A spatially shifted beam approach to subwavelength focusing
Loic Markley, Alex M. H. Wong, Yan Wang, George V. Eleftheriades
备注：
5 pages, 7 figures. Content updated following reviewer comments to match final published paper
发表信息：
L. Markley, A. M. H. Wong, Y. Wang, G. V. Eleftheriades, "Spatially shifted beam approach to subwavelength focusing," Physical Review Letters, vol. 101, pp. 113901, Sept. 2008
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.
This is a comment on "Guiding, Focusing, and Sensing on the Subwavelength Scale Using Metallic Wire Arrays" by G. Shvets, S. Trendafilov, J. B. Pendry and A. Sarychev published in Phys. Rev. Lett. 99, 053903 (2007), which demonstrates that the endoscope proposed in the letter does not demonstrate satisfactory subwavelength imaging performance.
We study theoretically light focusing at subwavelength scale inside a disordered strongly scattering open medium. We show that broadband time reversal at a single point antenna, in conjunction with near-field interactions and multiple scattering, produces spatial focusing with a quality comparable to that obtained in an ideal closed cavity. This gives new perspectives for super-resolved optical imaging and coherent control of single nanosources or absorbers in complex media.
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.
The existing metasurfaces with ultrathin volume for asymmetric transmission were often constructed by metal with low efficiency in optical frequency, and could not realize the optical asymmetric transmission and focusing simultaneously. Although the acoustic asymmetric focusing in asymmetric focusing lens (AFL) was realized, the obtained focal point was accompanied by large sidelobe. To solve those problems, an AFL with dual-layer metasurfaces designed by using dielectric materials can realize optical asymmetric transmission and focusing simultaneously in this paper. Furtherly, through optimiz…
A transmission screen with subwavelength slots is described which can focus electromagnetic radiation to a two-dimensional subwavelength spot. Unlike negative-refractive-index focusing implementations, this "meta-screen" does not suffer from image degradation when losses are introduced and is easily scalable from microwave to Terahertz frequencies and beyond. The slotted geometry is designed using a theory of shifted beams to determine the necessary weighting factors for each slot element, which are then converted to appropriate slot dimensions. The screen was designed using a pair of rotated …
We propose a mechanism for subwavelength focusing at optical frequencies based on the use of a tapered microtube fabricated from a glass capillary tube. Using coherent illumination at 671nm and a near-field scanning optical microscope probe which was mounted on a 3-axis piezo nanopositioning stage, a sequence of 2-D intensity profiles were obtained. Our experimental results reveal the smallest focal spot with a near diffraction-limited full width at half-maximum of ~435nm(0.65λ)at a distance of ~1.47μm (2.2λ) from the output endface of microtube. The experimental results are in excellent agree…
Optical absorption is usually considered deleterious, something to avoid if at all possible. We propose a broadband nanoabsorber that completely eliminates the diffracting wave, resulting in a subwavelength enhancement of the field. Broadband operation is made possible by engineering the dispersion of the complex dielectric function. The local enhancement can be significantly improved compared to the standard plane wave illumination of a metallic nanoparticle. Our numerical simulation shows that an optical pulse as short as 6 fs can be focused to a 11 nm region. Not only the local field, but a…
We demonstrate that a planar and ultrathin binary lens can focus an azimuthally polarized beam with vortical phase (APV) to a subwavelength spot of transverse polarization. The results elaborates that, in the multi-layer medium, this focused spot, which is beyond the Rayleigh diffraction limitation, can be well maintained for several wavelengths after travelling through the dielectric interfaces, which is not attainable by using other vector beams (i.e., radially, linearly and circularly polarized beams) as the illuminating light. This compact optical system can be valuable in data writing and…
We demonstrate experimentally and numerically that in fiber tips as they are used in NSOMs azimuthally polarized electrical fields (|E$_{\text{azi}}$|$^2$/|E$_{\text{tot}}$|$^2$ $\approx$ 55% $\pm $ 5% for 1.4μm tip aperture diameter and λ$_0$ = 1550nm), respectively subwavelength confined (FWHM $\approx$ 450nm $\approx$ λ$_0$/3.5) magnetic fields, are generated for a certain tip aperture diameter (d = 1.4μm). We attribute the generation of this field distribution in metal-coated fiber tips to symmetry breaking in the bend and subsequent plasmonic mode filtering in the truncated conical taper.
