Maxwell Fish-eye Lens Research Articles

Comment on “Perfect imaging with positive refraction in three dimensions”

Leonhard and Philbin [Phys. Rev. A 81, 011804(R) (2010)] have recently constructed a mathematical proof that the Maxwell's fish-eye lens provides perfect imaging of electromagnetic waves without negative refraction. In this comment, we argue that the unlimited resolution is an artifact of having introduced an unphysical drain at the position of the geometrical image. The correct solution gives focusing consistent with the standard diffraction limit.

Maxwell fish-eye and Eaton lenses emulated by microdroplets

Despite strong experimental and theoretical evidence supporting superresolution imaging based on microlenses, the imaging mechanisms involved are not well understood. Based on the transformation optics approach, we demonstrate that a microlens may act as a two-dimensional fish-eye or an inverted Eaton lens. An asymmetric inverted Eaton lens may exhibit considerable image magnification, which has been confirmed experimentally.

Enhancing imaging systems using transformation optics

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Comment on ‘Perfect imaging without negative refraction’

The prediction of ‘perfect’ imaging without negative refraction for Maxwell's fish-eye lens (Leonhardt U 2009 New J. Phys. 11 093040) is a consequence of imposing an active localized ‘drain’ at the image point rather than being a general property of the lens. This work then becomes analogous to other work using time-reversal symmetry and/or structured antennae to achieve super-resolution, which can be applied to many types of imaging system beyond the fish-eye lens.

Perfect focusing of scalar wave fields in three dimensions

A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analysed.

Comparative Design and Analysis of Luneburg and Half Maxwell Fish-Eye Lens Antennas

The design and performances is described of half Maxwell fish-eye (HMFE) and Luneburg lens antennas. Techniques to estimate the gradient index lens weights are first proposed and compared to measurements. Thanks to an analytical method based on spherical modal expansion, the radiation performances of Luneburg and HMFE lens antennas are then quantified and compared. The effects of the shell number, the lens diameter and the air gaps on the lens antenna directivity are investigated. Finally, a minmax optimized 9-shell 60 mm-diameter HMFE lens antenna is characterized at both 77 GHz and 110 GHz for on- and off- axis configurations to show its frequency behavior, focalization and beam scanning properties.

Fabrication of Maxwell fish-eye spherical lenses and research on distribution profiles of gradient refractive index

We establish the equation of distribution of the refractive index of Maxwell fish-eye spherical lenses and report fabrication of Maxwell fish-eye spherical lenses using optical glasses. The distribution profiles are discussed for the process of ion exchanging, and the experimental results accord with the theoretical analysis.

Scattering of Spherically and Hemispherically Stratified Lenses Fed by Any Real Source

An analytical method to compute the scattering of spherically and hemispherically stratified lens antennas is described. The expansion of any real source on spherical wave functions is detailed and validated by comparison to commercial software simulations and measurements at both 50 GHz and 77 GHz. A mode matching technique (MMT) based on spherical wave functions is first used to analyze the scattering by spherically stratified lens antennas. The far field patterns and directivity obtained are in excellent agreement with commercial software simulations and measurements for a six-shell Luneburg lens at 6 GHz. This MMT is then extended to hemispherically stratified lens antenna analysis. Its validation is also carried out by comparisons to both commercial software and measurements for a three-shell half Maxwell fish-eye lens fed by an open-ended waveguide at W-band. The expansion on spherical modes gives direct access to the field everywhere. To highlight the progressive focusing effect of inhomogeneous lens antennas, the electric field is mapped in terms of magnitude and phase in the neighborhood of the entire structure. One of the originalities of this work is the quantification of the reaction created by the scatterer on the feed. Narrowing the scatterer to a stratified lens does not affect the generality of the presented procedure. While providing controlled accuracy, the MMT tremendously reduces both computation time and memory load in comparison to commercial software.

