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This paper proposes a dielectric slabs-based lens for millimeter-wave beamforming systems. The proposed lens is based on the graded steps of the effective refractive index of the semi-spherical lens. It consists of multiple dielectric slabs that match the selected gradient effective refractive index. These slabs have the same thicknesses and different radii. The slab thickness in this lens should not exceed a quarter of the operating wavelength to keep on a similar effective refractive index of the original semi-spherical lens. A horn antenna is used to examine the performance of the designed lens at 28 GHz frequency in terms of the maximum gain, sidelobe level, and 3 dB beamwidth. Sixteen switchable horn antennas are used to demonstrate lens capability for millimeter-wave beamforming. Every single antenna element is selected individually, thus the dielectric lens steers and enhances the corresponding radiation of the selected element in the desired direction.

We propose a homogenization scheme for metamaterials that utilizes causality to determine their effective parameters. By requiring the Kramers-Kronig causality condition in the homogenization of metamaterials, we show that the effective parameters can be chosen uniquely, in contrast to the conventional parameter retrieval method which has unavoidable phase ambiguity arising from the multivalued logarithm function. We demonstrate that the effective thickness of metamaterials can also be determined to a specific value by saturating the minimum-error condition for the causality restriction. Our causal homogenization provides a robust and accurate characterization method for metamaterials.

The optical properties of Cu island films, in particular their plasmonic behaviour, are investigated. The films are fabricated by electron beam evaporation using different deposition parameters (deposited mass thickness and substrate temperature). The optical response can be tuned from a metal-like behaviour to well-defined localized surface plasmon resonances and is well correlated with the structural and morphological properties of the samples. Significant changes of optical properties take place with sample aging, including quenching and non-monotonic frequency shift of the plasmon resonance. These changes are interpreted in terms of Cu oxidization process, that appears to strongly depend on the initial morphology of samples. Theoretical calculations in the framework of effective medium theories qualitatively explain the experimental observations. Overall, the results give a detailed insight on the morphology dependence and time evolution of the optical response of Cu island films that may provide useful guidelines for applying these nanostructures in plasmonic applications.

Achieving zero backward scattering (ZBS) and zero forward scattering (ZFS), i.e., the so-called the first and second Kerker's conditions respectively, by sphere spherical particles is considered to be impossible due to the unavailability of naturally occurring magnetic materials in the visible frequency range. We report theoretical modeling to design composite metamaterials that present large optical magnetic permeability in the visible frequency range by employing Mie scattering theory and extended Maxwell Garnett theory. We numerically show that a careful selection of constituents of a composite metamaterial one can obtain metamaterials with sufficiently large artificial permeability that eventually provides the Kerker's criterion to achieve the Kereker's conditions. By taking realistic material parameters we demonstrate that the metamaterials exhibiting ZBS and ZFS have a small imaginary part of the refractive index than metallic structures that pave a path to design high-performance nanophotonic devices., 7 pages, 3 Figures

The effective medium theory (EMT) was recently developed to model the ultrasound backscatter from aggregating red blood cells [Franceschini, Metzger, and Cloutier, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2668–2679 (2011)]. The EMT assumes that aggregates can be treated as homogeneous effective scatterers, which have effective properties determined by the aggregate compactness and the acoustical characteristics of the cells and the surrounding medium. In this study, the EMT is further developed to decompose the differential backscattering cross section of a single cell aggregate into coherent and incoherent components. The coherent component corresponds to the squared norm of the average scattering amplitude from the effective scatterer, and the incoherent component considers the variance of the scattering amplitude (i.e., the mean squared norm of the fluctuation of the scattering amplitude around its mean) within the effective scatterer. A theoretical expression for the incoherent component based on the structure factor is proposed and compared with another formulation based on the Gaussian direct correlation function. This theoretical improvement is assessed using computer simulations of ultrasound backscatter from aggregating cells. The consideration of the incoherent component based on the structure factor allows us to approximate the simulations satisfactorily for a product of the wavenumber times the aggregate radius krag around 2.

