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

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

Order N photonic band structures for metals and other dispersive materials

We show, for the first time, how to calculate photonic band structures for metals and other dispersive systems using an efficient Order N scheme. The method is applied to two simple periodic metallic systems where it gives results in close agreement with calculations made with other techniques. Further, the approach demonstrates excellent numerical stablity within the limits we give. Our new method opens the way for efficient calculations on complex structures containing a whole new class of material.Comment: Four pages, plus seven postscript figures. Submitted to Physical Review Letter