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Here, we formally develop theoretical methods to topologically classify a wide class of bianisotropic continuous media. It is shown that for continuous media, the underlying wave vector space may be regarded as the Riemann sphere. We derive sufficient conditions that ensure that the pseudo-Hamiltonian that describes the electrodynamics of the continuous material is well behaved so that the Chern numbers are integers. Our theory brings the powerful ideas of topological photonics to a wide range of electromagnetic waveguides and platforms with no intrinsic periodicity and sheds light over the emergence of edge states at the interfaces between topologically inequivalent continuous media. [ABSTRACT FROM AUTHOR]

Here we theoretically predict and experimentally verify that permeability μ-near-zero (MNZ) materials give the opportunity to supercouple waveguides with highly mismatched cross sections. Rather distinct from the supercoupling provided by permittivity-near-zero materials we discovered several years ago, the MNZ supercoupling can take place when the transition channel cross section is much wider than that of the input and output waveguides. We develop a simple analytical model that captures the physical mechanisms that enable this remarkable effect. The MNZ supercoupling effect is experimentally verified with rectangular waveguide technology by mimicking the μ-near-zero response with the help of cylindrical split ring resonators. [ABSTRACT FROM AUTHOR]

We propose a first-principles effective medium formalism to study the propagation of electron waves in semiconductor heterostructures with a zero band gap. Our theory confirms that near the K point the dynamics of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer. Furthermore, we highlight that even though other superlattices based on semiconductors with a zincblende-type structure can have a zero band-gap and a linear energy-momentum dispersion, the corresponding effective medium Hamiltonian is rather different from that of graphene, and can be based on a single-component wave function. [ABSTRACT FROM AUTHOR]

We consider the effect of quantum friction at zero absolute temperature resulting from polaritonic interactions in closely positioned two-dimensional arrays of polarizable atoms (e.g., graphene sheets) or thin dielectric sheets modeled as such arrays. The arrays move one with respect to another with a nonrelativistic velocity v«c. We confirm that quantum friction is inevitably related to material dispersion, and that such friction vanishes in nondispersive media. In addition, we consider a classical analog of the quantum friction which allows us to establish a link between the phenomena of quantum friction and classical parametric generation. In particular, we demonstrate how the quasiparticle generation rate typically obtained from the quantum Fermi golden rule can be calculated classically. [ABSTRACT FROM AUTHOR]

I 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. I show that the conditions necessary for the formation of spatial solitons are radically different in presence of the nanowires. In particular, within the effective medium model, spatial solitons are allowed in the nanowire material only when 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. [ABSTRACT FROM AUTHOR]

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 quasistatic 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. [ABSTRACT FROM AUTHOR]

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 zinc-blende 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. [ABSTRACT FROM AUTHOR]

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 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 a regime may permit an ultrafast, 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 functional materials with a strong electrical response in the infrared regime. [ABSTRACT FROM AUTHOR]

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 may 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 nondiffractive far-field distribution. [ABSTRACT FROM AUTHOR]

Most metamaterial designs are based on the resonant response of either high permittivity or metallic particles embedded in a dielectric host (e.g. an array of metallic particles standing in air). As a consequence, the response of the material is typically narrowband, and this holds back many interesting applications. Here, we show that the key to achieve a broadband isotropic response may lie on a low-permittivity host with a plasmonic-type response. In particular, we demonstrate that a host medium with such characteristics may enable an effective permittivity εeff and permeability μeff simultaneously negative in a frequency range that may be quite broad as compared to typical designs based on metallic particles standing in a dielectric host. It is shown that the proposed configuration is largely insensitive to disorder and that a slab of the metamaterial may mimic to some extent the Veselago-Pendry's superlens, enabling negative refraction and imaging with super-resolution. [ABSTRACT FROM AUTHOR]

