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We quantize the macroscopic electromagnetic field in a system of non-dispersive polarizable bodies moving at constant velocities possibly exceeding the Cherenkov threshold. It is shown that in general the quantized system is unstable and neither has a ground state nor supports stationary states. The quantized Hamiltonian is written in terms of quantum harmonic oscillators associated with both positive and negative frequencies, such that the oscillators associated with symmetric frequencies are coupled by an interaction term that does not preserve the quantum occupation numbers. Moreover, in the linear regime the amplitudes of the fields may grow without limit provided the velocity of the moving bodies is enforced to be constant. This requires the application of an external mechanical force that effectively pumps the system., Comment: 52 pages, under review

We characterize the spatial optical solitons supported by arrays of metallic nanowires embedded in Kerr-type material. The array of nanowires is described using an effective medium model and is regarded as a continuous medium. It is shown that the conditions necessary for the formation of spatial-solitons are radically different in presence of the nanowires, and in particular within the effective medium model spatial-solitons are allowed in the nanowire material only in case the host material is a "self-defocusing" material. It is proven that the characteristic soliton beamwidth is related to the degree of hyperbolicity of the isofrequency surfaces of the photonic states, and that a sufficiently strong electric field amplitude may enable subwavelength solitary waves., Comment: 27 pages

We derive an effective medium model to characterize the macroscopic electromagnetic response of metallic nanowire arrays embedded in a host dielectric with a Kerr-type nonlinear permittivity function. It is shown that the macroscopic electromagnetic fields are coupled to the conduction current in the nanowires and to an additional quasi-static potential through a system of nonlinear equations. We prove that a weak nonlinearity leads to an electromagnetic response closer to that of an indefinite medium, and to isofrequency contours with increased hyperbolicity. For high-field intensities the negative refraction of electromagnetic waves at an air nanowire material interface is enhanced when the nanowires are embedded in a self-focusing Kerr medium., Comment: 43 pages in press (to appear in Phys. Rev. B)

The speed of integrated circuits is ultimately limited by the mobility of electrons or holes, which depend on the effective mass in a semiconductor. Here, building on an analogy with electromagnetic metamaterials and transformation optics, we describe a new transport regime in a semiconductor superlattice characterized by extreme anisotropy of the effective mass and a low intrinsic resistance to movement - with zero effective mass - along some preferred direction of electron motion. We theoretically demonstrate that such regime may permit an ultra fast, extremely strong electron response, and significantly high conductivity, which, notably may be weakly dependent on the temperature at low temperatures. These ideas may pave the way for faster electronic devices and detectors and new functional materials with a strong electrical response in the infrared regime., Comment: under review since Dec. 2011

Based on an analogy with electromagnetic metamaterials, we develop an effective medium description for the propagation of electron matter waves in bulk semiconductors with a zincblende structure. It is formally demonstrated that even though departing from a different starting point, our theory gives results for the energy stationary states consistent with Bastard's envelope function approximation in the long-wavelength limit. Using the proposed approach, we discuss the time evolution of a wave packet in a bulk semiconductor with a zero-gap and linear energy-momentum dispersion., Comment: 43 pages, 4 figures

In media with strong spatial dispersion the electric displacement vector and the electric field are typically linked by a partial differential equation in the bulk region. The objective of this work is to highlight that in the vicinity of an interface the relation between the macroscopic fields cannot be univocally determined from the bulk response of the involved materials, but requires instead the knowledge of internal degrees of freedom of the materials. We derive such relation for the particular case of "wire media", and describe a numerical formalism that enables characterizing the electromagnetic response of arbitrarily shaped spatially dispersive bodies formed by arrays of crossed wires. The possibility of concentrating the electromagnetic field in a narrow spot by tapering a metamaterial waveguide is discussed., Comment: 34 pages, 10 figures

