We examine some of the optical properties of a metamaterial consisting of thin layers of alternating metal and dielectric. We can model this material as a homogeneous effective medium with anisotropic dielectric permittivity. When the components of this permittivity have different signs, the behavior of the system becomes very interesting: the normally evanescent parts of a P-polarized incident field are now transmitted, and there is a preferred direction of propagation.We show that a slab of this material can form an image with sub-wavelength details, at a position which depends on the frequency of light used. The quality of the image is affected by absorption and by the finite width of the layers; we go beyond the effective medium approximation to predict how thin the layers need to be in order to obtain subwavelength resolution.

We investigate the problem of designing metamaterial structures which operate at very low frequencies. As an example, we consider the case of a DC magnetic cloak, which requires a variable, anisotropic magnetic permeability with both paramagnetic and diamagnetic components. We show that a structure based on superconducting components is the key to diamagnetism at low frequencies, and present a metamaterial design which meets the requirements of the cloak.

Electromagnetic metamaterials 1 are a class of materials which have been artificially structured on a subwavelength scale. They are currently the focus of a great deal of interest because they allow access to previously unrealisable properties like a negative refractive index 2 . Most metamaterial designs have so far been based on resonant elements, like split rings 3 , and research has concentrated on microwave frequencies and above. In this work, we present the first experimental realisation of a non-resonant metamaterial designed to operate at zero frequency. Our samples are based on a recently-proposed template 4 for an anisotropic magnetic metamaterial consisting of an array of superconducting plates. Magnetometry experiments show a strong, adjustable diamagnetic response when a field is applied perpendicular to the plates. We have calculated the corresponding effective permeability, which agrees well with theoretical predictions. Applications for this metamaterial may include non-intrusive screening of weak DC magnetic fields. The first metamaterials 3,5 were designed to operate at microwave frequencies. Since then, while there has been some research on radio-frequency metamaterials 6 , most of the research effort has been focused on higher frequencies: technologically-important microwaves or visible light 7 . The low-frequency end of the spectrum has remained relatively unexplored. In addition, the majority of metamaterials devised to date consist of an arrangement of resonant components. There is a good reason for this: the response of a resonator varies greatly as a function of the frequency at which it is being driven. Close to the resonant frequency, the amplitude of the response can be very large, while the phase changes. The range of available values of the response function, or susceptibility, is therefore very wide. One of the crowning achievements of (and driving forces behind) metamaterials research is the realization of a negative refractive index 2,8 , and a simple argument shows that this cannot be achieved without relying on resonant structures. However, the price of working close to the resonant frequency is that losses and frequency dispersion are greatest here. When a negative response is not required then a non-resonant structure is advantageous. Another recent development means that there is new demand for metamaterials with nonnegative anisotropic parameters. Transformation optics 9 is a design paradigm that allows a new level of control over electromagnetic fields. For a given design, it provides a recipe for the material parameters as a function of position. The parameters generated in this way are always non-negative and anisotropic. A spectacular demonstration of the technique was provided by the construction of an electromagnetic cloak 10 using metamaterials. The interior of the cloak is shielded from microwaves with minimal disruption to the exterior fields.

We present quantum Monte Carlo calculations of the surface energy of the electron gas ͑jellium͒. Our results agree with the best estimates obtained by other methods, thus appearing to resolve the controversy which currently exists and paving the way for future simulations of real surface systems.

The model periodic Coulomb interaction (Williamson et al 1997 Phys. Rev. B 55 R4851) is a replacement for the Ewald sum, developed to reduce finitesize errors in the simulation of extended 3D systems. We investigate the generalization of this technique to quasi-2D systems; we show through testing in quantum Monte Carlo simulations that while the new interaction reduces the calculation time dramatically it does not reduce finite-size errors. We explain this by analysing the finite-size errors generated when using the Ewald sum.