Negative refraction through a triangular prism may be explained without assigning a negative refractive index to the prism by using array theory. For the case of a beam incident upon the wedge, the array theory accurately predicts the beam transmission angle through the prism and provides an estimate of the frequency interval at which negative refraction occurs. Negative refraction effects not only occur in prisms made of traditional metamaterial unit cells, such as magneto-dielectric spheres, but also in solid prisms made of completely filled, homogenous unit cells. In both prisms, the hypotenuse has a staircase shape because they are built of cubic unit cells. The large phase delay imparted by each unit cell, combined with the staircase shape of the hypotenuse, creates the necessary conditions for negative refraction. Full wave simulations using the finite-difference time-domain method show that array theory accurately predicts the beam transmission angle for both solid prisms and prisms made of magneto-dielectric spheres.
This work demonstrates the existence of both negative refraction and a negative refractive index in an optical uniaxial absorbent medium that can be characterized by ordinary and extraordinary refractive indices. Negative refraction occurs in any absorbent uniaxial medium if the real part of the extraordinary index is less than its imaginary part. The refractive index is negative when the incident medium is sufficiently dense and the incident angle exceeds a critical angle that is defined here.
It has been shown that for left-handed metamaterials and generally for negative refraction media the refraction index cannot be entered unequivocally and cannot be considered as real, and especially as negative. This index for above referred media is not expedient
Focal-plane imaging with microwave and millimeter wave has many potential applications. The bad resolution is a main shortcoming of this technique at present. In this paper, influence of frequency of electromagnetic wave on the refractive energy is analyzed. According to the refractive mechanism of electromagnetic induction, the principle for designing artificial materials with enough refractive ability is proposed. The material of artificial molecules is fabricated with cage-shaped granules of conductor (CGC). The refractive index of CGC material to microwave was measured by assembling CGC pr…
We extended the refraction angle of the Eaton lens into arbitrary angles. The refractive index of the Eaton lens is not analytical and can be obtained by numerical calculations only except in the case of the retroreflector. We introduced an approximation for the refractive index of the generalized Eaton lens. It is simple but very close to the exact values obtained from numerical calculations.
This letter proposes a quasi-planar chiral resonator suitable for the design of negative refractive index matamaterial. It is presented an analytical model for the determination of its polarizabilities, and the viability of negative refraction in chiral and racemic arrangements with the proposed inclusions is analyzed. The present analysis is expected to pave the way to the design of negative refractive index matamaterials made of a single kind of inclusions feasible from standard photo-etching techniques.
By direct numerical simulations of the kinoform refractive lens within the quazioptical approach the effects of shape misalinement were investigated. The quazioptical approach was based on numerical integration of parabolic equation for complex wave amplitude by spep-by-step method with "splitting" procedure. The effect of 2pi- shift compensation was calculated for different orders and imperfections. The performance of kinoform lens was compared with the compound refractive lens and thin lens approximation.
We extended a previous study of the Eaton lens at specific refraction angles to the Eaton lens at any refraction angle. The refractive index of the Eaton lens is complicated and has not analytical form except at a few specific angles. We derived a more accessible form of the refractive index for any refraction angle with some accuracy by retroreflector approximation. The finding of this study will be useful for a rapid estimation of the refractive index, and the the design of various Eaton lenses.