Off-Axis Performances of Half Maxwell Fish-Eye Lens Antennas at 77 GHz

The off-axis performances at 77 GHz of multilayered half Maxwell fish-eye (HMFE) lenses fed by an open-ended waveguide is describes. When moving the feed with respect to (w.r.t.) the lens, it is shown that at least 40deg of scanning can be achieved. Several off-axis configurations of the lens antenna are investigated and compared using a full-wave electromagnetic software. The directivity, far field pattern and scan angle of the lens antenna are reported for a rectilinear and angular off-axis displacement of the feed and also for various distances between the feed and the lens. It is also shown that a three-shell lens is good enough to achieve a wide scan angle. Finally, off-axis measurements done with a three-shell 6.15 lambda0-diameter HMFE lens antenna are compared to computed results to validate the simulations

Design and characterization of half Maxwell fish-eye lens antennas in millimeter waves

This paper presents the performance of multilayered half Maxwell fish-eye (HMFE) lenses fed by aperture-coupled microstrip patch antennas. Manufacturing techniques are reviewed and the shell technique is retained. Many lens configurations are investigated and compared using a full-wave electromagnetic software at 50 GHz. We report the effects of the number of shells, diameter of the lens, and distance between the primary source and the lens on the input impedance, broadside directivity, and aperture efficiency. Thus, we show that aperture efficiencies up to 95% can be obtained for a one-wavelength-diameter lens with only three shells, justifying the interest in such lenses. An analytical optimization method is also proposed and detailed to choose the thickness and permittivity of a three-shell HMFE lens to approach the radial permittivity law as well as possible. Simulations of lens antennas whose shell characteristics are determined by various ways show that the optimized lens is the one that provides the highest broadside directivities. Finally, measurements done with a three-shell four-wavelength diameter lens fed by a 2 times 2 patch antenna array show the validity of these simulations. To our knowledge, this represents the first layered HMFE lens carried out in the millimeter-wave frequency range

A field picture of wave propagation in inhomogeneous dielectric lenses

This article presents the radiation and scattering patterns, and the interior field distributions, of three inhomogeneous dielectric lenses: the Luneburg (1944), Maxwell fish-eye (1860), and Eaton-Lippmann (1952) lenses. The purpose is to provide a picture of wave propagation through these lenses. A better understanding of the field picture, especially the nature of the focal points, is helpful to the practical design of the lenses.

Electromagnetic modes of Maxwell fisheye lens

We provide an analysis of the radial structure of TE and TM modes of the Maxwell fisheye lens, by means of Maxwell equations as applied to the fisheye case. Choosing a lens of size R = 1 cm, we plot some of the modes in the infrared range.

Beam propagation in gradient refractive-index media

A generalized beam propagation method is described that uses the ABCD matrices to treat optical systems that have modest amounts of aberrations including gradient refractive-index elements. We can make calculations from any point in the near or far field to any other point by using appropriate numerical algorithms. The variation of the reduced length is discussed as a limitation to accuracy. The diffraction properties of a complex stigmatic system may be represented by those of an equivalent elementary system. This facilitates calculations using the standard diffraction operations for homogeneous media. The modified propagation technique replaces the large number of diffraction steps commonly used for the split-step solution of inhomogeneous media with one step for stigmatic media and in general no more than a few steps for aberrated media. Maxwell's fisheye lens is discussed in detail to show application of the method.

Geometrical Optics in Inhomogeneous Chiral Media with Application to Polarization Correction of Inhomogeneous Microwave Lens Antennas

A novel geometric optics method for inhomogeneous chiral media is introduced applying normalized wave fields, which are certain complex combinations of the electric and magnetic fields. It is seen that for sufficiently small values of the chirality parameter, the geometrical optics rays can be calculated as for a chiral media and the main effect of the chirality is rotation of polarization along the ray. Thus, adding chirality to inhomogeneous lens antennas, their polarization properties can be improved. As an example, the Maxwell fish-eye lens is analyzed and two possible expressions for a chirality distribution capable of eliminating the inherent cross polarization, are derived.