The point of the paper is to show some limitations of geometrical optics in the analysis of subwavelength focusing. We analyze the resolution of the image of a line source radiating in the Maxwell fisheye and the Veselago-Pendry slab lens. The former optical medium is deduced from the stereographic projection of a virtual sphere and displays a heterogeneous refractive index n(r) which is proportional to the inverse of 1+r^2. The latter is described by a homogeneous, but negative, refractive index. It has been suggested that the fisheye makes a perfect lens without negative refraction [Leonhardt, Philbin arxiv:0805.4778v2]. However, we point out that the definition of super-resolution in such a heterogeneous medium should be computed with respect to the wavelength in a homogenized medium, and it is perhaps more adequate to talk about a conjugate image rather than a perfect image (the former does not necessarily contains the evanescent components of the source). We numerically find that both the Maxwell fisheye and a thick silver slab lens lead to a resolution close to lambda/3 in transverse magnetic polarization (electric field pointing orthogonal to the plane). We note a shift of the image plane in the latter lens. We also observe that two sources lead to multiple secondary images in the former lens, as confirmed from light rays travelling along geodesics of the virtual sphere. We further observe resolutions ranging from lambda/2 to nearly lambda/4 for magnetic dipoles of varying orientations of dipole moments within the fisheye in transverse electric polarization (magnetic field pointing orthogonal to the plane). Finally, we analyse the Eaton lens for which the source and its image are either located within a unit disc of air, or within a corona 1<r<2 with refractive index $n(r)=\sqrt{2/r-1}$. In both cases, the image resolution is about lambda/2.
Focusing of electromagnetic plane wave from a large size paraboloidal reflector, composed of layers of chiral and/or chiral nihility metamaterials, has been studied us- ing Maslov's method. First, the transmission and reflection of electromagnetic plane wave from two parallel layers of chiral and/or chiral nihility metamaterials are cal- culated using transfer matrix method. The effects of change of angle of incidence, chirality parameters and impedances of layers are noted and discussed. Special cases by taking very large and small values of permittivity of second layer, while assuming value …
In this letter, we introduce stacked fishnet metamaterial for steering light in microwave region. We numerically demonstrate that optical Bloch oscillations and a focus of as small as one sixth of a wavelength can be achieved. The flexibility of varying geometrical parameters of the fishnet slabs provides an efficient way for tuning its local effective media parameters and opens the possibility for controlling light arbitrarily. The experiment verifies subwavelength-sized light focusing effect by scanning magnetic field at the surface of the sample directly.
We designed and implemented a gradient index metasurface for the in-plane focusing of confined terahertz surface waves. We measured the spatial propagation of the surface waves by two-dimensional mapping of the complex electric field using a terahertz near-field spectroscope. The surface waves were focused to a diameter of 500 \micro m after a focal length of approx. 2 mm. In the focus, we measured a field amplitude enhancement of a factor of 3.
We design three-dimensional (3D) metallic nanowire media with different structures and numerically demonstrate that they can be homogeneous effective indefinite anisotropic media by showing that their dispersion relations are hyperbolic. For a finite slab, a nice fitting procedure is exploited to obtain the dispersion relations from which we retrieve the effective permittivities. The pseudo focusing for the real 3D wire medium agrees very well with the homogeneous medium having the effective permittivity tensor of the wire medium. Studies also show that in the long-wavelength limit, the hyperb…
The development of innovative terahertz (THz) imaging systems has recently moved in the focus of scientific efforts due to the ability to screen substances through textiles or plastics. The invention of THz imaging systems with high spatial resolution is of increasing interest for applications in the realms of quality control, spectroscopy in dusty environment and security inspections. One of the main restrictions of current THz imaging systems is the low spatial resolution which is limited by a lack of THz lenses with strong focusing capabilities. Here we present the design, fabrication and t…
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the loc…
An efficient reflective elastic metasurface with tunable focusing point is proposed. The metasurface is based on electric resonators embedded in a stretchable elastic substrate. The focal length is controlled by mean of the stretching applied applied to the sample. The results predicted by theory and numerical simulations are experimentally verified. Our proposal shows that smart engineering elastic metamaterials are an effective platform for new functional devices based on metamaterials.
In the past two decades, artificial structures known as metamaterials have been found to exhibit extraordinary material properties that enable the unprecedented manipulation of electromagnetic waves, elastic waves, molecules, and particles. Phenomena such as negative refraction, bandgaps, near perfect wave absorption, wave focusing, negative Poissons ratio, negative thermal conductivity, etc., all are possible with these materials. Metamaterials were originally theorized and fabricated in electrodynamics, but research into their applications has expanded into acoustics, thermodynamics, seismol…
We show that planar a plasmonic metamaterial with spatially variable meta-atom parameters can focus transmitted light into sub-wavelength hot-spots located beyond the near-field of the metamaterial. By nano-structuring a gold film we created an array of meta-lenses generating foci of 160 nm (0.2λ) in diameter when illuminated by a wavelength of 800 nm. We attribute the occurrence of sub-wavelength hotspots beyond the near field to the phenomenon of superoscillation.