Although parity-time (PT)-symmetric systems can exhibit real spectra in the exact PT-symmetry regime, PT-symmetry is actually not a necessary condition for the real spectra. Here, we show that non-PT-symmetric photonic crystals (PCs) carrying Dirac-like cone dispersions can always exhibit real spectra as long as the average non-Hermiticity strength within the unit cell for the eigenstates is zero. By building a non-Hermitian Hamiltonian model, we find that the real spectra of the non-PT-symmetric system can be explained using the concept of pseudo-Hermiticity. We demonstrate using effective medium theories that, in the long-wavelength limit, such non-PT-symmetric PCs behave like the so-called complex conjugate medium (CCM) whose refractive index is real but whose permittivity and permeability are complex numbers. The real refractive index for this effective CCM is guaranteed by the real spectrum of the PCs, and the complex permittivity and permeability come from non-PT-symmetric loss-gain distributions. We show some interesting phenomena associated with CCM, such as the lasing effect.

This is a peer-reviewed, un-copyedited version of an article accepted for publication/published in Journal of Physics D: Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6463/aae3a5. The arbitrary control of surface plasmon (SP) propagation has become an intense research topic for several decades. This is due to the fact that they can be used in a variety of fields such as optical trapping, nanoantennas and medical applications. In this communication, the graded index technique is applied in the design of several steerers able to tailor the direction of propagation of the incident SPs by simply changing the height of a dielectric block on top of a semi?infinite metal slab. The design procedure is shown and the structures are numerically evaluated demonstrating a good agreement with the analytical calculations, with the SPs deflected at the design angles (θ ranging from 10° to 60°) with a wide bandwidth steering of 60 nm around the design value (633 nm) V.P.-P. is supported by the Newcastle University (Newcastle University Research Fellow). M. B. acknowledges support by the Spanish Ministerio de Economía y Competitividad with European Union FEDER funds [TEC2014-51902-C2-2-R].

This paper reviews the current progress in mathematical modeling of anti-reflective subwavelength structures. Methods covered include effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), the Fourier modal method (FMM)/rigorous coupled-wave analysis (RCWA) and the finite element method (FEM). Time-based solutions to Maxwell’s equations, such as FDTD, have the benefits of calculating reflectance for multiple wavelengths of light per simulation, but are computationally intensive. Space-discretized methods such as FDTD and FEM output field strength results over the whole geometry and are capable of modeling arbitrary shapes. Frequency-based solutions such as RCWA/FMM and FEM model one wavelength per simulation and are thus able to handle dispersion for regular geometries. Analytical approaches such as TMM are appropriate for very simple thin films. Initial disadvantages such as neglect of dispersion (FDTD), inaccuracy in TM polarization (RCWA), inability to model aperiodic gratings (RCWA), and inaccuracy with metallic materials (FDTD) have been overcome by most modern software. All rigorous numerical methods have accurately predicted the broadband reflection of ideal, graded-index anti-reflective subwavelength structures; ideal structures are tapered nanostructures with periods smaller than the wavelengths of light of interest and lengths that are at least a large portion of the wavelengths considered.

It has been recently shown that ultrathin spiral metamaterials can support localized spoof plasmon modes whose resonant wavelength is much larger than the size of the structure. Here, an analytical model is developed to describe the electromagnetic properties of the two-dimensional version of these devices: a perfect conducting wire corrugated by spiral grooves. The emergence of localized spoof plasmons in this geometry is quantitatively investigated. Calculations show that these modes can be engineered through the spiral angle and the number of grooves. The theory also allows us to elucidate the contribution of magnetic and electric localized spoof plasmons to the optical response of these metamaterial devices. Finally, experimental evidence of the existence of these modes in extremely thin textured copper disks is also presented. ASTAR (Agency for Sci., Tech. and Research, S’pore) MOE (Min. of Education, S’pore)

