Multimode optical fiber Bragg gratings: modeling, simulation, and experiments
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Telecommunication networks based on optical fiber technology have become a major information-transmission system, satisfying the growing demand for bandwidth due to increased internet traffic and other applications such as video on demand, etc. Fiber Bragg gratings (FBGs), in recent years, have emerged as critical components for enabling high-capacity transmission since their response can be tailored to meet the needs of specific applications. FBGs are currently the focus of intense research interest in both the fiber communications and sensing fields. Optical fiber Bragg grating structures in single-mode fiber (SMFBGs) have been studied extensively since the discovery of photosensitivity in germanium-doped silica fiber. They have been used in numerous applications ranging from wavelength-selective filtering in wavelength-division-multiple-access (WDMA) systems to temperature and strain sensing. To a lesser extent, Bragg gratings in multimode fibers have also received attention because of easy coupling with light sources. Most of the MMFBGs related research work has demonstrated the formation of a Bragg grating in a graded-index MMF and briefly reported the measured transmission spectrum. So far, there are few theoretical studies on Bragg gratings in multimode fibers. In this thesis, we investigate Bragg gratings in multimode optical fibers both theoretically and experimentally. A comprehensive numerical model for MMFBGs has been established and the corresponding computer simulation software (MMFBG simulator combined with mode solver) developed. The optical properties of MMFBGs were systematically studied for the first time using our own MMFBG numerical software package. It effectively assists the design modeling for MMFBG-based optical devices. Bragg gratings in multimode fiber were also investigated experimentally. Our theoretical simulation results show good agreement with experiments and offer the insightful explanations for the underlying physics of the device. First, the guided modes were modeled and simulated for step index multimode fibers and graded index multimode fibers with emphasis on parabolic fiber structure. These are popular, standard and commercially available MM fibers, and employed throughout our experiments. This allows us for the simulation of fiber characteristics such as cut-off wavelength, mode effective index, propagation constants and optical field distribution. It also allows for calculation of mode coupling coefficients by overlap integral between any chosen guided modes. Therefore, it serves as a powerful model for the design and analysis of optical fibers. Second, the generalized MMFBG coupled mode theory formalism is derived. The physical mechanism of the behavior of MMFBGs is studied and discussed. The general solution to the MMF Bragg grating problem is achieved by Runge-Kutta, Newton-Raphson and shooting numerical methods. Our theoretical treatment, in particular, offers the advantages which can deal with not only self-coupling but also more complicated cross-coupling interactions and can solve arbitrary large number of mode coupling problems throughout the entire spectra simultaneously for multimode FBGs, thus allowing for a precise and quantitative study of MMFBGs. Such an intensive multimode fiber Bragg grating physical modeling and simulations have not been reported previously. It provides an effective means for the design and analysis of optical fiber devices based on Bragg gratings. Third, the optical properties of multimode FBGs were studies experimentally. Numerical predications of the grating spectral characteristics under fabrication and experimental condition are calculated. The results of the numerical calculations are compared with experimentally measured spectra of multimode gratings written by ultraviolet irradiation of deuterium-sensitized fiber with grating reflectivities ranging from 78% to 99.39%. Good agreement is obtained between the theoretical simulations and the experimental results. Thus, we provide quantitative explanations for the observed experimental phenomena. These explanations give both physical insight and a more complete understanding of the nature of the interaction between the wave propagation and multimode fiber gratings. Furthermore, the spectral simulation of the actual experiments prepares a theoretical guidance for the advanced experimental investigation and also presents a step toward MMFBG device design. Finally, the optical properties of MMFBGs were also studied theoretically. To our knowledge, this is the first detailed analysis and thorough investigation on grating characteristics in MMF. It is demonstrated that the transmission and reflection spectra of fiber Bragg gratings in multimode optical fibers strongly depend on the length of grating, index modulation, period of grating, mode excitation condition and physical structure of MMF. The simulation results allow us to deeply comprehend and visualize the more sophisticated behavior within a multimode fiber grating, and will also allow us to confidently predict and evaluate the performance of more complex structure MMFBGs. It provides the fundamental principles for designing the targeted spectrum performance and settles the theoretical rationale for realizing the practical applications. Overall, the comprehensive numerical model and MMFBG solver package developed in this thesis opens a clear and broad window for understanding MMFBG mechanisms from the physical point of view. Various simulation results and spectral characteristics have been researched and discussed under both ideal and experimental conditions for the purpose of experimental analysis and device design. The results of our study indicate that a new class of potential applications based on MMFBGs can be expected in optical fiber sensors and advanced communication systems.
