My PhD research was carried out at the Centre for Photonics and Photonic Materials, part of the Department of Physics of the University of Bath, under the supervision of Prof. David Bird. My subsequent postdoctoral research was carried out in Division 3 of the Max Planck research group (now known as the Max Planck Institute for the Science of Light) at the Friedrich-Alexander-University of Erlangen-Nuremberg in Erlangen, Germany. This research involved investigation of the electromagnetic modes in photonic crystal fibres (PCF) by theoretical and computational methods. In particular I worked on the development and application of plane-wave methods for solution of Maxwell's equations.
There follows a copy of the abstract of my PhD thesis and a list of publications resulting from my PhD and other research.
(From G.J. Pearce, Plane-wave methods for modelling photonic crystal fibre, unpublished PhD thesis, University of Bath, 2006.)
The work described in this thesis aims to develop and apply the fixed-frequency plane-wave method as a means of solving Maxwell's equations in photonic crystal fibre (PCF). It is first shown, by applying the method to a simple one-dimensional periodic dielectric structure, that the convergence of the method is dependent on the frequency of discrete sampling at the sharp interfaces present in the structure. This motivates the reformulation of the plane-wave method in generalised curvilinear coordinates, which provides the ability to achieve position-dependent sampling frequencies and hence enhance the convergence of the method. The improved convergence behaviour of the plane-wave method in generalised curvilinear coordinates is demonstrated by its application to realistic PCF structures.
The fixed-frequency plane-wave method is also applied to PCF structures that comprise materials with a large refractive index contrast. The difficulties associated with modelling such structures are discussed, including in particular the slow convergence of the linear solver used in eigenmode determination. An improved method of preconditioning based on an exact inverse of the linear problem corresponding to a smoothed structure is described. The fixed-frequency plane-wave method is then used to determine an appropriate hollow-core fibre structure for the guidance of light in the mid- to far-infrared wavelength region.
Finally the application of the fixed-frequency plane-wave method to fibre structures with a low index contrast is discussed, and a fibre is modelled that has been fabricated experimentally. A method to estimate the susceptibility of a fibre to bend loss is developed, and comparisons are drawn between the theoretical estimates and experimental results. The method also correctly reproduces the experimental finding that air-silica PCFs are much less susceptible to bend loss than low contrast fibres.
The conclusions drawn from this work, together with possible directions for future work, are summarised in the final chapter.
I have an Erdős number of not more than 6 (via P.J. Roberts, A. MacKinnon, H. Englisch, B. Simon, V. Totik, P. Erdős).