Metamaterials are characterized by counterintuitive phenomena, which have been debated since their first practical realization. Due to their anomalous backward power flow, it has been recently discussed whether even the classic definition of the Poynting vector, defining the power flux per unit surface, should be modified when dealing with metamaterials with exotic properties. Here, we settle this issue and fully clarify the physics of negative refraction, showing that the Poynting vector and other power relations in artificial materials may be unambiguously defined consistently with classic formulas for homogeneous media. [ABSTRACT FROM AUTHOR]

We critically analyze the anomalies in the frequency dispersion of the magnetic permeability, showing that it may be sometimes-without contradicting causality-inconsistent with the Kramers-Kronig relations for passive materials, as formulated by Landau and Lifshitz, even at extremely low frequencies where the permeability has definitely a very precise physical meaning. This suggests that in general the permeability may not satisfy the Kramers-Kronig formulas for passive materials, and an alternative set of relations to link the real and imaginary parts of the permeability in the frequency region where the permeability retains its physical meaning is proposed. [ABSTRACT FROM AUTHOR]

We propose a simple, robust, and versatile time domain approach to homogenize metamaterials, taking into account both frequency and spatial dispersion. The macroscopic electromagnetic response of optical metamaterials, such as the fishnet structure and plasmonic metamaterials with near zero parameters, is characterized in terms of local effective parameters ε and μ, under the assumption that the effects of spatial dispersion are weak. [ABSTRACT FROM AUTHOR]

For long wavelengths, three-dimensional connected metallic wire meshes are impenetrable by light and have an electromagnetic response similar to that of an electron gas below the plasma frequency. Surprisingly, here it is shown that when two opaque metallic meshes are spatially interlaced, the combined structure enables an anomalous light tunneling in the long wavelength regime. The effect is due to the destructive interference of the waves scattered by the two wire meshes, which leads to a Fano-type resonance. The Fano resonance occurs when the longitudinal (plasmon) mode satisfies the Fabry-Pérot condition. [ABSTRACT FROM AUTHOR]

We theoretically demonstrate that a system formed by two coupled graphene sheets enables a negative damping regime wherein graphene plasmons are pumped by a direct current. This effect is triggered by electrons drifting through one of the graphene sheets and leads to wave instabilities and a spontaneous light emission (spasing) in the midinfrared range. It is shown that there is a deep link between the drift-induced instabilities and wave instabilities in moving media, as both result from the hybridization of oscillators with oppositely signed frequencies. With a thickness of a few nanometers and wide spectral tunability, the proposed structure may find interesting applications in nanophotonic circuitry as an on-chip light source. [ABSTRACT FROM AUTHOR]

We study the role of topological edge states of light in the transport of thermally generated radiation in a closed cavity at a thermodynamic equilibrium. It is shown that even in the zero temperature limit--when the field fluctuations are purely quantum mechanical--there is a persistent flow of electromagnetic momentum in the cavity in closed orbits, deeply rooted in the emergence of spatially separated unidirectional edge state channels. It is highlighted that the electromagnetic orbital angular momentum of the system is nontrivial, and that the energy circulation is towards the same direction as that determined by incomplete cyclotron orbits near the cavity walls. Our findings open inroads in topological photonics and suggest that topological states of light can determine novel paradigms in the context of radiative heat transport. [ABSTRACT FROM AUTHOR]

In time-reversal invariant electronic systems the scattering matrix is antisymmetric. This property enables a spin-Hall effect, designated here as "scattering anomaly", such that the electron transport does not suffer from back reflections independent of the specific geometry of the propagation path or the presence of time-reversal invariant defects. In contrast, for a generic time-reversal invariant photonic system, the scattering matrix is symmetric and there is no similar anomaly. Here, it is theoretically proven that despite these fundamental differences there is a wide class of photonic platforms--in some cases formed only by time-reversal invariant media--in which a scattering anomaly can occur. It is shown that an optical system invariant under the action of the composition of the parity, time-reversal, and duality operators (P·T·D) is characterized by an antisymmetric scattering matrix. Specific examples of photonic platforms wherein the scattering anomaly occurs are given, and it is demonstrated with full wave numerical simulations that the proposed systems enable bidirectional waveguiding immune to arbitrary deformations of the propagation path. Importantly, our theory unveils a new class of fully three-dimensional structures wherein the transport of light is fully protected against reflections and uncovers unsuspected links between the electrodynamics of reciprocal and nonreciprocal materials. [ABSTRACT FROM AUTHOR]