Materials which possess a high local density of states varying at a subwavelength scale theoretically permit to focus waves onto focal spots much smaller than the free space wavelength. To do so metamaterials -manmade composite media exhibiting properties not available in nature- are usually considered. However this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto $λ/15$ subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerica…
Micro-sized spheres can focus light into subwavelength spatial domains: a phenomena called photonic nanojet. Even though well studied in three-dimensional (3D) configurations, only a few attempts have been reported to observe similar phenomena in two-dimensional (2D) systems. This, however, is important to take advantage of photonic nanojets in integrated optical systems. Usually, surface plasmon polaritons are suggested for this purpose, but they suffer notoriously from the rather low propagation lengths due to intrinsic absorption. Here, we solve this problem and explore, theoretically, nume…
This is the second article in a series of two dealing with the concept of "resonant metalens" we introduced recently [Phys. Rev. Lett. 104, 203901 (2010)]. It is a new type of lens capable of coding in time and radiating efficiently in the far field region sub-diffraction information of an object. A proof of concept of such a lens is performed in the microwave range, using a medium made out of a square lattice of parallel conducting wires with finite length. We investigate a sub-wavelength focusing scheme with time reversal and demonstrate experimentally spots with focal widths of λ/25. Throug…
The subwavelength focusing based on surface plasmon polaritons (SPP) has been widely explored in tapered metallic structures. However, the efficiency of energy localization is relatively weak, largely due to high propagation loss and strong back reflection. Here, we propose a straight-tapered 3-dimensional (3D) one-way surface magnetoplasmon (SMP) waveguide with the ending surface of $\sim 10^{-4}λ_0 \times 10^{-4}λ_0$ to achieve energy focusing in the microwave regime. Due to low propagation loss of SMP, we achieve huge magnetic field enhancement in such an ultra-subwavelength area, by five o…
Flat lens concept based on negative refraction proposed by Veselago in 1968 has been mostly investigated in monochromatic regime. It was recently recognized that time development of the super-lensing effect discovered in 2000 by Pendry is yet to be assessed and may spring surprises: Time-dependent illumination could improve the spatial resolution of the focusing. We investigate dynamics of flexural wave focusing by a 45\degre-tilted square lattice of circular holes drilled in a Duraluminium plate. Time-resolved experiments reveal that the focused image shrinks with time below diffraction limit…
Many advances in reflective metasurfaces have been made during the last few years, implementing efficient manipulations of wavefronts, especially for plane waves. Despite numerous solutions that have been developed throughout the years, a practical method to obtain subwavelength focusing without the generation of additional undesired scattering is a challenge to this day. In this paper, we introduce and discuss lossless reflectors for focusing incident waves into a point. The solution is based on the so-called power flow-conformal surfaces that allow theoretically arbitrary shaping of reflecte…
Generation of a photonic nanojet by a linearly polarized wave beam or a plane wave impinging a dielectric microcylinder implies partial conversion of the propagating waves into the evanescent ones. This conversion is manifested in nanojet waist of subwavelength effective width. However, this known near-field effect is relatively weak. We theoretically show that the incidence of a wave beam formed by two plane waves enables much stronger near-field effects: a deeply subwavelength focusing of the incident beam and a strong enhancement of the electric field on the whole cylinder surface and near …
Recently a hypothesis explaining the non-resonant mechanism of subwavelength imaging granted by a dielectric microsphere has been suggested. In accordance to the hypothesis, the far-field image of a subwavelength scatterer strongly coupled to a microsphere by near fields is offered by the scatterer polarization normal to the sphere surface. The radiation of a closely located normally oriented dipole is shaped by the microsphere so that the transmitted wave beam has a practically flat phase front. Then this beam turns out to be imaging -- keeping the subwavelength information about the dipole l…
A general method for tight focusing of waves, based on compensation of the angular spectrum, is established. We apply the method to monochromatic, polychromatic and diffusive waves. Diffusive and monochromatic waves may form spatially localized waves in free space, whereas polychromatic waves form light sheets or non-decaying traveling evanescent modes confined to subwavelength regions in media where the frequency depends on the wave vector. We suggest an analogy between our compensation method and the transformation of frequencies between inertial, relativistic coordinate systems.
Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provide extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This paper provides a relation between the achievable focus spot size, the amplification available and the focal length. This may be considered as a revised version of Abbe's diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations, as well as determining whe…
Remote focusing of light in a graded-index medium via mode interference is demonstrated using exact analytical solutions of the wave equation. Strong focusing of light occurs at extremely long distances and it revivals periodically with distance due to mode interference. High efficiency transfer of a strongly focused subwavelength spot through optical waveguide over large distances takes place with a period of revival. Super-oscillatory hot-spots with the sizes which are beyond the conventional Abbe diffraction limit can be observed at large distances from the source. This can provide the poss…
Breaking the diffraction limit and focusing laser beams to subwavelength scale are becoming possible with the help of recent developments in plasmonics. Such subwavelength focusing bridges different length scales of laser beams and matter. Here we consider optical vortex, or laser beam carrying orbital angular momentum (OAM) and discuss potential subwavelength magnetic phenomena induced by such laser. On the basis of numerical calculations using Landau-Lifshitz-Gilbert equation, we propose two OAM-dependent phenomena induced by optical vortices, generation of radially anisotropic spin waves an…
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…
A metamaterial made by stacked hole-array layers known as a fishnet metamaterial behaves as a hyperbolic metamaterial at wavelength much longer than hole-array period. However, the analytical formulae of effective parameters of a fishnet metamaterial have not been reported hindering the design of deep-subwavelength imaging devices using this structure. We report the new closed-form formulae of effective parameters comprising anisotropic dispersion relation of a fishnet metamaterial working at terahertz or microwave frequency. These effective parameters of a fishnet metamaterial are consistent …
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…
Recently Merlin and co-workers demonstrated, both theoretically and in the microwave range experimentally, subwavelength focusing of evanescent waves by patterned plates. The present paper extends these ideas and the design procedure to scatterers of arbitrary shapes and to the optical range of wavelengths. The analytical study is supported by numerical results. The most intriguing feature of the proposed design is that, in the framework of classical electrodynamics of continuous media, focusing can in principle be arbitrarily sharp, subject to the constraints of fabrication.
Metamaterials and metasurfaces are widely used to manipulate electromagnetic waves over a broad range of wavelengths. Several recent efforts have focused on metalenses, ultra-thin optical elements that focus light using subwavelength structures. Compared to their refractive counterparts, metalenses offer reduced size and weight, improved manufacturability, and new functionality such as polarization control. However, metalenses that correct chromatic aberration also suffer from markedly reduced focusing efficiency. Here we introduce a Hybrid Achromatic Metalens (HAML), that overcomes this trade…
A method is presented for generation of a subwavelength (0.43 lambda) longitudinally polarized beam, which propagates without divergence over lengths of about 4 lambda in free space. This is achieved by controlling the amplitude, phase and polarization property of the Bessel-Gaussian field on the aperture of a high numerical aperture focusing lens.
We show that an analog of the physics at the Planck scale can be found in the propagation of tightly focused laser beams. Various equations that occur in generalized quantum mechanics are formally identical to those describing the nonlinear nonlocal propagation of nonparaxial laser beams. The analysis includes a generalized uncertainty principle and shows that the nonlinear focusing of a light beam with dimensions comparable to the wavelength corresponds to the spontaneous excitation of the so-called maximally localized states. The approach, driven by the ideas of the quantum gravity physics, …
The digital holographic interferometry (DHI) was utilized for investigating the optical properties of polymer and optical fibers. The samples investigated here were polyvinylidene fluoride (PVDF) polymer fiber and graded-index (GRIN) optical fiber. The phase shifting Mach-Zehnder interferometer was used to obtain five phase-shifted holograms, in which the phase difference between two successive holograms is pi/2, for each fiber sample. These holograms were recorded using a CCD camera and were combined to gain a complex wavefield, which was numerically reconstructed using the convolution approa…
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…
We simulate the focusing of a partially-coherent X-ray beam emitted by an undulator in a fourth-generation storage ring performing coherent mode decomposition and wave optics propagation. The focus position is shifted, and its size is enlarged when an entrance slit crops the beam. This is the usual case when a slit is used to select the coherent fraction. The pairing of two focusing elements (mirrors, lenses or transfocators) to ensure a fixed focal position is also analyzed. Our results show that the image of a partially coherent source, such an undulator in a low-emittance storage ring, is a…
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 [Leonhard…
