Based on boundary condition and dispersion relation, the superluminal group velocity in an anisotropic metamaterial (AMM) is investigated. The superluminal propagation is induced by the hyperbolic dispersion relation associated with the AMM. It is shown that a modulated Gaussian beam exhibits a superluminal group velocity which depends on the choice of incident angles and optical axis angles. The superluminal propagation does not violate the theory of special relativity because the group velocity is the velocity of the peak of the localized wave packet which does not carry information. It is proposed that a triglycine sulfate (TGS) crystal can be designed and the superluminal group velocity can be measured experimentally.
The energy propagation of electromagnetic fields in the effective medium of a one-dimensional photonic crystal consisting of dielectric and metallic layers is investigated. We show that the medium behaves like Drude and Lorentz medium, respectively, when the electric field is parallel and perpendicular to the layers. For arbitrary time-varying electromagnetic fields in this medium, the energy density formula is derived. We prove rigorously that the group velocity of any propagating mode obeying the hyperbolic dispersion must be slower than the speed of light in vacuum, taking into account the …
We propose a leaky optical waveguide achieved with a uniaxially anisotropic metamaterial that supports both forward and backward leaky waves. The backward leaky nature is exploited in a sub-diffraction imaging system.
We study metamaterials with an anisotropic effective permittivity tensor in which one component is near zero. We find that such an anisotropic metamaterial can be used to control wave propagation and construct almost perfect bending waveguides with a high transmission rate (>95%). This interesting effect originates in the power flow redistribution by the surface waves on the input and output interfaces, which smoothly matches with the propagating modes inside the metamaterial waveguide. We also find that waves in such anisotropic epsilon-near-zero materials can be reflected by small-sized perf…
Metal-dielectric multilayer metamaterials with extreme loss-anisotropy, in which the longitudinal component of the permittivity tensor has ultra-large imaginary part, are proposed and designed. Diffraction-free deep subwavelength beam propagation and manipulation, due to the nearly flat iso-frequency contour (IFC), is demonstrated in such loss-anisotropic metamaterials. It is also shown that deep subwavelength beam propagation can be realized in practical multilayer structures with large multilayer period, when the nonlocal effect is considered.
We verify the extraordinary transmission enhancement and collimation induced by the material loss in anisotropic near-zero permittivity (ENZ) metamaterials, and reveal the physical mechanism of this exotic electromagnetic phenomenon via the iso-frequency contour (IFC) analysis. In addition, we demonstrate the possibility in realization of such loss enhanced transmission of Gaussian beam in realistic silver-germanium multilayered structures by applying full-wave numerical simulations.
We demonstrate that metamaterial devices requiring anisotropic dielectric permittivity and magnetic permeability may be emulated by specially designed tapered waveguides. This approach leads to low-loss, broadband performance. Based on this technique, we demonstrate broadband electromagnetic cloaking in the visible frequency range on a scale ~100 times larger than the wavelength.
Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a metamaterial may be realized quite simply as a random mixture of electrically small (possibly nanoscale) spheroidal particles of at least two different isotropic dielectric materials, one of which must be dissipative but the other active. The dielectric properties of this metamaterial are influenced by the volume fraction, spatial distribution, particle shape and siz…
Based on the Ewald-Oseen extinction theorem, the omnidirectional total transmission of waves incident from vacuum into an anisotropic dielectric-magnetic metamaterials is investigated. It is shown that the omnidirectional total transmission need not limit at the interface associated with the conventional nonmagnetic anisotropic medium. The recent advent of a new class of anisotropic dielectric-magnetic matermaterial make the omnidirectional total transmission become available. It is found that the inherent physics underlying the omnidirectional total transmission are collective contributions o…
We present the blueprint for a novel negative-index metamaterial. This structure is fabricated via three-dimensional two-photon direct laser writing and silver shadow evaporation. The comparison of measured linear optical spectra with theory shows good agreement and reveals a negative real part of the refractive index at around 3.85 micrometer wavelength - despite the fact that the metamaterial structure is bi-anisotropic due to the lack of inversion symmetry along its surface normal.
