Boundary Conditions and Fresnel Equations for Weakly Spatially Dispersive Media

Abstract

Although usually negligible for natural materials for optical and lower frequencies, spatial dispersion is a significant effect for metamaterials. In this thesis the electromagnetics of such media are investigated using a second order in k approximation for the polarisation and assuming centro-symmetric inclusions. Boundary conditions derived by Lange and Raab to electric-octopole - magnetic quadrupole order are taken a step further by also accounting for multipole surface effects. Yaghjian and Silveirinha s boundary conditions and Fresnel equations are taken a step further by also accounting for dipolarisations for a medium with a non-zero electric quadrupolarisation. Lastly, two attempts at modelling interface behaviour for a general second order spatially dispersive medium are made. For one of the attempts, Fresnel equations are obtained.