Normal Incident Plane Wave Research Articles

Polarization independent and tunable plasmonic structure for mimicking electromagnetically induced transparency in the reflectance spectrum

This paper proposes a plasmonic metamaterial that is able to mimic electromagnetically induced transparency in the reflectance spectrum within the GHz frequency range. Each meta-atom consists of a cross-slot structure as the bright resonator positioned on one side of the FR-4 substrate, and four spiral structures as the dark resonator located on the opposite side. Free space experimental results demonstrate that at normal incidence of plane wave, the metamaterial possesses the properties of tunability and polarization independence. In addition, based on simulation results the metamaterial also possesses slow wave property, with group refractive index of 56; and refractive-index-based sensing capability, with figure of merit of 6.1. In the strong coupling configuration, the plasma frequency and coupling constant of the metamaterial were calculated to be approximately 5.4 × 1010 rad s−1 and 9.8 × 109 rad s−1 respectively. While the respective damping constants of the bright resonator and dark resonator were calculated to be approximately 4.6 × 1010 rad s−1 and 1.9 × 1010 rad s−1.

Acoustic radiation force on a fluid cylindrical particle immersed in water near an impedance boundary.

This work presents a theoretical model to calculate the acoustic radiation force of a fluid cylindrical particle immersed in water near a boundary. A solution of the acoustic radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface area, is derived for a cylinder near a boundary in normal incident plane wave by applying the translation addition theorem of cylindrical function. The effects of impedance boundary on acoustic radiation force of a fluid oleic acid cylinder and a mixture fluid cylinder immersed in water are analyzed with particular emphasis on the radius of fluid cylinder and the distance from its center to the impedance boundary. The results reveal that the existence of particle trapping behavior depends on the choice of the nondimensional frequency ka as well as the offset distance from the impedance boundary. This study provides a theoretical basis for acoustic manipulation, which may be of benefit to the improvement and development of the acoustic control technology.

Finite-Difference Modeling of Broadband Huygens’ Metasurfaces Based on Generalized Sheet Transition Conditions

An explicit time-domain finite-difference technique for modeling zero-thickness Huygens’ metasurfaces based on generalized sheet transition conditions (GSTCs) is proposed and demonstrated using full-wave simulations. The Huygens’ metasurface is modeled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens’ metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time domain. Identifying the exact equivalence between Huygens’ metasurfaces and coupled RLC oscillator circuits, the field equations are then subsequently solved using standard circuit modeling techniques based on a finite-difference formulation. Several examples, including generalized refraction, are shown to illustrate the temporal evolution of scattered fields from the Huygens’ metasurface under plane-wave normal incidence, in both harmonic steady-state and broadband regimes. In particular, due to its inherent time-domain formulation, a significant strength of the methodology is its ability to model time-varying metasurfaces, which is demonstrated with a simple example of a pumped metasurface leading to new frequency generation and wave amplification.

Dark Mode Driven Extra-narrow and Multiband Absorber

Recently, metamaterial absorbers have received tremendous amount of interest because of their remarkable ability to manipulate the amplitude, phase, and polarization of light. However, most absorbers rely on the direct coupling of electric or magnetic field with external excitation, which lead to inevitable energy leakage to the surrounding environment and depress the quality factor of the structure. In this work, we investigate the multiband absorption property by exciting dark plasmonic modes in reflective symmetric and asymmetric metamaterials. Theoretically, the existence of dark plasmonic modes in asymmetric metamaterials is unambiguously illustrated by the improved eigen-mode theory. With the introduction of asymmetry, dark modes in metamaterials can be easily excited by normal incident plane wave. Moreover, we also directly excite the dark modes in symmetric absorber with oblique incidence. The dark modes splitting mechanism is also clarified with the excitation of designer surface plasmon. Dominated by magnetic dipole or higher-order multipole, these dark modes possess high quality factors (Q). Numerical results indicate that the metamaterial absorber maintains high absorbance within a wide-angle incidence (0~50°). The high Q asymmetric metamaterial absorber can be an excellent candidate for multiband plasmonic sensor.