Internal physical structure can drastically modify the properties of waveguides: photonic crystal fibers are able to confine light inside a hollow air core by Bragg scattering from a periodic array of holes, while metamaterial loaded waveguides for microwaves can support propagation at frequencies well below cutoff. Anisotropic metamaterials assembled into cylindrically symmetric geometries constitute light-guiding structures that support new kinds of exotic modes. A microtube of anodized nanoporous alumina, with nanopores radially emanating from the inner wall to the outer surface, is a manif…
We study theoretically the effect of ultraslow phase and group velocities in an anisotropic metamaterial. The ultraslow phase propagation is induced by the hyperbolic dispersion relation. While the inherent physics underlying the slow group velocity are collective operations of the frequency and spatial dispersion. We show that a Gaussian wave packet exhibits simultaneous slow phase and group velocities which depend on the choice of incident angles and principal axis angles. The anisotrocpic metamaterial slab can be constructed and the ultraslow phase and group velocities can be measured exper…
We present a detailed study of oscillating modes in a slab waveguide with air core and anisotropic metamaterial cladding. It is shown that, under specific dielectric configurations, slow and even stopped electromagnetic wave can be supported by such an air waveguide. We propose a linearly tapped waveguide structure that could lead the propagating light to a complete standstill. Both the theoretical analysis and the proposed waveguide have been validated by full-wave simulation based on finite-difference time-domain method.
We develop an approach to utilize anisotropic metamaterials to solve one of the fundamental problems of modern plasmonics -- parasitic scattering of surface waves into free-space modes, opening the road to truly two-dimensional plasmonic optics. We illustrate the developed formalism on examples of plasmonic refractor and plasmonic crystal, and discuss limitations of the developed technique and its possible applications for sensing and imaging structures, high-performance mode couplers, optical cloaking structures, and dynamically reconfigurable electro-plasmonic circuits.
We present an ultra broadband thin-film infrared absorber made of saw-toothed anisotropic metamaterial. Absorbtivity of higher than 95% at normal incidence is supported in a wide range of frequencies, where the full absorption width at half maximum is about 86%. Such property is retained well at a very wide range of incident angles too. Light of shorter wavelengths are harvested at upper parts of the sawteeth of smaller widths, while light of longer wavelengths are trapped at lower parts of larger tooth widths. This phenomenon is explained by the slowlight modes in anisotropic metamaterial wav…
Using a multiple scattering technique, we derived closed-form expressions for effective constitutive parameters and electro/magneto-strictive tensor components for 2D bi-anisotropic metamaterials. Using the principle of virtual work, we obtained the electromagnetic stress tensor that can be used to calculate the optical force density inside such media. The analytic expressions are tested against full wave numerical simulations. Our effective medium theory is essential for providing a complete macroscopic description of the optical and opto-mechanical properties of bi-anisotropic composites.
