Algorithms and technologies for photonic crystal modelling

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 cylindrical rods. 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.