Predicting Sound Absorption of Stacked Spheres: Combining an Analytical and Numerical Approach

Tire-road noise is a serious problem, but can be significantly reduced by the use of porous asphalt concrete. Here, the sound absorption of the porous asphalt concrete is important and can be predicted by ground impedance models. Yet, modeling porous asphalt concrete is complex, especially when nonlocal effects and scattering effects are considered. The objective of this research is to predict the sound absorption coefficient for a three-dimensional porous structure. The proposed solution is obtained using a novel modeling approach, in which the total solution of the sound field is found by combining the solutions of two subsystems: a background sound field and a scattered sound field. The background sound field contains the (analytical) solution of the sound field including the viscothermal energy dissipation inside the pores of the porous asphalt concrete. In the second subsystem, the (numerical) solution for the scattering on the rigid stone skeleton of the pavement is found. For both subsystems, we use a model containing two layers: an air layer and a viscous air layer with a certain granular structure. The main advantage of this modeling approach is the (relatively) low computation time. In this paper, the proposed modeling approach and the validation of this approach are described. The modeling approach is validated for normal incident plane waves absorbed and scattered by various structures of stacked marbles, using the impedance tube technique. This approach can be applied to predict the absorption coefficient of porous structures, like asphalt concrete roads. Moreover, it can be used as design tool to optimize the sound absorption of new road surfaces.

Electromagnetic origins of negative refraction in coupled plasmonic waveguide metamaterials

A metamaterial composed of stacked plasmonic waveguides which support backward propagation along the layers has been shown to exhibit a nearly spherical equifrequency contour (EFC) in which the Floquet-Bloch wave vector ${\mathbf{k}}_{\mathrm{FB}}$ and Poynting vector $\mathbf{S}$ point in opposite directions everywhere on this surface. Experiments performed on this structure have also shown that polarized light beams incident from free space refract to the same side of normal over a wide range of incidence angles. Together, these observations have led researchers to describe this structure as a homogeneous medium with three-dimensionally isotropic negative refractive index; however, a close inspection of the fields throughout the structure as provided in this paper would suggest otherwise. Here, we rigorously analyze the relationship between phase and power flow within the structure by introducing a method to calculate the power flow of all Floquet-Bloch harmonics, information which cannot be obtained from either conventional analysis of EFCs or effective medium theory. Access to power flow of all harmonics enables us to demonstrate the origin of backward power (defined with respect to the direction of ${\mathbf{k}}_{\mathrm{FB}})$, and in doing so, verify the validity of the claimed three-dimensionally isotropic left-handed response and the validity of describing the medium by a simple negative effective index of refraction $n=\ensuremath{-}1$. Knowledge regarding the distribution of power flow across the harmonics can also be used to design highly efficient methods to couple light into and out of these structures. As an example, we show that tailored wave excitation can achieve coupling efficiencies of up to 96%, over 5 times greater than that achieved by normal-incidence plane-wave excitation.

Diffraction of plane waves by a periodic array of nonlinear circular cylinders

It is well known that standing waves, as special bound states in the radiation continuum, may exist on a periodic array of dielectric cylinders at a discrete set of frequencies if the medium is linear. Recent numerical studies indicate that nonlinear standing waves could exist continuously with respect to the frequency on a periodic array of cylinders with a Kerr nonlinearity. In this paper, we study the diffraction of a normal incident plane wave by a periodic array of circular cylinders with a Kerr nonlinearity. Using a perturbation method and a highly accurate numerical method, we show that a plane incident wave may couple to a nonlinear standing wave, and in general, there are four different couplings leading to four asymmetric solutions in two pairs. The existence of these asymmetric solutions provides another example for the symmetry-breaking phenomenon. Importantly, it seems that the asymmetric solutions (thus the symmetry-breaking phenomenon) appear for incident waves of arbitrarily low intensity.

Effective-surface modeling of infinite periodic metascreens exhibiting the extraordinary transmission phenomenon

The consistent analysis of metallic screens perforated with subwavelength apertures of diverse geometrical patterns (metascreens) by means of a systematic methodology is presented in this paper. The principal concept of the new technique stems from the efficient characterization—via the use of effective surface parameters—of the metascreen’s complementary array of scatterers (i.e., a metafilm) and the proper utilization of the Babinet duality principle. To this end, a previously developed model for metafilms is carefully extended (for normal plane wave incidence) in order to apply to frequencies where the extraordinary transmission phenomenon typically occurs. General-purpose analytical formulas for the reflection and transmission coefficients of an arbitrary metascreen are also derived as part of this generalized framework. Finally, the predictions for the extraordinary transmission spectra through various metascreens operating in the microwave regime, as obtained via two distinct realizations of the proposed formulation, are compared with the results of a commercial computational package in order to verify the precision of the developed technique and provide instructive physical insights.