We investigate the emission of electromagnetic waves from biaxial subwavelength metamaterials. For tunable anisotropic structures that exhibit a vanishing dielectric response along a given axis, we find remarkable variation in the launch angles of energy associated with the emission of leaky wave radiation. We write closed form expressions for the energy transport velocity and corresponding radiation angle $ϕ$, defining the cone of radiation emission, both as a functions of frequency, and material and geometrical parameters. Full wave simulations exemplify the broad range of directivity that c…
The behavior of strongly coupled Radial Photonic Crystals shells is investigated as a potential alternative to transfer electromagnetic energy wirelessly. These sub-wavelength resonant microstructures, which are based on anisotropic metamaterials, can produce efficient coupling phenomena due to their high quality factor. A configuration of selected constitutive parameters (permittivity and permeability) is analyzed in terms of its resonant characteristics. The coupling to loss ratio between two coupled resonators is calculated as a function of distance, the maximum (in excess of 300) is obtain…
Extremely anisotropic metal-dielectric multilayer metamaterials are designed to have the effective permittivity tensor of a transverse component (parallel to the interfaces of the multilayer) with zero real part and a longitudinal component (normal to the interfaces of the multilayer) with ultra-large imaginary part at the same wavelength, including the optical nonlocality analysis based on the transfer-matrix method. The diffraction-free deep-subwavelength optical beam propagation with near-zero phase variation in the designed multilayer stack due to the near-flat iso-frequency contour is dem…
We present a technique capable of producing subwavelength focal spots in the far-field of the source in planar non-resonant structures. The approach combines the diffraction gratings that generate the high-wavevector-number modes and planar slabs of homogeneous anisotropic metamaterials that propagate these waves and combine them at the subwavelength focal spots. In a sense, the technique combines the benefits of Fresnel lens, near-field zone plates, hyperlens, and superlens, and at the same time resolves their fundamental limitations. Several realizations of the proposed technique for visible…
In this article, it has been theoretically shown that broad angle negative refraction is possible with asymmetric anisotropic metamaterials constructed by only dielectrics or loss less semiconductors at the telecommunication and relative wavelength range. Though natural uniaxial materials can exhibit negative refraction, the maximum angle of negative refraction and critical incident angle lie in a very narrow range. This notable problem can be overcome by our proposed structure. In our structures, negative refraction originates from the highly asymmetric elliptical iso-frequency.This is artifi…
This paper presents experimental verification of below-cutoff transmission through miniaturized waveguides whose interior is coated with a thin anisotropic metamaterial liner possessing epsilon-negative and near-zero (ENNZ) properties. These liners are realized using a simple, printed-circuit implementation based on inductively loaded wires, and introduce an HE$_{11}$ mode well below the natural cutoff frequency. The inclusion of the liner is shown to substantially improve the transmission between two embedded shielded-loop sources. A homogenization scheme is developed to characterize the line…
The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amph…
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…
Black phosphorus (BP) as a promising two-dimensional material with extraordinary optical properties constitutes an excellent building block in multilayer hyperbolic metamaterials. In this work, we design a multilayer structure composed of BP/dielectric layer stacking unit cells patterned on a gold mirror and theoretically demonstrate the tunable anisotropic absorption in the infrared regime. The electric dipole resonance between the adjacent unit cells drives the structure in the critical coupling state, and impedance of the structure matches to that of free space, showing the perfect absorpti…
Plasmonic beam collimation effect has been thoroughly investigated based on the well-known nanometer-scale bull's eye structure formed by complex and high-cost fabrication processes. In this work, we report our effort for attaining beam collimation using an anisotropic metamaterial (AMM) slab that consists of a stack of alternating metal/dielectric layers and an integrated top metal grating. The results show that AMM slab allows creating the beam collimation effect similar to that of the bull's eye structure, an enabling technology for practical application due to its simple architecture and c…
Metamaterials based on effective media have achieved a lot of unusual physics (e.g. negative refraction and invisibility cloaking) owing to their abilities to tailor the effective medium parameters that do not exist in nature. Recently, coding metamaterials have been suggested to control electromagnetic waves by designing the coding sequences of digital elements '0' and '1', which possess opposite phase responses. Here, we propose the concept of anisotropic coding metamaterial at terahertz frequencies, in which coding behaviors in different directions are dependent on the polarization status o…