We develop an effective medium approach to characterize the propagation of matter waves in periodic structures, such as graphene or semiconductor superlattices. It is proven that the time evolution of the states that are not more localized in space than the characteristic period of the structure can be described exactly through an effective Hamiltonian, and that the electronic band structure of the system can be exactly determined from the effective Hamiltonian. As an illustration of the application of the method, we characterize the mesoscopic response of graphene superlattices. It is shown that these structures may be described using simply two effective parameters: a dispersive potential, and an anisotropy tensor that characterizes the pseudospin. Our model predicts that a graphene superlattice characterized by an indefinite anisotropy tensor - such that the eigenvalues of the tensor have opposite signs - may permit the perfect tunneling of all the stationary states with a specific value of the energy when it is paired with a dual graphene superlattice with positive definite anisotropy tensor., Comment: 36 pages

We investigate the radiation properties of two types of elementary sources embedded in a uniaxial wire medium: a short dipole parallel to the wires and a lumped voltage source connected across a gap in a generic metallic wire. It is demonstrated that the radiation pattern of these elementary sources have quite anomalous and unusual properties. Specifically, the radiation pattern of a short vertical dipole resembles that of an isotropic radiator close to the effective plasma frequency of the wire medium, whereas the radiation from the lumped voltage generator is characterized by an infinite directivity and a non-diffractive far-field distribution., Comment: 10 pages, 4 figures

Here, we investigate the physical mechanisms that may enable squeezing a complex electromagnetic field distribution through a narrow and/or partially obstructed region with little amplitude and phase distortions. Following our recent works, such field manipulations may be made possible by a procedure in which the incoming wave is first "sampled" "pixel by pixel" using an array of metallic waveguides, and in a second step the energy corresponding to each individual pixel is "squeezed" through a very narrow channel filled with a permittivity-near zero material. In this work, we study in detail these processes in scenarios where the electromagnetic wave is compressed along a single direction of space, and present theoretical models that enable the analytical modeling of such phenomena. Full-wave results obtained with an electromagnetic simulator, demonstrate the possibility of compressing an incoming wave several folds through ultranarrow channels filled with silicon carbide. The "sampling and squeezing" concept may enable unparalleled control of electromagnetic waves in the nanoscale.

A simple quasi-static model applicable to a wide class of wire media is developed that explains strong non-locality in the dielectric response of wire media in clear physical terms of effective inductance and capacitance per unit length of a wire. The model is checked against known solutions and found to be in excellent agreement with the results obtained by much more sophisticated analytical and numerical methods. Special attention is given to suppression of the spatial dispersion effects in wire media., Comment: 22 pagees, 4 figures

Here, we report a numerical implementation of the nonlocal homogenization approach recently proposed in [M. Silveirinha, Phys. Rev. B 75, 115104 (2007)], using the finite difference frequency-domain method to discretize the Maxwell-Equations. We apply the developed formalism to characterize the nonlocal dielectric function of several structured materials formed by dielectric and metallic particles, and in particular, we extract the local permittivity, permeability and magnetoelectric coupling parameters when these are meaningful. It is shown that the finite differences frequency domain implementation of the homogenization method is stable and robust, yielding very accurate results.

Several recent works have emphasized the role of spatial dispersion in wire media, and demonstrated that arrays of parallel metallic wires may behave very differently from a uniaxial local material with negative permittivity. Here, we investigate using local and non-local homogenization methods the effect of spatial dispersion on reflection from the mushroom structure introduced by Sievenpiper. The objective of the paper is to clarify the role of spatial dispersion in the mushroom structure and demonstrate that under some conditions it is suppressed. The metamaterial substrate, or metasurface, is modeled as a wire medium covered with an impedance surface. Surprisingly, it is found that in such configuration the effects of spatial dispersion may be nearly suppressed when the slab is electrically thin, and that the wire medium can be modeled very accurately using a local model. This result paves the way for the design of artificial surfaces that exploit the plasmonic-type response of the wire medium slab., Comment: submitted for publication, under review

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., Comment: 2 pages, an updated version with results of numerical simulations confirming our statements

Following our recent interest in metamaterial-based devices supporting resonant tunneling, energy squeezing and supercoupling through narrow waveguide channels and bends, here we analyze the fundamental physical mechanisms behind this phenomenon using a transmission-line model. These theoretical findings extend our theory, allowing us to take fully into account frequency dispersion and losses and revealing the substantial differences between this unique tunneling phenomenon and higher-frequency Fabry-Perot resonances. Moreover, they represent the foundations for other possibilities to realize tunneling through arbitrary waveguide bends, both in E and H planes of polarization, waveguide connections and sharp abruptions and to obtain analogous effects with geometries arguably simpler to realize., Comment: 35 pages, 9 figures

