Modelling of photonic crystal fibres

Abstract

The work in this thesis is to understand, through theory and simulation, a guidance mechanism due to the weak interaction of modes in photonic crystal fibres (PCFs). Firstly, two common kinds of PCFs, that guide light by total internal reflection and by photonic bandgaps, are reviewed. Several typical PCF structures for which light propagation is governed by weak mode interaction are then discussed and particularly compared with bandgap-guiding PCFs. Two independent methods are developed to model a set of related rectangular hollow-core PCF structures. The boundary element method is derived for a general PCF configuration and applied to our model structures. This method numerically provides some basic features about the guided modes, such as the propagation constant and field profile. The calculations show an ideal confinement in our model structure by considering a scalar wave equation and a high dielectric constant at the glass intersections. However, in realistic guidance, both confinement loss and the field of the guided modes indicate a raised leakage due to mode interactions. The analytic methodology starts by solving the ideal case considered in boundary element calculations and leads to analytic solutions for the perfectly guided modes. A perturbation method corresponding to the realistic guidance is then applied to these analytic solutions. This method can provide insight into understanding the formation of leakage through an analysis of mode interactions. An approximate analytic method for obtaining the attenuation of guided modes from the perturbation interaction is demonstrated. Attenuations calculated in this way give good agreement with boundary element results in magnitude and trends in variation. The influences of frequency and fibre parameters on features of the attenuation are also investigated. An overall interpretation of this guidance mechanism and suggestions for fibre optimisation are made in the final chapter, where further development of this work is also proposed.

Date of Award	1 Oct 2009
Original language	English
Awarding Institution	University of Bath
Supervisor	David Bird (Supervisor)