The capability to support optical waves with very large wave vectors (high‐k) is one of the principle features of hyperbolic metamaterials (HMMs). These waves play the key role in HMM applications such as imaging and lifetime engineering. Effective medium approximation (EMA) as widely used analytical method to predict HMMs behavior, has shortcomings in calculating high‐k modes of practical structures. EMA is applicable to a subwavelength unit cell of implicitly infinite periodic structures. Using conventional EMA, in the present paper, boundary effects and spatial dispersion are taken into consideration to properly compute the high‐k modes of finite‐thickness multilayer HMMs. Applying nonlocal homogenization to stacks of alternating metal‐dielectric layers, the corresponding effective medium is examined as a high‐k waveguide sandwiched between the substrate and an ambient superstrate. The developed theory enables us to recognize two types of bulk waves coined as short‐range and long‐range propagating modes. Number of such modes as well as their cutoff conditions are quantified for the first time. Validity of the developed theory is verified both numerically by rigorous simulations of the multilayer structures with the transfer matrix method and experimentally by optical characterization of the HMMs in infrared regime.

The coatings having refractive index changing with the thickness present interesting optical performance, improved mechanical properties and smaller light scattering in comparison with classical multilayer stacks. Lot of theoretical work and experimental advances have been done for designing and production of mixture layers with such particular performances. The effective refractive index of the mixture coatings can be calculated by the use of effective medium theories. The refractive index profile characterization of inhomogeneous films that are mixtures of SiO 2 and Nb 2 O 5 is presented. The composition is linearly changed through the thickness of the layers. Ex-situ spectrophotometric measurements, i.e. reflectance and transmittance at different incidence angles, are used for the precise characterization of the refractive index profiles. Linear, Maxwell-Garnet, Bruggeman and Lorentz-Lorenz effective medium theories are applied and quality and differences of the results are studied and analyzed. It is shown that the Lorentz-Lorenz model is the most appropriate for the given mixture, suggesting components are well mixed and there are no separated phases.

We elaborate on an operator approach to effective medium theory for homogenization of the periodic multilayered structures composed of nonmagnetic isotropic materials, which is based on equating the spatial evolution operators for the original structure and its effective alternative. We show that the zeroth-, first-, and second-order approximations of the operator effective medium theory correspond to electric dipoles, chirality, and magnetic dipoles plus electric quadrupoles, respectively. We discover that the spatially dispersive bianisotropic effective medium obtained in the second-order approximation perfectly replaces a multilayered composite and does not suffer from the effective medium approximation breakdown that happened near the critical angle of total internal reflection found previously in the conventional effective medium theory. We establish the criterion of the validity of the conventional effective medium theory depending on the ratio of unit-cell length to the wavelength, the number of unit cells, and the angle of incidence. The operator approach to effective medium theory is applicable for periodic and nonperiodic layered systems, being a fruitful tool in the fields of metamaterials and subwavelength nanophotonics.

We analyze the existence of localized waves in the vicinities of the interface between two dielectrics, provided one of them is uniaxial and lossy. We found two families of surface waves, one of them approaching the well-known Dyakonov surface waves (DSWs). In addition, a new family of wave fields exists which are tightly bound to the interface. Although its appearance is clearly associated with the dissipative character of the anisotropic material, the characteristic propagation length of such surface waves might surpass the working wavelength by nearly two orders of magnitude. This research was funded by the Spanish Ministry of Economy and Competitiveness under the Project TEC2013-50416-EXP.

Carbon nanotube forests are vertically grown tubular formations of graphene. Samples were grown with an injection chemical vapor deposition method on substrates of silicon with various deposited layers and bare fused silica. The morphology of the forest is characterized by the height, density, and presence of defects. Total diffuse reflectance and transmittance measurements were taken in the 2-16 ���m spectral range and correlated to the forest���s specific morphology. From these correlations, the conditions necessary to maximize the absorption of the forest were found and exploited to cater sample growth for specific substrates to make ideal absorbers. From the transmittance data, the absorption coefficient is found via Beer-Lambert���s Law and also correlated to sample morphology, giving us an indication of the height of the forest needed for ideal absorption. Two models were used to attempt to reproduce the experimental absorption coefficient: an effective medium theory using a Maxwell Garnett approximation and by treating the carbon nanotube forest as an effective cylindrical waveguide with walls of graphite. Each model leads to a set of fitting parameters providing a better physical understanding of the forests. It was found that the effective medium theory gave results loosely corroborated with electron microscopy, but had trouble fitting the experimental data, and the index of refraction it provides does not behave like a unified medium. The waveguide model fits the data well, but it requires more experimental evidence to be more conclusive. The theoretical models need more work, but fabrication of ideal absorbers has been achieved on various substrates providing framework for their usage in radiometry and spectroscopy.

