A modal approach for analysing optical systems with applications to solar light trapping and digital removal of GRIN lens aberrations [electronic resource]
Keywords: Electrical Engineering.

This thesis is based on applying a mode approach in optical problems that usually were not solved with that in mind or used it implicitly. It is well known that for a very large number of applications in optics, the equations can be considered to be linear, either with respect to a scalar field, vector field or the intensity. The beauty of thinking of problems in terms of modes is that they are an obvious way to bridge ones thinking between designing for optical applications and considering information transfer in a channel. Whether it is sunlight that needs to be channeled into a solar cell's active region, a heating element in solar thermal or the spatial information of the field channeled through a microscope onto a pixel-based camera thinking in terms of the modes of the system can be very useful. The purpose of this thesis is to show and present 2 applications where this framework is exploited, one in solar power and one in microscopy imaging. In chapter two the solar light trapping application is discussed by first introducing some solar cell basics and also highlighting the difference between thick and thin film solar cells with regards to coherence effects as thin films require a full wave solution while thick films require a geometric optics solution. Additionally, the light trapping limit as presented by Cambell is shown and a derivation for the maximum concentration achievable is discussed. Finally, a concentrator design is proposed to achieve light trapping and an optimisation is carried out with an amorphous silicon and a CIGS solar cell. The third chapter discusses imaging and electromagnetic field propagation in terms of modes. As an example free space is used and the angular spectrum method is derived. Using this modal approach it is shown how one can digitally refocus out of focus intensity measurements when the field is coherent. Two ways of achieving this are suggested. In the first the phase of the field at the measurement planes is retrieved and then the field is back propagated at the plane of interest and in the second the field is retrieved at the plane of interest directly. In the fourth chapter Graded Index (GRIN) Rods are discussed, presenting their imaging properties as well as where the theory fails. Fletcher first proposed a refractive index profile that would relay an image perfectly in the ray optics approximation and Yariv derived the modes for a similar profile. The two are presented and compared and using the modes of the GRIN rod a simulation is done showing how the field can be recovered as well as how this is superior to trying to recover the phase and then propagate the field at the plane of interest. Additionally, it is shown that with a large field of view a lot of information is not available in the recovery because of the poor mapping from the GRIN modes to the pixel basis of the image sensor. With a smaller field of view the image is recovered in its entirety. Finally, a simple experiment is set up and the field retrieval algorithm is applied. The field is improved, however, some distortions still remain and are discussed.