Adiabatic waveguide taper and on-chip wavelength demultiplexer are the key components of photonic integrated circuits. However, these two kinds of devices which designed by traditional semi-analytic methods or brute-force search methods usually have large size. Here, based on regularized digital metamaterials, we have designed, fabricated and characterized a two-channel focused wavelength demultiplexer with a footprint of 2.4 x 10 um2. The designed demultiplexer can directly connect to a grating coupler under the absence of an adiabatic waveguide taper. The objective first method and modified …
Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states. Typically the periods of such structures are comparable to the wavelength. However, in many cases, the unit cell becomes deeply subwavelength and hence the entire metamaterial can be described in terms of the effective material parameters. Here, focusing on subwavelength topological metamaterials, we identify the behavior of permittivity and permeability accompa…
We present a gradient-index (GRIN) metamaterial based on an array of annular slots. The structure allows a large variation of the effective refractive index under normal-to-plane incidence and thus enables the construction of GRIN devices consisting of only a small number of functional layers. Using full-wave simulations, we demonstrate the annular slot concept by means of a 3-unit-cell thin GRIN lens for the terahertz (THz) range. In the presented realizations, we achieved an index contrast of Delta n = 1.5 resulting in a highly refractive lens suitable for focusing THz radiation to a spot si…
We considered the experimental realization of a Tamm medium that is optically equivalent to the collision of two linearly polarized gravitational plane waves as a piecewise homogeneous metamaterial. Our formulation was based on the homogenization of remarkably simple arrangements of oriented ellipsoidal nanoparticles of isotropic dielectric-magnetic mediums. The inverse Bruggeman homogenization was used to estimate the constitutive parameters, volume fractions, and shape parameters for the component mediums. The presented formulation is appropriate for the regions of spacetime where the two gr…
Sub-wavelength confinement of light in nonlinear hyperbolic metamaterials due to formation of spatial solitons has attracted much recent attention because of its seemingly counter-intuitive behavior. In order to achieve self-focusing in a hyperbolic wire medium, a nonlinear self-defocusing Kerr medium must be used as a dielectric host. Here we demonstrate that this behavior finds natural explanation in terms of analogue gravity. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2+1 dimensional Lorentz symmetry. The role of time in the correspo…
We analyze the properties of a nonlinear metamaterial formed by integrating nonlinear components or materials into the capacitive regions of metamaterial elements. A straightforward homogenization procedure leads to general expressions for the nonlinear susceptibilities of the composite metamaterial medium. The expressions are convenient, as they enable inhomogeneous system of scattering elements to be described as a continuous medium using the standard notation of nonlinear optics. We illustrate the validity and accuracy of our theoretical framework by performing measurements on a fabricated …
We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. …
We propose to employ the quasiisotropic metamaterial (QIMM) slab to construct a polarization insensitive lens, in which both E- and H-polarized waves exhibit the same refocusing effect. For shallow incident angles, the QIMM slab will provide some degree of refocusing in the same manner as an isotropic negative index material. The refocusing effect allows us to introduce the ideas of paraxial beam focusing and phase compensation by the QIMM slab. On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through a QIMM slab is presented. Because of the ne…
Although negative-refractive-index metamaterials have successfully achieved subwavelength focusing, image resolution is limited by the presence of losses. In this Letter, a metal transmission screen with subwavelength spaced slots is proposed that focuses the near-field beyond the diffraction limit and furthermore, is easily scaled from microwave frequencies to the optical regime. An analytical model based on the superposition of shifted beam patterns is developed that agrees very well with full-wave simulations and is corroborated by experimental results at microwave frequencies.
Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in the usual sense . In fact, the energy in such systems does not go from object to its "image", but from object and its "image" to an intersection point inside a metamaterial layer, or vice versa. A possibility of applying this phenomenon to a creation of entangled states of two atoms is discussed.
Centre de Nanosciences et Nanotechnologies, CNRS, UMR 9001, Université Paris-Sud, Université Paris-Saclay（纳米科学与技术中心）；École Centrale de Lyon, INSA Lyon, CNRS, Université Lyon 1, CPE Lyon, INL（里昂中央理工学院）
Conceptual studies and numerical simulations are performed for imaging devices that transform a near-field pattern into magnified far-zone images and are based on high-order spatial transformation in cylindrical domains. A lens translating a near-field pattern from an almost circular input boundary onto a magnified far-field image at a flat output boundary is considered. The lens is made of a metamaterial with anisotropic permittivity and permeability both depending on a single 'scaling' parameter of the transformation. Open designs of the lens with a truncated body ('3/4-body' and '1/4-body' …