Very special electronic phases brought upon by the superstructuring in layered materials have held the interest of researchers for decades. This thesis deals with the effects of the lattice superstructuring on optical and transport properties of pure and doped samples of 1T-TaS2 and 1T-TiSe2. This work brings the first ever analysis of the optical properties of the nearly-commensurate charge density wave (NCCDW) phase of 1T-TaS2 at temperatures below 200 K. Optical response of the NCCDW phase is for the first time analyzed with the nano-composite-like nature of the phase in mind. Modeling of the optical response using the Bruggeman effective medium theory is suggested and demonstrated. As a result, localized surface plasmon feature is identified in the optical spectrum, as well as the asymmetry of the optical phonon modes brought upon by the coupling of spatially distinct nano-sized domains which comprise the material. A novel analysis of the superstructure-related phonon peaks which allows the determination of the charge redistribution over the star-like superstructure is presented. Lastly, this work also presents the study of the 1T-TiSe2 compound, where the analysis is focused on the properties of the high temperature phase of the material. The contributions of electron and hole pockets are resolved for the first time, as well as the spectral weights and the scattering rates for each channel. Calculated energy ranges of the quasi-2D hole band settle the ongoing debate and determine that 1T-TiSe2 in the high-temperature phase is a semimetal, with scattering which gets stronger over a wide interval as the temperature approaches the phase transition. Vrlo posebne elektronske faze koje nastaju superstrukturiranjem slojastih materijala već desetljećima zaokupljaju pažnju istraživača. Ovaj doktorski rad proučava efekte superstrukturiranja kristalne rešetke na optička i transportna svojstva čistih i dopiranih uzoraka 1T-TaS2 i 1T-TiSe2. Rad donosi prvu analizu optičkih svojstava faze približno sumjerljivog vala gustoće naboja (engl. NCCDW) 1T-TaS2 na temperaturama ispod 200 K. Po prvi put je optički odziv NCCDW faze analiziran uzimajući u obzir njenu nanokompozitnu prirodu, te je predloženo i provedeno modeliranje optičkog odziva pomoću Bruggemanove teorije efektivnog medija. Kao rezultat, u optičkom spektru je identificiran učinak lokalnog površinskog plazmona, kao i asimetrija fononskih modova do koje dolazi zbog vezanja optičkog odziva prostorno razdvojenih nano-domena. Nadalje, predložena je nova analiza intenziteta super-strukturnih fononskih vrhova koja omogućava određivanje redistribucije naboja u zvjezdastoj superstrukturi. Napose, ovaj rad predstavlja i istraživanje 1T-TiSe2, gdje je analiza usredotočena na svojstva visokotemperaturne faze materijala. Po prvi put su razlučeni doprinosi elektronskih i šupljinskih pobuđenja, te njihova spektralna težina i jačina raspršenja. Proračuni energijskog raspona kvazi-dvodimenzionalne šupljinske vrpce omogućuju zaključenje dugotrajne debate u korist zaključka da je 1T-TiSe2 u visokotemperaturnoj fazi “polumetal” (engl. semimetal), s raspršenjem koje jača preko vrlo širokog intervala u kojem se temperatura približava točki prijelaza.

A set of simplified and rigorous electromagnetic vector theories is used for analyzing the transmittance characteristics of diffraction phase gratings. The scalar diffraction theory and the effective medium theory are validated with the exact results obtained via the rigorous coupled-wave theory and the finite-difference time-domain method. The effects of surface profile parameters and also the angle of incidence is demonstrated to be a limiting factor in the accuracy of these theories. Therefore, the error of both simplified theories is also analyzed in non-paraxial domain with the intention of establishing a specific range of validity for both simplified theories. This work was supported by the Ministerio de Economía y Competitividad of Spain under projects FIS2011-29803-C02-01, FIS2011-29803-C02-02 and by the Generalitat Valenciana of Spain under projects PROMETEO/2011/021, ISIC/2012/013, ACOMP/2013/075 and GV/2012/099.