Space-time (ST) wave packets are a class of pulsed optical beams whose spatio-temporal spectral structure results in propagation invariance, tunable group velocity, and fascinating refractive phenomena. Here, we investigate the refraction of ST wave packets at a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface. We verify this new refraction law in ZnSe and CdSe, both of which man…
We theoretically propose that Weyl semimetals may exhibit negative refraction at some frequencies close to the plasmon frequency, allowing transverse magnetic (TM) electromagnetic waves with frequencies smaller than the plasmon frequency to propagate in the Weyl semimetals. The idea is justified by the calculation of reflection spectra, in which \textit{negative} refractive index at such frequencies gives physically correct spectra. In this case, a TM electromagnetic wave incident to the surface of the Weyl semimetal will be bent with a negative angle of refraction. We argue that the negative …
An array of pairs of parallel gold nanorods is shown to have a negative refractive index n'=-0.3 at the optical communication wavelength of 1.5 micron. This effect results from the plasmon resonance in the pairs of nanorods for both the electric and magnetic components of light. The refractive index is retrieved from the direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with our finite difference time domain simulations. The refraction critically depends on the phase of the transmitted wave, which emphasizes the importance of phase me…
We introduce an improved and simplified structure made of periodic arrays of pairs of H-shaped metallic wires that offer a potentially simpler approach in building negative-index materials. Using simulations and microwave experiments, we have investigated the negative-index n properties of these structures. We have measured experimentally both the transmittance and the reflectance properties and found unambiguously that a negative refractive index with Re(n)<0 and Im(n) <Re(n). The same is true for epsilon and mu. Our results show that H-shaped wire pairs can be used very effectively in produc…
We propose a device with a positive isotropic refractive index that creates an approximate magnified perfect real image of an optically homogeneous three-dimensional region of space within geometrical optics. Its key ingredient is a new refractive index profile that can work as an approximate perfect lens on its own, having a very moderate index range.
Effective refractive index of disordered all-dielectric metasurfaces consisting of gallium phosphide (GaP) spheres is studied by means of three-dimensional finite-difference time-domain (FDTD) simulations at the wavelength of 532~nm. It is shown that a mixture of the high index nanoparticles with sizes close to the first magnetic and electric resonances randomly dispersed on metasurface may possess negative refraction. The dependence of the metasurface effective refractive index on the nanoparticle concentration and size is constructed. The feasibility of negative refraction at large concentra…
A simple optical lens plays an important role for exploring the microscopic world in science and technology by refracting light with tailored spatially varying refractive index. Recent advancements in nanotechnology enable novel lenses, such as, superlens, hyperlens, Luneburg lens, with sub-wavelength resolution capabilities by specially designing materials' refractive indices with meta-materials and transformation optics. However, these artificially nano/micro engineered lenses usually suffer high losses from metals and are highly demanding in fabrication. Here we experimentally demonstrate f…
The optical Kerr effect of material with negative refraction is estimated for the first time. This is done via three-dimensional finite-difference time-domain (FDTD) simulations of disordered bidisperse metasurfaces consisting of high index (GaP) spheres at the wavelength of 532~nm. The metasurfaces comprise spherical particles randomly arranged on plane having two sizes close to the magnetic and electric dipole Mie resonances. The real part of the effective nonlinear refractive index of the metasurfaces is computed in the vicinity of the Mie resonances where the metasurface possesses the nega…
Artificial magnetism, negative permeability and negative refractive index are demonstrated in 3D-chiral metamaterial that shows giant polarization rotation and circular dichroism.
When light travels through a medium in which the refractive index is rapidly changing with time, the light will undergo a shift in its frequency. Large frequency shifting effects have recently been reported for transparent conductive oxides. These observations have been interpreted as emerging from temporal changes to the propagation phase in a bulk medium resulting from temporal variations in the refractive index, an effect referred to as temporal refraction. Here, we show that the frequency shift in an epsilon-near-zero (ENZ) layer made of indium tin oxide (ITO) originates not only from this…
Has the ten-year old quest for the optical superlens, based on Veselago's hypothesis of negative refraction, been a chimera? We argue that Pendry's alternative prescription of the silver superlens is nothing more than an application of the natural phenomenon of surface plasmon resonance that occurs in the noble metal films. This phenomenon does not predict the reality of Veselago's negative refractive index materials. We give a simple explanation of how this resonance achieves a field intensity enhancement at the interface of silver and air without involving the concept of negative refraction.