We present an effective medium theory that can predict the effective permittivity and permeability of a geometrically anisotropic two-dimensional metamaterial composed with a rectangular array of elliptical cylinders. It is possible to obtain a closed-form analytical solution for the anisotropic effective medium parameters if the aspect ratio of the lattice and the eccentricity of elliptical cylinder satisfy certain conditions. The derived effective medium theory can recover the well-known Maxwell-Garnett results in the quasi-static regime. More importantly, it is valid beyond the long-wavelen…
In this article, a few-layered graphene-dielectric multilayer (metamaterial) electro-optic modulator has been proposed in the mid and far infrared range that works on electro-absorption mechanism. Graphene, both mono layer and few layer, is an actively tunable optical material that allows control of inter-band and intra-band transition by tuning its chemical potential. Utilizing this unique feature of graphene, we propose a multilayer graphene dielectric stack where few layer graphene is preferred over mono layer graphene. Although the total thickness of the stack still remains in the nanomete…
Multimode interference couplers are a fundamental building block in many integrated photonic systems, ranging from high-speed coherent receivers to quantum splitters. However, their basic structure has remained fundamentally unchanged for almost four decades, limiting their size and operation bandwidth. Using sub-wavelength metamaterials, photonic devices with break-through size and performance have been recently reported. Leveraging the inherent anisotropy of these structures, here we derive a semi-analytic expression that enables the design of compact and ultra broadband multimode interferen…
We theoretically demonstrate the strong Purcell effect in $\varepsilon$-near-zero ultra-anisotropic uniaxial metamaterials with elliptic isofrequency surface. Contrary to the hyperbolic metamaterials, the effect does not rely on the diverging density of states and evanescent waves. As a result, both the radiative decay rate and the far-field emission power are enhanced. The effect can be realized in the periodic layered metal-dielectric nanostructures with complex unit cell containing two different metallic layers.
To design a uniaxial anisotropic metamaterial a layered cylindrical metamaterial is introduced for TE polarization. Unlike to the previous work, which the layers were in radial direction, here the layers are in azimuthal direction. Scattering efficiency for this metamaterial in different frequency is analyzed with solving Maxwell's wave equation. It is observed that in some frequencies when the effective permittivity of the structure goes to zero the scattering efficiency would be negligible. This result approves the previous predictions. It is also found out that the scattering cancellation d…
We show that anisotropic negative effective dispersion relation can be achieved in pure dielectric rod-type metamaterials by turning from the symmetry of a square lattice to that of a rectangular one, i.e. by breaking the rotation symmetry of effective homogeneous medium. Theoretical predictions and conclusions are verified by both numerical calculations and computer based simulations. The proposed anisotropic metamaterial, is used to construct a refocusing slab-lens and a subdiffraction hyperlens. The all-dielectric origin makes it more straightforward to address loss and scaling, two major i…
Propagation of light in a metamaterial medium which mimics curved spacetime and acts like a black hole is studied. We show that for a particular type of spacetimes and wave polarization, the time dilation appears as dielectric permittivity, while the spatial curvature manifests as magnetic permeability. The optical analogue to the relativistic Hamiltonian which determines the ray paths (null geodesics) in the anisotropic metamaterial is obtained. By applying the formalism to the Schwarzschild metric, we compare the ray paths with full-wave simulations in the equivalent optical medium.
The trapped rainbow effect has been mostly found on tapered anisotropic metamaterials (MMs) made of low loss noble metals, such as gold, silver, etc. In this work, we demonstrate that an anisotropic MM waveguide made of high loss metal tungsten can also support the trapped rainbow effect similar to the noble metal based structure. We show theoretically that an array of tungsten/germanium anisotropic nano-cones placed on top of a reflective substrate can absorb light at the wavelength range from 0.3 micrometer to 9 micrometer with an average absorption efficiency approaching 98%. It is found th…
We demonstrate how broadband angular selectivity can be achieved with stacks of one-dimensionally periodic photonic crystals, each consisting of alternating isotropic layers and effective anisotropic layers, where each effective anisotropic layer is constructed from a multilayered metamaterial. We show that by simply changing the structure of the metamaterials, the selective angle can be tuned to a broad range of angles; and, by increasing the number of stacks, the angular transmission window can be made as narrow as desired. As a proof of principle, we realize the idea experimentally in the m…
