Modelling and optimization of photonic crystal fibres

Abstract

Photonic Crystal Fibres (PCFs) have attracted much attention due to their unusual optical properties, such as extra-large chromatic dispersion, small or large mode field area, wide range single mode operations, etc. The objective of this research is to develop an accurate and efficient modelling tool for automated optimal design of PCFs. In this thesis, we have studied both electromagnetic (EM) modelling and optimization methodologies. For EM modelling of PCFs, the space filling mode (SFM)effective index (EI) method and the finite element method (FEM) are formulated, implemented, and tested. The SFM-EI is a semi-analytical method and it is efficient, but it can only treat repeated lattice structures. The FEM is a full vectorial numerical tool which can handle complicated geometries. Generally speaking, FEM is accurate, flexible and quite efficient, however, it is still very time-consuming when used for optimal design where hundreds or thousands of individual solutions are needed. For optimization, genetic algorithms (GA) and particle swarm optimization (PSO) are studied, implemented, tested and compared. Both G A sand PSO are population based stochastic optimization techniques. G A s mimic the concept of biological genetics and natural evolution while PSO is inspired by social behavior and bird flocking or fish schooling. Either the SFM-EI or the FEM can be selected as the EM solver to be combined with an optimization engine which could be either the GA or the PSO. The EM solvers and optimization engines are validate with examples. A comprehensive example of dispersion control for a PCF design presented shows the full optimal design processing.