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|
|Supervisor||David Bird (Supervisor)|