Forward models for the Mueller Matrix (MM) components of materials with relative magnetic permeability tensor μ \neq 1 are studied. 4x4 matrix formalism is employed to produce general solutions for the complex reflection coefficients and MMs of dielectric-magnetic materials having arbitrary crystal symmetry and arbitrary laboratory orientation. For certain orientations of materials with simultaneously diagonalizable ε and μ tensors (with coincident principal axes), analytic solutions to the Berreman equation are available. For the single layer thin film configuration of these materials, analyt…
We study the main nonlinear solutions of plasmonic slot waveguides made from an anisotropic metamaterial core with a positive Kerr-type nonlinearity surrounded by two semi-infinite metal regions. First, we demonstrate that for a highly anisotropic diagonal elliptical core, the bifurcation threshold of the asymmetric mode is reduced from GW/m threshold for the isotropic case to 50 MW/m one indicating a strong enhancement of the spatial nonlinear effects, and that the slope of the dispersion curve of the asymmetric mode stays positive, at least near the bifurcation, suggesting a stable mode. Sec…
We show that asymmetric transmission for linear polarizations can be easily achieved by a monolayer of anisotropic chiral metamolecules through the constructive and destructive interferences between the contributions from anisotropy and chirality. Our analysis is based on the interaction of electromagnetic waves with the constituent electric and magnetic dipoles of the metamaterials, and an effective medium formulation. In addition, asymmetric transmission in amplitude can be effectively controlled by the interference between spectrally detuned resonances. Our findings shed light on the design…
Anisotropic and inhomogeneous metamaterial shells are studied in order to exploit all their resonant mode richness. These multilayer structures are based on a cylindrical distribution of radially dependent constitutive parameters including an inner void cavity. Shell, cavity and whispering gallery modes are characterized, and special attention is paid to the latter ones. The whispering gallery modes are created at the boundary layers of the shell with the background and energy localization is produced with highly radiative characteristics. These low-Q resonant states have frequencies that are …
We investigate the wave propagation in the anisotropic metamaterial with single-sheeted hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves can exhibit the same single-sheeted hyperboloid or straight dispersion relation, while the two polarized waves exhibit dif…
Based on the concept of sub-wavelength imaging through compensated bilayer of anisotropic metamaterials (AMMs), which is an expansion of the perfect lens configuration, we propose two dimensional prism pair structures of compensated AMMs that are capable of manipulating two dimensional sub-wavelength images. We demonstrate that through properly designed symmetric and asymmetric compensated prism pair structures planar image rotation with arbitrary angle, lateral image shift, as well as image magnification could be achieved with sub-wavelength resolution. Both theoretical analysis and full wave…
We investigate the ab-initio homogenization of separable metamaterials with factorized dielectric permittivity profile which can be achieved through suitable grey-scale permittivity design techniques. Separability allows such metamaterials to be physically regarded as the superposition of three fictitious 1D generating media. We prove that, in the long-wavelength limit, separable metamaterials admit simple and analytical description of their electromagnetic bi-anisotropic response which can be reconstructed from the properties of the 1D generating media. Our approach provides a strategy which …
We demonstrate that use of the field effect to tune the effective optical parameters of a layered hyperbolic metamaterial leads to topological transitions in its dispersion characteristics in the optical regime. Field effect gating electrically modulates the permittivity in transparent conductive oxides via changes in the carrier density. These permittivity changes lead to active extreme modulation of ~200% of the effective electromagnetic parameters along with active control of the anisotropic dispersion surface of hyperbolic metamaterials and enable the opening and closing of photonic band g…
Exact solutions are obtained for all the modes of wave propagation along an anisotropic cylindrical waveguide. Closed-form expressions for the energy flow on the waveguide are also derived. For extremely anisotropic waveguide where the transverse permittivity is negative while the longitudinal permittivity is positive, only transverse magnetic (TM) and hybrid modes will propagate on the waveguide. At any given frequency the waveguide supports an infinite number of eigenmodes. Among the TM modes, at most only one mode is forward wave. The rest of them are backward waves which can have very larg…
Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order seems to be uncommon except in small-band-gap semiconductors with strong spin-orbit interactions. In this Article we show that artificial electromagnetic structures, known as metamaterials, provide an attractive platform for designing photonic analogues of topological insulators. We demonstrate that a judicious choice of the metamaterial parameters can crea…
Based on the dyadic Green's function (DGF) method, we present a formalism to study the propagation of electromagnetic fields with slowly varying amplitude (EMFSVA) in dispersive anisotropic media with two dyadic constitutive parameters, the dielectric permittivity and the magnetic permeability. We find the matrix elements of the envelope DGFs by applying the formalism for uniaxial anisotropic metamaterials. We present the relations for the velocity of the EMFSVA envelopes which agree with the known definition of the group velocity in dispersive media. We consider examples of propagation of the…
In this article, a 2D plasmonic waveguide loaded with all dielectric anisotropic metamaterial, consisting of alternative layers of Si-SiO2, has been theoretically proposed and numerically analyzed. Main characteristics of waveguide i.e. propagation constant, propagation length and normalized mode area have been calculated for different values of ridge width and height at telecommunication wavelength. The respective 1D structure of the waveguide has been analytically solved for the anisotropic ridge as a single uniaxial medium with dielectric tensor defined by Effective Medium Theory (EMT). The…
In this paper we reveal the physics behind the formation of tri- and tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric coupling and describe the anti-crossing splitting phenomenon in the hyperbolic dispersion which arises due to the hybridization of the plasmonic and magnetic Bloch high-k polaritons. This considerably deepens the understanding of the high-k polaritons and the topology of the optical iso-frequency surfaces in k-space and will find applications in optical nano-resolution imaging and emission rate and directivity control. To accomplish this, we develop …
We derive an exact expression for the time-averaged electromagnetic energy inside a chiral dispersive sphere irradiated by a plane wave. The dispersion relations correspond to a chiral metamaterial consisting of uncoupled single-resonance helical resonators. Using a field decomposition scheme and a general expression for the electromagnetic energy density in bi-anisotropic media, we calculate the Lorenz-Mie solution for the internal fields in a medium that is simultaneously magnetic and chiral. We also obtain an explicit analytical relation between the internal electromagnetic field and the ab…
Additional electromagnetic waves and additional boundary conditions (ABCs) in non-local materials attracted a lot of attention in the past. Here we report the possibility of additional propagating and evanescent waves in local anisotropic and bi-anisotropic linear materials. We investigate the possible options for ABCs and describe how to complement the conventional 4 Maxwells boundary conditions in the situations when there are more than 4 waves that need to be matched at the boundary of local and linear quartic metamaterials. We show that these ABCs must depend on the properties of the inter…
The use of metamaterial as a way to mitigate the negative effects of absorption in metals on the Purcell effect in metal-dielectric structures is investigated. A layered metal-dielectric structure is considered as an anisotropic medium in the long-wavelength limit. The dispersion of the surface plasmon appearing at the boundary between such a structure and a different dielectric material, as well as the position of the peak in the local density of states are studied for various combinations of materials and filling factors of the periodic structure. The calculated frequency dependence of the P…
High-index dielectrics can confine light into nano-scale leading to enhanced nonlinear response. However, increased momentum in these media can deteriorate the overlap between different harmonics which hinders efficient nonlinear interaction in wavelength-scale resonators in the absence of momentum matching. Here, we propose an alternative approach for light confinement in anisotropic particles. The extra degree of freedom in anisotropic media allows us to control the evanescent waves near the center and the radial momentum away from the center, independently. This can lead to a strong light c…
We analyze spectrum of waveguide modes of an arbitrary uniaxial anisotropic metamaterial slab with non-local electromagnetic response whose permittivity tensor could be described within Drude approximation. Spatial dispersion was introduced within the hydrodynamical model. Both anisotropy and spatial dispersion were considered as perturbations. This helps to distinguish their effect on the spectrum of the slab and to analyze lifting of the degeneracy of eigenmodes at plasma frequency in detail. Spatial dispersion is shown to result in break of the singularity in the den- sity of optical states…