Light-absorbing materials are widely used, and their optical properties are an important factor. Snell's law does not hold in materials that partially absorb light. Hence, the optical path in refraction is calculated from Maxwell's law. We used it to obtain the deviation angle when a light passes through a prism made of light absorbing material. As a result, the deviation angle has a local maximum point. The deviation angle near the local maximum is sensitive to the real and imaginary parts of the refractive index. The local maximum deviation angle and its incident angle are used to determine …
Which systems are ideal to obtain negative refraction with no absorption? Electromagnetically induced transparency (EIT) is a method to suppress absorption and make a material transparent to a field of a given frequency. Such a system has been discussed in [1]; however the main limitations for negative refraction introduced are the necessity of resonant electric and magnetic dipole transitions, and the necessity of very dense media. We suggest using frequency translators in a composite system that would provide negative refraction for a range of optical frequencies while attempting to overcome…
Bi-isotropic and isotropic negative refractive index (NRI) 3D metamaterials made from periodic arrangements of chiral split ring resonators (SRRs) are proposed and demonstrated. An analytical theory for the characterization and design of these metamaterials is provided and validated by careful full-wave electromagnetic simulations. The reported results are expected to pave the way to the design of practical 3D bi-isotropic and isotropic NRI metamaterials made from a single kind of inclusions.
Refraction is a well-known optical phenomenon that alters the direction of light waves propagating through matter. Microscopes, lenses and prisms based on refraction are indispensable tools for controlling the properties of light beams at visible, infrared, ultraviolet and X-ray wavelengths. The large absorption of extreme-ultraviolet (XUV) radiation in matter, however, hinders the development of refractive lenses and prisms in this spectral region. Here, we demonstrate control over the refraction of XUV radiation by using a gas jet with a density gradient across the XUV beam profile. A gas ph…
A nanofabricated regular array of coupled gold nano-pillars is employed to detect local indices of refraction of different liquids using a shift of an antisymmetric plasmon resonance peak observed in the reflection spectra. The peak spectral position is found to be a unique function of the local refractive index for a wide range of indices. We discuss possible applications of the fabricated nanostructured arrays in bio and chemical sensors.
Specially designed metal-dielectric composites can have a negative refractive index in the optical range. Specifically, it is shown that arrays of single and paired nanorods can provide such negative refraction. For pairs of metal rods, a negative refractive index has been observed at 1.5 micrometer. The inverted structure of paired voids in metal films may also exhibit a negative refractive index. A similar effect can be accomplished with metal strips in which the refractive index can reach -2. The refractive index retrieval procedure and the critical role of light phases in determining the r…
The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wavevectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that: (i) negative (positive) refraction can arise even though the phase velocity is positive (negative); (ii) counterposition can arise in ins…
We theoretically show the negative refraction existing in Möbius molecules. The negative refractive index is induced by the non-trivial topology of the molecules. With the Möbius boundary condition, the effective electromagnetic fields felt by the electron in a Möbius ring is spatially inhomogeneous. In this regard, the $D_{N}$ symmetry is broken in Möbius molecules and thus the magnetic response is induced through the effective magnetic field. Our findings open up a new architecture for negative refractive index materials based on the non-trivial topology of Möbius molecules.
The Poggendorff illusion in its classical form of parallel lines interrupting a transversal is viewed from the perspective of being related to the everyday experience of observing the light refraction in water. It is argued that, if one considers a transversal to be a light ray in air and the parallel lines to form an occluding strip of a medium with the refractive index being between that of air and water, then one should be able to account, both qualitatively and quantitatively, for most of the features associated with the Poggendorff illusion. Statistical treatment of the visual experiments…
We discuss the feasibility of negative refraction with reduced absorption in coherently driven atomic media. Coherent coupling of an electric and a magnetic dipole transition by laser fields induces magneto-electric cross-coupling and negative refraction at dipole densities which are considerably smaller than necessary to achieve a negative permeability. At the same time the absorption gets minimized due to destructive quantum interference and the ratio of negative refraction index to absorption becomes orders of magnitude larger than in systems without coherent cross-coupling. The proposed sc…
A robust wedge setup is proposed to unambiguously demonstrate negative refraction for negative index metamaterials. We applied our setup to several optical metamaterials from the literature and distinctly observed the phenomena of negative refraction. This further consolidates the reported negative-index property. It is found there generally exists a lateral shift for the outgoing beam through the wedge. We derived a simple expression for calculating this beam shift and interestingly, it provides us a strategy to quantitatively estimate the loss of the wedge material (Im[n]). Addition- ally, w…
A type of 3-dimensional optical negative-refractive-index metamaterials composed of all dielectric nanospheres is proposed and demonstrated theoretically. The metamaterials are constructeded by pairing together two kinds of dielectric nanospheres as concentric shells embedded in a host medium. Mie-based extended effective theory shows that the dielectric core and the dielectric shell provide the negative permeability and the negative permittivity, respectively, both due to the strong Mie resonances. Within the coupled resonant frequency region, the negative index of refraction can be achieved.