Analysis of TLM air-vent model applicability to EMC problems for normal incident plane wave

Analysis of TLM air-vent model applicability to EMC problems for normal incident plane wave

On- and off-optical-resonance dynamics of dielectric microcylinders under plane wave illumination

We explore the on-resonance and off-resonance optical response of dielectric cylinders excited by normal incident plane waves. Both the analytical method, based on Mie theory, and the numerical method, implemented with the spectral element method, are undertaken in the study. We demonstrate that the whispering gallery mode characteristic of resonance behavior is strongly dependent on the refractive index and radius changes. Detuning of either parameter deteriorates the resonance action and creates yet another exciting phenomenon known as photonic nanojets. The subwavelength light focusing property can be associated with nanojets, and engineering the parameters yields strong field confinement and slowly diffracting beam propagation. The current work investigates the optical properties of the dielectric microcylinders at close proximity to the resonance condition. Both strong field focusing associated with photonic nanojets and enhanced field localization linked with the resonance condition are desired for photon manipulation scenarios in nanophotonics.

Design of a terahertz even splitter and its tolerance analysis

A novel method is presented in this paper to realize terahertz even beam splitting by using a subwavelength binary simple periodic rectangular structure, for making comprehensive application of both the RCWA (Rigorous Couple-Wave Analysis) and the GA (Genetic Algorithm). By applying RCWA, the efficiency of each diffraction order can be numerically solved by using the structure parameters. To design an even beam splitter with a subwavelength structure is to find the optimal duty cycle f, period d, the grating depth h1 and the substrate thickness h2 to approach the minimum zero-order diffraction efficiency, the maximum sum of each non-zero-order diffraction efficiency, and the uniform distribution. Considering the three goals above, an evaluation function is established. GA is applied to optimize the evaluation function F, and then the optimal parameters of the splitter are obtained. When its period, groove depth, substrate thickness and duty ratio respectively equal to 269.7 μm, 175.2 μm, 18.1 μm and 0.409, the normal-incident TE-polarized terahertz plane wave with its frequency equal to 2.52 THz is divided evenly into the diffraction orders±1 and±2. It has a total efficiency up to 92.23% with a preferable result of reducing zero-order diffraction efficiency to 0.192% and an error of uniformity down to 6.51×10- 6, indicating an excellent performance of diffraction efficiency, uniformity and zero-order suppression as a terahertz even splitter. These results break the limitation of realizing even beam splitting in which the traditional scalar theory applies. In addition, this paper exposes the law of influence of the structure parameters, including ridge width, groove width, groove depth, duty ratio and substrate thickness, on the diffraction efficiency and its uniformity. It is found that only a small deviation of the structure parameters, corresponding to a deviation of ridge width a, groove width b, groove depth h1, and substrate thickness h2, less than 1 μm from the optimum design values, the element maintains good beam splitting performance. P0 is permitted to suppress to less than 2%, the error of uniformity U is better than 19.60%, and the diffraction efficiency maintains higher than 79.10%. With a substantial deviation from the design values of the structure parameters, the performance of the splitter will severely degrade and need to be redesigned.

Suppression of Specular Reflections by Metasurface with Engineered Nonuniform Distribution of Reflection Phase

We make preliminary investigations on a new approach to reducing radar cross section (RCS) of conducting objects. This approach employs novel planar metasurfaces characterizing nonuniform distribution of reflection phase. The operation principle of this approach and the design rule of the associated metasurfaces are explained using a simplified theoretical model. We then present a design example of such metasurfaces, in which three-layer stacked square patches with variable sizes are utilized as the reflecting elements. The proposed RCS-reduction approach is verified by both numerical simulations and measurements on the example, under the assumption of normal plane wave incidence. It is observed that, in a fairly wide frequency band (from 3.6 to 5.5 GHz), the presented example is capable of suppressing the specular reflections of conducting plates significantly (by more than 7 dB) for two orthogonal incident polarizations.

