nonlinear medium with anomalous dispersion at the pump wavelength 1550 nm. The evolution of pump power propagating along the fiber is mapped using the Brillouin interaction with the probe lightwave. The measured longitudinal power traces are processed to extract the impact of MI on the pump power. It is experimentally demonstrated that distributed fiber sensors with orthogonally-polarized pumps suffer less from modulation instability. As the scalar modulation instability of each pump reduces, vector modulation instability occurs because of interaction between the pumps; however, the overall performance improves. A version of the coupled nonlinear Schrödinger equations known as the Manakov system is shown to describe the behavior of two-pump distributed fiber sensors employing optical fibers with random birefringence. The excellent agreement between the experimental and numerical results indicates that the performance limit of two-pump distributed fiber sensors is determined by polarization modulation instability.

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