Optical Limits in Left-Handed Media

This thesis determines the response of Left-Handed Media (LHM) to surface effects. A LHM half-space with a roughened interface, modelled by a graded index boundary, is shown to give rise to an analytical solution for the propagation of electromagnetic radiation through this inhomogeneous layer. Significant field localization is generated within the layer, caused by the coherent superposition of evanescent waves. The localization is shown to greatly deteriorate transmission when losses are present. The addition of a second interface to the LHM, creating a perfect lens configuration, allows for the exploration of evanescent mode propagation through a perfect lens with roughened boundaries. The effects of the field localisations at the boundaries serves to diminish the resolving capability of the lens. Specifically the layers produce an effect that is qualitatively similar to nonlinearly enhanced dissipation. Ray-optics is used to analyse negative refraction through a roughened interface, prescribed by Gaussian statistics. This shows that rays can focus at smaller distances from the interface due to the negative refractive effects. Moreover, a new reflection mechanism is shown to exist for LHM. Consequently an impedance matched configuration involving LHM (such as the perfect lens) with a roughened interface can still display reflection. A physical-optics approach is used to determine the mean intensity and fluctuations of a wave passing into a half-space of LHM through a roughened interface in two ways. Firstly through the perturbation analysis of Rice theory which shows that the scattered field evolves from a real Gaussian process near the surface into a complex Gaussian process as distance into the second media increases. Secondly through large-scale Monte-Carlo simulations that show that illuminating a roughened interface between air and a LHM produces a regime for enhanced focussing of light close to the boundary, generating caustics that are brighter, fluctuate more, and cause Gaussian speckle at distances closer to the interface than in right-handed matter.