Harnessing spatial dispersion in wire media to control the shape of electromagnetic fields

Boyd, Taylor and Gratus, Jonathan and Letizia, Rosa (2020) Harnessing spatial dispersion in wire media to control the shape of electromagnetic fields. PhD thesis, Lancaster University.

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Abstract

We have detailed the development of our method for field profile shaping of longitudinal electric fields by exploiting the spatial dispersion of wire media. The development of this method involved a theoretical analysis of the problem where we derived the required variation in the electromagnetic properties of a medium that can be described by a 1D spatially dispersive model. Integrating this with information on how the wire radius affects the electromagnetic properties of our structures, taken from numerical simulations, we were able to develop our field profiling method. This method allows us to generate a function for the radius variation of our wires that should produce the desired profile. These profiles come from the solutions of Mathieu's equation. We have validated our method for a variety of realisations of wire media, comprising metal and dielectric wires, in eigenmode simulations, with work also undertaken in the time domain.