Hart, Elizabeth E.
Algorithms and technologies for photonic crystal modelling.
University of Southampton, School of Engineering Sciences,
In this thesis an investigation into the behaviour of light when passing through photonic
crystals was carried out using numerical methods. Photonic crystals are expensive and
difficult to fabricate so there is a requirement for computer simulations that can quickly
and accurately model how the crystal structure will affect the behaviour of light. A finite
difference method was written to model two-dimensional photonic crystals. The results
from the finite difference method modelling agreed with known results for standard
photonic crystal structures created by the plane wave expansion method. Once validated
the finite difference method was used in a genetic algorithm optimisation. It found that
novel shaped rods can increase the size of photonic band gaps when compared with
A new meshless method algorithm was developed to solve Maxwell's equations. Simulations
were carried out using an equation with known analytical solutions; how the accuracy
of the results was affected by different designs of experiment and different radial
basis functions was recorded. The meshless method was developed further to model photonic
crystals. The meshless method requires the creation of large dense matrices and
then forms a generalised eigenvalue problem. A new set of algorithms were developed
that can model photonic crystals accurately. Exploration of alternative technologies
was carried out to try to obtain a speed up in the modelling process. A graphics processing
unit was used to do general purpose computation. Graphics processing units
generally show signifcant speed up when compared to central processing unit for filling
the matrices required for the meshless method. For accelerating numerical methods a
heterogenous approach is preferable to a strict graphics processing unit implementation.
Nature has evolved complex nanostructures that provide very specific and often very
special optical effects, at present these are not well understood and cannot be replicated.
In this thesis a new meshless method has been developed which will enable the
development of complex crystal geometries.
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