Mixture material layers are used in gradient index optical systems due to their tailorable refractive index. To be able to realize the required optical performance of the system it is necessary to relate refractive index profile of the design to the volume fraction of the components of the mixture. In this study it is found that for electron beam co-deposited Nb2O5 – SiO2 mixtures the most appropriate effective medium theory that relates these properties is Lorentz-Lorenz theory. Optical properties of a mixture are related to the structure of the composite. The structural properties of the studied mixtures justify the appropriateness of application of Lorentz-Lorenz theory to this kind of effective medium.

We analyze the properties of acoustic and electromagnetic metamaterials with anisotropic constitutive parameters. Particularly, we analyze the so-called Radial Wave Crystals, which are radially periodic structures verifying the Bloch theorem. This type of crystals can be designed and implemented in acoustics as well as in electromagnetism by using anisotropic metamaterials. In acoustics, we have previously predicted that they can be employed as acoustic cavities with huge quality factors and also like dynamically driven antennas. Similar functionalities are here proven in the electromagnetic domain with, in particular, an analysis of the functionality of practical devices operating in the microwave regime. Starting from our recent works on anisotropic structures and their comparison in both application fields, we present a complete discussion concerning their properties in acoustics and electromagnetics.

The influence of the substrate temperature on the effective optical behavior ofAg-SiO 2 composites obtained by electron beam evaporation was studied. Optical characteriza-tion of the composites was performed by means of spectroscopic ellipsometry measurements.Theeffectivedielectricfunctionofthecomposites,modeledusingamultipleoscillatorapproach,could be widely tuned by controlling the deposition temperature. The spectral dependence ofthe composite absorption appeared to be better described with a Gaussian line shape than withthe classical Lorentz oscillator model. The description of the effective dielectric function usingstandard effective medium theories failed and the experimental results could be explained onlyin the general framework of the Bergman spectral density theory. C 2011 Society of Photo-OpticalInstrumentation Engineers (SPIE) . [DOI: 10.1117/1.3590238] Keywords: metal-dielectric composites; metal island films; surface plasmon resonance; opticalconstants; effective medium theory; spectroscopic ellipsometry.Paper 11015SSR received Jan. 28, 2011; revised manuscript received Apr. 15, 2011; acceptedfor publication Apr. 15, 2011; published online May 13, 2011.

The perfectly conducting stacked fishnet metamaterial is studied in this paper. The analysis is based on a combination of the mode matching method together with the generalized eigenvalue problem, and takes into account wave propagation along all three Cartesian axes. The analysis has been developed for a fishnet of square lateral periodicity and for two particular polarizations, namely TE and TM, corresponding to the two most common excitations. The 1D and 2D dispersion characteristics are calculated for both polarizations, showing that the TM waves undergo negative refraction in a narrow frequency band just below Wood’s anomaly, whereas TE polarized waves exhibit ordinary positive refraction. Finally, possible homogenization of the fishnet metamaterial is considered, showing that only for small angles of incidence and in the immediate vicinity of Wood’s anomaly can the fishnet be seen as homogenizable uniaxial medium. Ministerio de Educación y Ciencia de España y Fondos FEDER de la Unión Europea-TEC2007-65376, TEC2007-68013-C02-01, y CSD2008-00066 Junta de Andalucía-TIC-253 Czech Grant Agency-102/09/0314 Czech Technical University in Prague-SGS10/271/OHK3/3T/13