Following our recent theoretical and experimental results that show how zero-permittivity metamaterials may provide anomalous tunneling and energy squeezing through ultranarrow waveguide channels, here we report an experimental investigation of the bending features relative to this counterintuitive resonant effect. We generate the required effectively-zero permittivity using a waveguide operating at the cut-off of its dominant mode, and we show how sharp and narrow bends may be inserted within the propagation channel without causing any sensible reflection or loss., Comment: 13 pages, 6 figures

In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional boundary condition is considered. The additional boundary condition is derived by taking into account the specific microstructure of the wire medium. To illustrate the application of the result, we characterize a substrate formed by an array of tilted metallic wires connected to a ground plane, demonstrating that in such configuration the wire medium behaves essentially as a material with extreme optical anisotropy and that in some circumstances the substrate can be seen as an impedance surface., Comment: 26 pages; under review

In this work, we investigate the detailed theory of the supercoupling, anomalous tunneling effect, and field confinement originally identified in [M. Silveirinha, N. Engheta, Phys. Rev. Lett. 97, 157403, (2006)], where we demonstrated the possibility of using materials with permittivity near zero to drastically improve the transmission of electromagnetic energy through a narrow irregular channel with very subwavelength transverse cross-section. Here, we present additional physical insights, describe new applications of the tunneling effect in relevant waveguide scenarios (e.g., the "perfect" or "super" waveguide coupling), study the effect of metal losses in the metallic walls, and the possibility of using epsilon-near zero materials to confine energy in a subwavelength cavity with gigantic field enhancement. In addition, we systematically study the propagation of electromagnetic waves through narrow channels filled with anisotropic epsilon-near zero materials. It is demonstrated that these materials may have interesting potentials, and that for some particular geometries the reflectivity of the channel is independent of the specific dimensions or parameters of epsilon-near zero transition. We also describe several realistic metamaterial implementations of the studied problems, based on standard metallic waveguides, microstrip line configurations, and wire media., Comment: under review

Following our recent idea of using plasmonic and non-plasmonic nanoparticles as nanoinductors and nanocapacitors in the infrared and optical domains [N. Engheta, A. Salandrino, and A. Alu, Phys. Rev. Letts., Vol. 95, 095504, (2005)], in this work we analyze in detail some complex circuit configurations involving series and parallel combinations of these lumped nanocircuit elements at optical frequencies. Using numerical simulations, it is demonstrated that, after a proper design, the behavior of these nanoelements may closely mimic that of their lower frequency (i.e., radio frequency (RF) and microwave) counterparts, even in relatively complex configurations. In addition, we analyze here in detail the concepts of nanoinsulators and nanoconnectors in the optical domain, demonstrating how these components may be crucial in minimizing the coupling between adjacent optical nanocircuit elements and in properly connecting different branches of the nanocircuit. The unit nanomodules for lumped nanoelements are introduced as building blocks for more complex nanocircuits at optical frequencies. Numerical simulations of some complex circuit scenarios considering the frequency response of these nanocircuits are presented and discussed in details, showing how practical applications of such optical nanocircuit concepts may indeed be feasible within the current limits of nanotechnology., Comment: under review

In this work, we study the realization of realistic polarization transformers formed by long metallic helices. To this end, we propose a new homogenization model to characterize the propagation of electromagnetic waves in medium formed by infinitely long helices. We derive approximate analytical expressions for the effective permittivity, effective permeability and the magnetoelectric tensor of the composite material, taking into account the effects of spatial dispersion. We apply the new homogenization model to characterize novel linear-to-circular polarization transformers. Our results show that the metamaterial screen may be designed in such a way that an incoming linearly polarized wave may be transformed into a circularly polarized transmitted wave, and that the transmission efficiency of such polarization transformer may be as high as 95%. The theoretical results are supported by full wave simulations., Comment: 43 pages