Here, building on our previous work [Phys. Rev. B 92, 125153 (2015)], it is shown that the propagation of unidirectional gapless edge states at an interface of two topologically distinct electromagnetic continua with a well-behaved asymptotic electromagnetic response is rigorously predicted by the bulk-edge correspondence principle. We work out detailed examples demonstrating that when the spatial cutoff of the nonreciprocal part of the material response is considered self-consistently in the solution of the relevant electromagnetic problem, the number of unidirectional gapless edge modes is identical to the difference of the Chern numbers of the bulk materials. Furthermore, it is shown how the role of the spatial cutoff can be imitated in realistic systems using a tiny air gap with a specific thickness. This theory provides a practical roadmap for the application of topological concepts to photonic platforms formed by nonreciprocal electromagnetic continua. [ABSTRACT FROM AUTHOR]

Electronic topological insulators are one of the breakthroughs of 21st century condensed matter physics. So far, the search for a light counterpart of an electronic time-reversal invariant topological insulator has remained elusive. This is due to the fundamentally different natures of light and matter and the different spins of photons and electrons. Here, it is shown that the theory of electronic topological insulators has a genuine analog in the context of light wave propagation in time-reversal invariant continuous materials. We introduce a gauge invariant Z2 index that depends on the global properties of the photonic band structure and is robust to any continuous weak variation of the material parameters that preserves the time-reversal invariance. A nontrivial Z2 index has two possible causes: (i) the lack of smoothness of the pseudo-Hamiltonian in the k→∞ limit and (ii) the entanglement between positive and negative frequency eigenmode branches. In particular, it is proven that electric-type plasmas and magnetic-type plasmas are topologically inequivalent for a fixed wave polarization. We propose a bulk-edge correspondence that links the number of edge modes with the topological invariants of two continuous bulk materials and present detailed numerical examples that illustrate the application of the theory. [ABSTRACT FROM AUTHOR]

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 instead requires knowledge of internal degrees of freedom of the materials. We derive such a relation for the particular case of "wire media" and describe a numerical formalism that enables characterization of 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. [ABSTRACT FROM AUTHOR]

We study the Cherenkov emission in the vicinity of (or within) a nanowire metamaterial, and demonstrate that due to the anomalously high density of electromagnetic states in such structures, it is possible to boost the Cherenkov emission by several orders of magnitude as compared to natural media, and produce Cherenkov radiation with no threshold for the velocity of the charged particles. [ABSTRACT FROM AUTHOR]

A local thickness-dependent permittivity is derived in closed form for bounded nonlocal wire-medium structures. The model takes into account spatial dispersion (as an average per length of the wires) and the effect of the boundary, and shows that an effective local model of a nonlocal medium is thickness dependent. The permittivity is comprised of a local bulk (Drude) term and a boundary- and thickness-dependent term, the latter including the effect of spatial nonlocality. Results are obtained for different wire-medium topologies which possess strong spatial dispersion, demonstrating good agreement with a nonlocal homogenization model and full-wave simulation results. [ABSTRACT FROM AUTHOR]

It is shown that a racemic array of helical-shaped metallic wires may have a dual electromagnetic response, such that for arbitrarily large wavelengths it concurrently supports two modes with hyperbolic- and elliptical-type dispersions. Importantly, one of the eigenwaves is nearly dispersionless and sees the metamaterial as a medium with extreme magnetic anisotropy. The metamaterial may thus behave as the magnetic analog of the conventional wire medium formed by a set of parallel straight metallic wires. It is demonstrated that the magnetic wire medium enables channeling the subwavelength details of transverse electric (TE) polarized waves. [ABSTRACT FROM AUTHOR]