This work analyzes the electromagnetic wave propagation through periodically stacked fishnets from zero frequency to the first Wood's anomaly. It is shown that, apart from Fabry-Perot resonances, these structures support two transmission bands that can be backward under the appropriate conditions. The first band starts at Wood's anomaly and is closely related to the well-known phenomena of extraordinary transmission through a single fishnet. The second band is related to the resonances of the fishnet holes. In both cases, the in-plane periodicity of the fishnet cannot be made electrically small, which prevents any attempt of homogenization of the structure along the fishnet planes. However, along the normal direction, even with very small periodicity transmission is still possible. An homogenization procedure can then be applied along this direction, thus making that the structure can behave as a backward-wave transmission line for such transmission bands. Closed-form design formulas will be provided by the analytical formulation here presented. These formulas have been carefully validated by intensive numerical computations. Ministerio de Educación y Ciencia TEC2007-65376, TEC2007-68013-C02-01, CSD2008- 00066 Junta de Andalucía TIC-253 Czech Grant Agency 102/08/0314

The absorption coefficient of composite films consisting of niobia (Nb2O5) and silica (SiO2) mixtures is studied for photon energies around the band gap. The films were deposited by co-evaporation and their composition was varied by changing the ratio of deposition rates of the two materials. Both, as-deposited and thermally annealed films were characterized by different techniques: the absorption coefficient was determined by spectrophotometric measurements and the structural properties were investigated using infrared spectroscopy, transmission electron microscopy and X-ray diffraction. The correlation between the variations of absorption properties and film composition and structure is established. The absorption coefficients determined experimentally are compared with the results derived from effective medium theories in order to evaluate the suitability of these theories for the studied composites.

We employ the generalized Lorentz-Lorenz method to investigate how both magnetoelectric coupling and spatial dispersion influence the artificial magnetic capabilities at terahertz frequencies of the representative case of a metamaterial consisting of a three-dimensional (3D) lattice of TiO2 microspheres. The complex wavenumber dispersion relations pertaining to modes supported by the array, traveling along one of the principal axes of the array with electric or magnetic field polarized transversely and longitudinally (with respect to the mode traveling direction), are studied and thoroughly characterized. One mode with transverse polarization is dominant at any given frequency for the analyzed dimensions, proving that the 3D lattice can be treated as a homogeneous medium with defined electromagnetic material parameters. We show, however, that bianisotropy is a direct consequence of magnetoelectric coupling, and the dyadic expressions of both effective and equivalent material parameters are derived. In particular, we analyze the effect of spatial dispersion on the effective parameters relative to a composite material made by a 3D lattice of TiO2 microspheres with filling fraction around 30% and near the first Mie magnetic dipolar resonance. Finally, we homogenize the metamaterial in terms of equivalent index and impedance, and by comparison with full-wave simulations, we explain the presence of the unphysical antiresonance permittivity behavior observed in previous work. © 2014 Optical Society of America.

Recent progress is emerging on nondiffracting subwavelength fields propagating in complex plasmonic nanostructures. In this paper, we present a thorough discussion on diffraction-free localized solutions of Maxwell’s equations in a periodic structure composed of nanowires. This self-focusing mechanism differs from others previously reported, which lie on regimes with ultraflat spatial dispersion. By means of the Maxwell–Garnett model, we provide a general analytical expression of the electromagnetic fields that can propagate along the direction of the cylinder’s axis, keeping its transverse waveform unaltered. Numerical simulations based on the finite element method support our analytical approach. In particular, moderate filling fractions of the metallic composite lead to nonresonant-plasmonic spots of light propagating with a size that remains far below the limit of diffraction. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120-C05-01.

We analyzed surface-wave propagation that takes place at the boundary between a semi-infinite dielectric and a multilayered metamaterial, the latter with indefinite permittivity and cut normally to the layers. Known hyperbolization of the dispersion curve is discussed within distinct spectral regimes, including the role of the surrounding material. Hybridization of surface waves enable tighter confinement near the interface in comparison with pure-TM surface-plasmon polaritons. We demonstrate that the effective-medium approach deviates severely in practical implementations. By using the finite-element method, we predict the existence of long-range oblique surface waves. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120-C05-01, by the Serbian Ministry of Education and Science under the project III 45016, and by the Qatar National Research Fund under the project NPRP 09-462-1-074. CJZR gratefully acknowledges a financial support from the Generalitat Valenciana (grant BEST/2012/060).