In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the effects of frequency dispersion, magneto-electric coupling, and spatial dispersion, even in frequency band-gaps or when the materials are lossy. We formulate a homogenization problem to characterize a generic microstructured artificial material, and demonstrate that it is equivalent to an integral-differential system. We prove that this complex system can be reduced to a standard integral equation and solved using standard methods. To illustrate the application of the proposed method, we homogenize several important metamaterial configurations involving split ring resonators and metallic wires., Comment: 44 pages - Physical Review B (2007) (in press)

In this work, we study the electrodynamics of metamaterials that consist of resonant non-magnetic inclusions embedded in an epsilon-near-zero (ENZ) host medium. It is shown that the inclusions can be designed in such a way that both the effective permittivity and permeability of the composite structure are simultaneously zero. Two different metamaterial configurations are studied and analyzed in detail. For a particular class of problems, it is analytically proven that such matched zero-index metamaterials may help improving the transmission through a waveguide bend, and that the scattering parameters may be completely independent of the specific arrangement of the inclusions and of the granularity of the crystal. The proposed concepts are numerically demonstrated at microwaves with a metamaterial realization based on an artificial plasma., Comment: 38 pages, 10 Figures, under review

We demonstrate that an array of metallic nanorods enables sub-wavelength (near-field) imaging at infrared frequencies. Using an homogenization approach, it is theoretically proved that under certain conditions the incoming radiation can be transmitted by the array of nanorods over a significant distance with fairly low attenuation. The propagation mechanism does not involve a resonance of material parameters and thus the resolution is not strongly affected by material losses and has wide bandwidth. The sub-wavelength imaging with $\lambda/10$ resolution by silver rods at 30 THz is demonstrated numerically using full-wave electromagnetic simulator., Comment: 12 pages, 16 figures, submitted to PRB

In this work, we investigate the response of epsilon-near-zero (ENZ) metamaterials and plasmonic materials to electromagnetic source excitation. The use of these media for tailoring the phase of radiation pattern of arbitrary sources is proposed and analyzed numerically and analytically for some canonical geometries. In particular, the possibility of employing planar layers, cylindrical shells or other more complex shapes made of such materials in order to isolate two regions of space and to tailor the phase pattern in one region, fairly independent of the excitation shape present in the other, is demonstrated with theoretical arguments and some numerical examples. Physical insights into the phenomenon are also presented and discussed together with potential applications of the phenomenon., Comment: 37 pages, 24 figures

We propose an effective permittivity model to homogenize an array of long thin epsilon-negative rods arranged in a periodic lattice. It is proved that the effect of spatial dispersion in this electromagnetic crystal cannot be neglected, and that the medium supports dispersionless modes that guide the energy along the rod axes. It is suggested that this effect may be used to achieve sub-wavelength imaging at the infrared and optical domains. The reflection problem is studied in detail for the case in which the rods are parallel to the interfaces. Full wave numerical simulations demonstrate the validity and accuracy of the new model., Comment: (10 pages)

The restrictions on the resolution of transmission devices formed by wire media (arrays of conductive cylinders) recently proposed in [Phys. Rev. B, 71, 193105 (2005)] and experimentally tested in [Phys. Rev. B, 73, 033108 (2006)] are studied in this paper using both analytical and numerical modeling. It is demonstrated that such transmission devices have sub-wavelength resolution that can in principle be made as fine as required by a specific application by controlling the lattice constant of the wire medium. This confirms that slabs of the wire medium are unique imaging devices at the microwave frequency range, and are capable of transmitting distributions of TM-polarized electric fields with nearly unlimited sub-wavelength resolution to practically arbitrary distances., Comment: 10 pages, 12 figures, submitted to PRE

In this paper, it is proved that the continuity of the tangential components of the average electric and magnetic fields is insufficient to describe the reflection of plane waves by a set of thin parallel wires embedded in a dielectric host using a homogenization approach. It is shown that an additional boundary condition is required to conveniently model a slab of the homogenized metamaterial. In order to understand how the different electromagnetic modes are excited at the interface, the problem of reflection of a plane wave by a set of semi-infinite parallel wires is solved analytically within the thin-wire approximation. Based on the derived result and other arguments, a new boundary condition is proposed for the homogenized wire medium. Extensive numerical simulations support our theoretical analysis, and show that when the additional boundary condition is considered the agreement between full wave results and homogenization theory is very good even for wavelengths comparable with the lattice constant.