In this paper, we show that HgCdTe heterostructures may support, within the envelope function approximation, bound electronic states embedded in the continuum, such that the discrete energy spectrum overlaps the continuous spectrum. Although the proposed heterostructures are generally penetrable by an incoming electron wave, it is shown that they may support spatially localized trapped stationary states with an infinite lifetime. We discuss the possibility of a free electron being captured by the proposed open resonator and present a detailed study of the trapping lifetime in the case of a detuned resonator. [ABSTRACT FROM AUTHOR]

The realization of mesoscopic media that mimic an ideal continuous indefinite material remains a challenging problem, particularly because current designs are plagued by spatial dispersion effects and are based on inclusions whose size may be a significant fraction of the wavelength. Here we show that a structure formed by an array of inductively loaded metallic rods terminated by metallic patches at both ends may enable to largely overcome these problems, and imitate more closely indefinite dielectric media with a local response. In particular, we report a strong all-angle negative refraction effect, even in scenarios where the characteristic size of the material is deeply subwavelength. The response of the proposed structure is characterized using a homogenization model developed for the uniaxial wire medium with impedance loadings. [ABSTRACT FROM AUTHOR]

We investigate the causality relations in homogenized metamaterial arrays and determine the reasons why metamaterial effective (bulk) constitutive parameters obtained using classic point-dipole approximations may violate basic causality conditions represented by the Kramers-Kronig relations. We show that noncausality is inherently introduced by the use of point-dipole approximations within Maxwell-Garnett homogenization procedures and that these artifacts become particularly significant for more densely packed arrays. In contrast we show that properly defined and exactly computed bulk constitutive parameters of periodic metamaterial arrays always satisfy causality for a fixed spatial frequency in a rigorous homogenization framework. Finally we show how the Maxwell-Garnett approach can be modified to effectively remove the noncausal effects. [ABSTRACT FROM AUTHOR]

Here, inspired by the operation of conventional semiconductor transistors, we introduce a novel class of bulk materials with nonreciprocal and non-Hermitian electromagnetic response. Our analysis shows that material nonlinearities combined with a static electric bias may lead to a linearized permittivity tensor that lacks the Hermitian and transpose symmetries. Remarkably, the material can either dissipate or generate energy, depending on the relative phase of the electric field components. We introduce a simple design for an electromagnetic isolator based on an idealized "MOSFET-metamaterial" and show that its performance can in principle surpass conventional Faraday isolators due to the material gain. Furthermore, it is suggested that analogous material responses may be engineered in natural media in nonequilibrium situations. Our solution determines an entirely novel paradigm to break the electromagnetic reciprocity in a bulk nonlinear material using a static electric bias. [ABSTRACT FROM AUTHOR]

Transistors are key elements of electronic circuits as they enable, for example, the isolation or amplification of voltage signals. While conventional transistors are point-type (lumped-element) devices, it may be interesting to realize a distributed transistor-type optical response in a bulk material. Here, we show that low-symmetry two-dimensional metallic systems may be the ideal solution to implement such a distributed-transistor response. To this end, we use the semiclassical Boltzmann equation approach to characterize the optical conductivity of a two-dimensional material under a static electric bias. Similar to the nonlinear Hall effect, the linear electro-optic (EO) response depends on the Berry curvature dipole and can lead to nonreciprocal optical interactions. Most interestingly, our analysis uncovers a novel non-Hermitian linear EO effect that can lead to optical gain and to a distributed transistor response. We study a possible realization based on strained bilayer graphene. Our analysis reveals that the optical gain for incident light transmitted through the biased system depends on the light polarization, and can be quite large, especially for multilayer configurations.

