Focus on Perfect Imaging

We calculate the frequency spectra of absolute optical instruments using the Wentzel–Kramers–Brillouin (WKB) approximation. The resulting eigenfrequencies approximate the actual values very accurately; in some cases they even give the exact values. Our calculations confirm the results obtained previously by a completely different method. In particular, the eigenfrequencies of absolute instruments form tight groups that are almost equidistantly spaced. We demonstrate our method and its results applied to several examples.

We analyse frequency spectra of absolute optical instruments and show that they have very specific properties: the eigenfrequencies form tight groups that are almost equidistantly spaced. We prove this by theoretical analysis and demonstrate by numerically calculated spectra of various examples of absolute instruments. We also show that in rotationally and spherically symmetric absolute instruments a source, its image and the centre of the device must lie on a straight line.

We numerically study the focusing and bending effects of light and sound waves through heterogeneous isotropic cylindrical and spherical devices. We first point out that transformation optics and acoustics show that the control of light requires spatially varying anisotropic permittivity and permeability, while the control of sound is achieved via spatially anisotropic density and isotropic compressibility. Moreover, homogenization theory applied to electromagnetic and acoustic periodic structures leads to such artificial (although not spatially varying) anisotropic permittivity, permeability and density. We stress that homogenization is thus a natural mathematical tool for the design of structured metamaterials. To illustrate the two-step geometric transform-homogenization approach, we consider the design of cylindrical and spherical electromagnetic and acoustic lenses displaying some artificial anisotropy along their optical axis (direction of periodicity of the structural elements). Applications are sought in the design of Eaton and Luneburg lenses bending light at angles ranging from 90° to 360°, or mimicking a Schwartzchild metric, i.e. a black hole. All of these spherical metamaterials are characterized by a refractive index varying inversely with the radius which is approximated by concentric layers of homogeneous material. We finally propose some structured cylindrical metamaterials consisting of infinitely conducting or rigid toroidal channels in a homogeneous bulk material focusing light or sound waves. The functionality of these metamaterials is demonstrated via full-wave three-dimensional computations using nodal elements in the context of acoustics, and finite edge-elements in electromagnetics.

It is theoretically known that a pair of phase-conjugating surfaces can function as a perfect lens, focusing propagating waves and enhancing evanescent waves. However, the known experimental approaches based on thin sheets of nonlinear materials cannot fully realize the required phase conjugation boundary condition. In this paper, we show that the ideal phase-conjugating surface is, in principle, physically realizable and investigate the necessary properties of nonlinear and nonreciprocal particles which can be used to build a perfect lens system. The physical principle of the lens operation is discussed in detail and directions of possible experimental realizations are outlined.

Perfect imaging with Maxwell's fish eye opens the exciting prospect of passive imaging systems with a resolution no longer limited by the wave nature of light. But it also challenges some of the accepted wisdom of super-resolution imaging and therefore has been subject to controversy and discussion. Here we describe an idea for even simpler perfect-imaging systems based on geometrical optics and prove by experiment that it works.

Leonhardt (2009 New J. Phys. 11 093040) demonstrated that the two-dimensional (2D) Maxwell fish eye (MFE) lens can focus perfectly 2D Helmholtz waves of arbitrary frequency; that is, it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a 'perfect point drain' located at the corresponding image point. Moreover, a prototype with λ/5 super-resolution property for one microwave frequency has been manufactured and tested (Ma et al 2010 arXiv:1007.2530v1; Ma et al 2010 New J. Phys. 13 033016). However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here, we present steady-state simulations with a non-perfect drain for a device equivalent to the MFE, called the spherical geodesic waveguide (SGW), which predicts up to λ/500 super-resolution close to discrete frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.

Recent work suggesting that 'perfect' far-field imaging is possible using Maxwell's fish-eye lens (Leonhardt 2009 New J. Phys. 11 093040) has raised a number of questions and controversies about the nature of imaging and field localization in inhomogeneous media. In this brief paper we present analogous results for a purely reflector-based imaging system—an elliptical cavity. With a source at one focus of the ellipse we show that sub-wavelength field localization can be achieved at the other focus when an active 'drain' is present there, but not without it. Does this show that far-field 'perfect' imaging is possible even without refraction (negative or positive)? Unfortunately not, giving further evidence that these are solely drain-induced effects.

In this paper, we present a method for the evaluation of the signal-to-noise ratio in magnetic resonance imaging (MRI) coils loaded with resonant ring metamaterial lenses, in the presence of a conducting phantom resembling human tissue. The method accounts for the effects of the discrete and finite structure of the metamaterial. Numerical computations are validated with experimental results, including laboratory measurements and MRI experiments.

We investigate the optical properties of periodic composites containing metamaterial inclusions in a normal material matrix. We consider the case when these inclusions have sharp corners and, following Hetherington and Thorpe, use analytic results to argue that it is then possible to deduce the shape of the corner (its included angle) by measurements of the absorptance of such composites when the scale size of the inclusions and period cell is much finer than the wavelength. These analytic arguments are supported by highly accurate numerical results for the effective permittivity function of such composites as a function of the permittivity ratio of inclusions to the matrix. The results show that this function has a continuous spectral component with limits independent of the area fraction of inclusions, and with the same limits for both square and staggered square arrays. For staggered arrays where the squares are almost touching, the absorption spectrum is an extremely sensitive probe of the inclusion separation distance and acts like a Vernier scale.

We investigate imaging by spherically symmetric absolute instruments that provide perfect imaging in the sense of geometrical optics. We derive a number of properties of such devices, present a general method for designing them and use this method to propose several new absolute instruments, in particular a lens providing a stigmatic image of an optically homogeneous region and having a moderate refractive index range.