Negative reflection and negative refraction are exotic phenomena that can be achieved by platforms such as double-negative metamaterial, hyperbolic metamaterial, and phase-discontinuity metasurface. Recently, natural biaxial van der Waals (vdW) materials, which support extremely anisotropic, low-loss, and highly confined polaritons from infrared to visible regime, are emerging as promising candidates for planar reflective and refractive optics. Here, we introduce three degrees of freedom, namely interface, crystal direction, and electric tunability to manipulate the reflection and refraction o…
Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electric field, emitted by the object surface, towards the image surface producing the same field distribution in both surfaces. In particular, a Dirac delta electric field in the object surface is focused without diffraction limit to the Dirac delta electric field in the image surface. The Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive r…
We show numerically for the first time that ultra-refractive phenomena do exist in one-dimensional photonic crystals: we exhibit the main features of ultra-refraction, that is the enlargement and the splitting of an incident beam. We give a very simple explanation of these phenomena in terms of the photonic band structure of these media.
We demonstrate that homogeneous naturally-occurring materials can form non-magnetic negative refractive index systems, and present specific realizations of the proposed approach for the THz and far-IR frequencies. The proposed structure operates away from resonance, thereby promising the capacity for low-loss devices.
Quantum optical techniques may yield immersion fluids with high indices of refraction without absorption. We describe one such technique in which a probe field experiences a large index of refraction with amplification rather than absorption, and examine its practicality for an immersion lithography application. Enhanced index can be observed in a three-level system with a tunable, near-resonant, coherent probe and incoherent pump field that inverts population of the probe transition. This observation contradicts the common belief that large indices of refraction are impossible without absorpt…
We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $Λ$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagat…
This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the validity of this method using the traditional spherical mirror and thin-lens Gaussian equations.
In light refraction between two transparent media, Snell's law describes the relationship between the incident angle and refraction angle. The refractive index is usually determined from Snell's law using the minimum deviation angle through a prism. A medium that partially absorbs light has complex permittivity (or permeability), and its refractive index has an imaginary part. Because of the imaginary part, Snell's law does not hold for light-absorbing media. Accordingly, other methods is required to determine the complex value of the refractive index in a light-absorbing medium. The exact sol…
We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been extensively studied and proposed as non-absorbing and isotropic metamaterials. We show that negative refraction, observed in ordered particle arrays, is due to diffraction and that an effective medium theory yields constitutive parameters that do not reproduce the observations in these composites, whose transmission also depends on the sample shape. This is fu…
We study the propagation of light in a three-dimensional double-periodic Ag/TiO2 multilayer metamaterial composed of coupled plasmonic waveguides operating in the visible and UV spectral range. For these frequencies, light propagation in the plane of the waveguides is described by a negative phase velocity, while for the orthogonal direction light propagation is described by a Bloch wave composed of a large number of harmonics. As a result, the material cannot generally be described by a single phase index: decomposing the Bloch wave into different harmonics we show that for the wavelength ran…
Recent results by Hoffman et al. showed that it is possible to build a Negative Refractive Material (NIM) by interleaving InGaAs/AlInAs using current nanofabrication technologies. Their findings provide the first experimental proof of a negative refractive semiconductor long posited by transformation optics. In this paper an overview on semiconductor refractive index theory and negative refraction is presented, focusing on the results of Hoffman et al. and the future of the subject based on the theory of Transformation Optics and its importance to tailor materials electrodynamics properties.
