Numerical Modeling for the Propagation Characteristics of Optical Fibers with Arbitrary Index Profiles

• Main Authors: Chih-cheng Chou, 周志城
• Other Authors: Nai-hsiang Sun
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/23399831048287207681

博士 === 義守大學 === 電機工程學系博士班 === 97 === In this dissertation, we present a direct and rigorous numerical method to analyze guided modes and leaky modes in circularly symmetric fibers with arbitrary multilayer refractive index profile. Both the modified Bessel function and the Hankel function of the second kind are individually used to express the field component of leaky modes in the outermost cladding. The characteristic equation of fiber structures, which consist of graded and uniform layers, is derived by combining the Runge-Kutta method and the exact solution of a homogeneous layer. Moreover, because for both guided and leaky modes the field distributions in the outermost cladding region have the same expression, the leaky mode can be easily obtained by choosing an improper solution, and therefore the calculation of leaky modes demonstrates the simplicity of this method. An approximation rule of branch choices for lossy material is also derived. Since the complex root searching is the key technique for evaluating the leaky modes, we also present a numerical algorithm for solving the characteristic equation of optical fibers. The procedure does not make any approximation and assumption. We applied the present method to accurately evaluate the dispersion and leaky-mode losses of optical fibers with an arbitrary refractive index profile. The results are in good agreement with the results of previously published papers. Moreover, we applied this numerical method to analyze an acoustics-induced fiber Bragg grating reflectors, which is a tapered step-index fiber prewritten Bragg grating together with an applied flexural wave (microbending) in the tapered region. The phase matching between a core mode and cladding modes is analyzed by using our development method. With these coupling mechanisms, the previously reported reflection wavelength switching could be well interpreted. Based on the phase-matching calculations, the relationship between cladding radius and flexural wave period with a chosen wavelength for reflection switching will be provided.