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with few modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break down and the Chern topology becomes ill defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be noninteger notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.

It is theoretically demonstrated that electron states in semiconductors or graphene can be perfectly transmitted through a complementary material with dual properties, independent of the angle of incidence. It is shown that such complementary material may also provide a strong spatial delocalization of bounded electronic states, changing dramatically the confinement of the wave function, and acting effectively as a lens for the probability wave. The results are the electron analogue of a perfect lens for electromagnetic waves proposed in an earlier work.

We describe a mesoscopic excitation in strongly coupled grids of metallic nanorods, resulting from the hybridization of weakly bounded plasmons. It is shown both theoretically and experimentally that the characteristic spatial scale of the interlaced plasmons is determined by geometrical features, rather than from the electrical length of the nanorods, and that due to their wide band nature, weak sensitivity to metallic absorption, and subwavelength mode sizes, such plasmons may have exciting applications in waveguiding in the nanoscale.

Plasmonic cloaking is a scattering-cancellation technique based on the local negative polarizability of metamaterials. Here we report its first experimental realization and measurement at microwave frequencies. An array of metallic fins embedded in a high-permittivity fluid has been used to create a metamaterial plasmonic shell capable of cloaking a dielectric cylinder, yielding over 75% reduction of total scattering width.

A prism of glass separates white light into its spectral components in such a manner that colors associated with shorter wavelengths are more refracted than the colors associated with longer wavelengths. Here, we demonstrate that this property is not universal, and that a lossless metamaterial prism with a suitable microstructure may enable a broadband regime of anomalous dispersion, where the spectral components of light are separated in an unconventional way, so that "violet light" is less refracted than "red light." This phenomenon is fundamentally different from conventional anomalous dispersion effects, which are invariably accompanied by significant loss and are typically very narrow band.

The manipulation of optical waves in the subwavelength scale is limited by diffraction. In the vicinity of a narrow aperture, the amplitude of the electric field is approximately uniform and the transmissivity is extremely low. Here we show that despite these fundamental constraints it may be possible to transport and redirect a complex electromagnetic image through a tiny subwavelength hole with diameter considerably smaller than the diameter of the image, without losing the subwavelength details. The proposed concepts hold promise for an unprecedented manipulation of the electromagnetic and optical fields in the nanoscale with potential applications in imaging and sensing.

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.

In this work, we assess theoretically the physical response of metamaterial composite structures that emulate the behavior of negative-permittivity materials in certain relevant setups. The metamaterials under analysis consist of metallic parallel-plate implants embedded in a dielectric host in a two-dimensional geometry. Simple design rules and formulas are presented, fully considering the effect and consequences of excitation of higher-order diffraction modes at the metamaterial-dielectric interface. Following the ideas of transparency and cloaking developed by us [Alù and Engheta, Phys. Rev. E 72, 016623 (2005)], we demonstrate, analytically and numerically, that it is possible in this way to design metamaterial cloaks that significantly reduce the total scattering cross section of a given two-dimensional dielectric obstacle in some frequency band. This effect, which may be realized in a feasible way, may find interesting applications in electromagnetic cloaking, total scattering cross section reduction, and noninvasive probing.

The objective of this work is to investigate in which circumstances the scattering of electromagnetic waves by a thin metamaterial slab can be characterized using known effective parameters of the associated unbounded periodic bulk medium. It is proved that the classical approach or classical boundary conditions may become less accurate or incomplete if the size of inclusions is not significantly smaller than the wavelength. To circumvent this problem we demonstrate that the interaction of waves with metamaterial structures may in many cases with practical interest be conveniently described using a transverse averaged-field technique, and that this approach can be very accurate even for wide incident angles, evanescent waves, and for large and moderately large wavelengths.

We propose an effective permittivity model to homogenize an array of long thin epsilon-negative rods arranged in a periodic lattice. It is proven 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 subwavelength 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.