We investigate, in the probe limit, the negative refraction in the generalized superconductors with the Born-Infeld electrodynamics. We observe that the system has a negative Depine-Lakhtakia index in the superconducting phase at small frequencies and the greater the Born-Infeld corrections the larger the range of frequencies or the range of temperatures for which the negative refraction occurs. Furthermore, we find that the tunable Born-Infeld parameter can be used to improve the propagation of light in the holographic setup. Our analysis indicates that the Born-Infeld electrodynamics plays a…
Besides the well-known negative refraction, a negative refractive-index material can exhibit another two hallmark features, which are the inverse Doppler effect and backward Cherenkov radiation. The former is known as the motion-induced frequency shift that is contrary to the normal Doppler effect, and the latter refers to the Cherenkov radiation whose cone direction is opposite to the source's motion. Here we combine these two features and discuss the Doppler effect inside the backward Cherenkov cone. We reveal that the Doppler effect is not always inversed but can be normal in negative refra…
The physical origins of negative refractive index are derived from a dilute microscopic model, producing a result that is generalized to the dense condensed phase limit. In particular, scattering from a thin sheet of electric and magnetic dipoles driven above resonance is used to form a fundamental description for negative refraction. Of practical significance, loss and dispersion are implicit in the microscopic model. While naturally occurring negative index materials are unavailable, ferromagnetic and ferroelectric materials provide device design opportunities.
We examine the response of a plane wave incident on a flat surface of a medium characterized by simultaneously negative electric and magnetic susceptibilities by solving Maxwell's equations explicitly and without making any assumptions on the way. In the literature up to date, it has been assumed that negative refractive materials are necessarily frequency dispersive. We propose an alternative to this assumption by suggesting that the requirement of positive energy density should be relaxed, and discuss the implications of such a proposal. More specifically, we show that once negative energy s…
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial inhomogeneous composite. Measuring the complex transmission and reflection coefficients is one of the most rigorous ways to obtain this parameter. We dispute Grigorenko's statement (Optics Letters 31, 2483 (2006)) that measuring only the reflection intensity spectrum is sufficient for determining the effective refractive index. We discuss fundamental drawbacks of …
Optically tunable linear and nonlinear enhancement of index of refraction
Institute of Nuclear Sciences, Hacettepe University（哈克特佩大学核科学研究所）；Department of Nanotechnology and Nanomedicine, Graduate School of Science and Engineering, Hacettepe University（哈克特佩大学理工研究生院纳米技术与纳米医学系）；Department of Physics, Akdeniz University（安塔利亚地中海大学物理系）；Türkiye National Observatories, TUG（土耳其国家天文台）；Department of Nanoscience and Nanotechnology, Faculty of Arts and Science, Burdur Mehmet Akif Ersoy University（布尔杜尔穆罕默德阿基夫埃尔索伊大学文理学院纳米科学与纳米技术系）
We develop an approach to use nanostructured plasmonic materials as a non-magnetic negative-refractive index system at optical and near-infrared frequencies. In contrast to conventional negative refraction materials, our design does not require periodicity and thus is highly tolerant to fabrication defects. Moreover, since the proposed materials are intrinsically non-magnetic, their performance is not limited to proximity of a resonance so that the resulting structure has relatively low loss. We develop the analytical description of the relevant electromagnetic phenomena and justify our analyt…
We study linear guided waves propagating in a slab waveguide made of a negative-refraction- index material, the so-called left-handed waveguide. We reveal that the guided waves in left-handed waveguides possess a number of peculiar properties, such as the absence of the fundamental modes, mode double degeneracy, and sign-varying energy ux. In particular, we predict the existence of novel types of guided waves with a dipole-vortex structure of the Pointing vector.
