Optical waveguide analysis using transmission lines
Optical fibres have been used as a key medium for telecommunication and networking for more than two decades because in principle they offer sufficient transmission capacity, reaching total rates as high as Tbits/s per fibre. Critical fibre properties such as mode field profiles, single-mode propagation conditions and dispersion characteristics can all be related to the optical fibre refractive index profiles. For this reason, it is of fundamental importance to be able to determine the optical fibre refractive index profiles. In this thesis, a novel Transmission-Line technique has been studied and extended for both the forward and inverse solutions. In the forward solution of the Transmission-Line technique, it is shown that the technique is not only capable of determining exactly the propagation constants in optical fibres with real refractive index profiles, but also evaluating accurately the complex propagation constants in single-mode fibres with arbitrary complex refractive index profiles. To illustrate the effectiveness of this technique, it is applied to the evaluation and manipulation of the gain in a typical 980 nm pumped Erbium-Doped fibre as well as to the calculation of the attenuation of optical fibres when radial loss factors are presented. Moreover, based on the Transmission-Line equivalent circuit model, the exact analytical formulas are derived for a recursive algorithm which allows direct and efficient calculation of dispersion of arbitrary refractive index profile optical fibres. The proposed algorithm computes dispersion directly from the propagation constants without the need for curve fitting and successive subsequent numerical differentiation. The algorithm results in savings for both storage memory and computation time. In the inverse solution using the Transmission-Line technique, the optical fibre refractive index profile synthesis from the given mode electric field distribution is developed and demonstrated. The application of the Transmission-Line principles in the study of optical fibre properties was developed for the first time in the early 80's. However, until now the potential of using Transmission-Line technique for the design of optical fibres based on the given electric field pattern had not been examined. From Maxwell's equations, the Transmission-Line equivalent circuits are derived for a homogeneous symmetric optical fibre. This work demonstrates how to use the Transmission-Line model to reconstruct the exact refractive index profile from the electric field data. The accuracy of the reconstructed optical fibre refractive index profile is examined numerically.