Near Field Lenses in Two Dimensions

It has been shown that a slab of materials with refractive index = -1 behaves like a perfect lens focussing all light to an exact electromagnetic copy of an object. The original lens is limited to producing images the same size as the object, but here we generalise the concept so that images can be magnified. For two dimensional systems, over distances much shorter than the free space wavelength, we apply conformal transformations to the original parallel sided slab generating a variety of new lenses. Although the new lenses are not `perfect' they are able to magnify two dimensional objects. The results apply equally to imaging of electric or magnetic sub wavelength objects in two dimensions. The concepts have potential applications ranging from microwave frequencies to the visible.Comment: PDF fil

Analysis of selected medicinal plants as antioxidants with therapeutic potential for treating diseases related to free radical damage

Oxidative damage is implicated in the pathogenesis of a number of diseases. Scientific research shows positive links between accumulated free radical damage and age-related diseases such as atherosclerosis and osteoarthritis. There is great interest in the possibility that the antioxidant potential of plant-derived compounds such as flavonoids may reduce the risk of developing these conditions. The aim of this study was to evaluate the antioxidant activity of selected non-food plants, traditionally used by herbalists in their treatment of osteoarthritis, using crude plant extracts and herbal tinctures, the most commonly used form of plant extract. As herbalists traditionally argue that herbs used in combinations or formulae will increase in efficacy when used together, an exploratory study was further carried out to investigate whether the antioxidant activity of two herbs tested in combination was greater than the sum of both herbs tested singly. Eight plants were selected for phytochemical analysis and investigation for antioxidant activity, based on discussions with clinic supervisors from four herbal medicine training clinics and a review of patient's case notes. The prescriptions from a pilot study investigating outcomes for the herbal treatment of osteoarthritis were used as selection criteria. Chromatographic analysis of each plant by TLC, HPLC and GCMS confirmed the presence of a number of flavonoids reported in the literature and of other compounds which were not possible to identify. Previous studies have established that certain flavonoids in vitro can exert pro-oxidant or antioxidant effects according to the concentration and presence of transition metal ions such as copper and iron. In view of the pro-oxidant effects observed for some extracts during biochemical analysis, metal analysis by ICP was carried out on the selected plant material to test for the presence of selected metal ions known to catalyse free radical reactions. ICP analysis showed the presence of most of the selected metals in all the plant samples. Several pathways, by which flavonoids and other plant phenolics may exert their effects on chemical oxidation have been identified, one of which is their free radical scavenging capacity to halt the propagation stage of lipid peroxidation. Since lipid peroxidation is implicated in the pathogenesis of osteoarthritis, assays to measure this in vitro were investigated and the following two assays selected: - lipid peroxide assay using the ferric thiocyanate method for the detection of peroxides and an assay using the stable free radical 1,1-diphenyl-2-picrylhydrazyl (DPPH) an established method for investigating the potential free radical scavenging activity of plant extracts. The lipid peroxide assay and method of analysis was re-evaluated and a standardised procedure established. All eight crude plant extracts showed marked antioxidant activity in both assays. Results for the crude plant extract in the lipid peroxide assay varied according to concentration, with 0.1% w/v giving the best results. The crude plant extracts in almost all cases seemed to be more active as antioxidants than tinctures (fluid extracts). When combinations of crude plant extracts were tested in pairs for antioxidant activity, results demonstrated synergy from five of the pairs and antagonism from three, approximately one third of the possible 28 two-herb combinations tested. The synergistic interactions observed could form the foundation for the future development of an antioxidant formula to offset the effects of free radical damage

The Theory of SNOM: A Novel Approach

In this paper we consider the application of electromagnetic theory to the analysis of the Scanning Near-field Optical Microscope (SNOM) in order to predict experimentally observable quantities such as the transmission or reflection coefficients for a particular tip-surface configuration. In particular we present the first application of a transfer matrix based calculation to this challenging problem by using an adaptive co-ordinate transformation to accurately model the shape of the SNOM tip. We also investigate the possibility of increasing the transmitted light through the SNOM tip by introducing a metal wire into the centre of the tip. This converts the tip into a co-axial cable. We show that, in principle, this can dramatically improve the transmission characteristics without having a detrimental effect on the resolution.Comment: 19 pages, 11 figures. To be published in the Journal of Modern Optic

Focussing Light Using Negative Refraction

A slab of negatively refracting material, thickness d, can focus an image at a distance 2d from the object. The negative slab cancels an equal thickness of positive space. This result is a special case of a much wider class of focussing: any medium can be optically cancelled by an equal thickness of material constructed to be an inverted mirror image of the medium, with, $\epsilon$ and $\mu$ reversed in sign. We introduce the powerful technique of coordinate transformation, mapping a known system into an equivalent system, to extend the result to a much wider class of structures including cylinders, spheres, and intersecting planes and hence show how to produce magnified images. All the images are perfect in the sense that both the near and far fields are brought to a focus and hence reveal sub wavelength details.Comment: pdf file onl

Imaging the Near Field

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multi-layer stack of positive and negative refractive media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near-field. The deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures

Calculating photonic Green's functions using a non-orthogonal finite difference time domain method

In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain (FDTD) method, originally proposed by Yee, also known as the Order-N method, which has recently become a popular way of calculating photonic band structures. We give a new, transparent derivation of the Order-N method which, in turn, enables us to give a simple yet rigorous derivation of the criterion for numerical stability as well as statements of charge and energy conservation which are exact even on the discrete lattice. We implement this using a general, non-orthogonal co-ordinate system without incurring the computational overheads normally associated with non-orthogonal FDTD. We present results for local densities of states calculated using this method for a number of systems. Firstly, we consider a simple one dimensional dielectric multilayer, identifying the suppression in the state density caused by the photonic band gap and then observing the effect of introducing a defect layer into the periodic structure. Secondly, we tackle a more realistic example by treating a defect in a crystal of dielectric spheres on a diamond lattice. This could have application to the design of super-efficient laser devices utilising defects in photonic crystals as laser cavities.Comment: RevTex file. 10 pages with 8 postscript figures. Submitted to Phys Rev

Calculation of material properties and ray tracing in transformation media

Complex and interesting electromagnetic behavior can be found in spaces with non-flat topology. When considering the properties of an electromagnetic medium under an arbitrary coordinate transformation an alternative interpretation presents itself. The transformed material property tensors may be interpreted as a different set of material properties in a flat, Cartesian space. We describe the calculation of these material properties for coordinate transformations that describe spaces with spherical or cylindrical holes in them. The resulting material properties can then implement invisibility cloaks in flat space. We also describe a method for performing geometric ray tracing in these materials which are both inhomogeneous and anisotropic in their electric permittivity and magnetic permeability