Acoustic scattering from an infinitely long cylindrical shell with an internal mass attached by multiple axisymmetrically distributed stiffeners

A thin infinitely long elastic shell is stiffened by J in number identical lengthwise ribs distributed uniformly around the circumference and joined to a rod in the center. The 2D model of the substructure is a rigid central mass supported by J axisymmetrically placed linear springs. The response of the shell–spring–mass system is quite different from a fluid filled shell or that of a solid cylinder due to the discrete number of contact points which couple the displacement of the shell at different locations. Exterior acoustic scattering due to normal plane wave incidence is solved in closed form for arbitrary J. The scattering matrix associated with the normal mode solution displays a simple structure, composed of distinct sub-matrices which decouple the incident and scattered fields into J families. The presence of a spring–mass substructure causes resonances which are shown to be related to the subsonic shell flexural waves, and an approximate analytic expression is derived for the quasi-flexural resonance frequencies. Numerical simulations indicate that the new solution for J≥3 springs results in a complicated scattering response for plane wave incidence. As the number of springs becomes large enough, the total scattering cross-section is asymptotically zero at low frequencies and slightly increased compared to the empty shell at moderate frequencies due to the added stiffness and mass. It is also observed that the sensitivity to the angle of incidence diminishes as the number of springs is increased. This system can be tuned by selecting the shell thickness, spring stiffness and added mass to yield desired quasi-static effective properties making it a candidate element for graded index sonic crystals.

Fano collective resonance as complex mode in a two-dimensional planar metasurface of plasmonic nanoparticles

Fano resonances are features in transmissivity/reflectivity/absorption that owe their origin to the interaction between a broad bright resonance and a dark (i.e., sub-radiant) narrower one. They may emerge in the optical properties of planar two-dimensional (2D) periodic arrays (metasurfaces) of plasmonic nanoparticles. In this letter, we provide a thorough assessment of their nature for the general case of normal and oblique plane wave incidence, highlighting when a Fano resonance is affected by the mutual coupling in an array and its capability to support free modal solutions. We analyze the representative case of a metasurface of plasmonic nanoshells at ultraviolet frequencies and compute its absorption under TE- and TM-polarized, oblique plane-wave incidence. In particular, we find that plasmonic metasurfaces display two distinct types of resonances observable as absorption peaks: one is related to the Mie electric dipolar resonance of each nanoparticle and the other is due to the forced excitation of free modes with small attenuation constant, usually found at oblique incidence. The latter is thus an array-induced collective Fano resonance. This realization opens up to manifold flexible designs at optical frequencies mixing individual and collective resonances. We explain the physical origin of such Fano resonances using the modal analysis through which we calculate the free modes with complex wavenumber supported by the metasurface. We define equivalent array dipolar polarizabilities that are directly related to the absorption physics at oblique incidence and show a direct dependence between array modal phase and attenuation constants and Fano resonances. We thus provide a more complete picture of Fano resonances that may lead to the design of filters, energy-harvesting devices, photodetectors, and sensors at ultraviolet frequencies. Similar resonances may be also extended to the visible range with an appropriate choice of geometries and materials.

ϵ-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves

Graded index ϵ-near-zero (GRIN-ENZ) quasi-optical components such as beam steerers and power splitters are designed, simulated and analyzed. The GRIN-ENZ medium is realized using stacked narrow hollow waveguides whose infinite array shows the first transmission peak at 1.0002 THz. Several GRIN-ENZ beam steerers to channel a normal incident plane wave to different output angles (15, 45, 65 and 80°) with good impedance matching (low reflection) are analytically and numerically demonstrated using planar structures with a thickness of 5λ0 = 1500 μm along the z-axis. Moreover, symmetrical and asymmetrical power splitters are designed with output angles (±45°) and (−80, +35°), respectively.

Broadband Absorptance High Efficiency Silicon Nanowire Fractal Arrays for Photovoltaic Applications

ABSTRACTNanowire arrays have been proposed to enhance light trapping, increase efficiencies, and reduced material cost in photovoltaic solar cells. In this work we present a new crystalline silicon nanowire array structure, inspired by fractal geometry. The array structure is assumed to be an infinite 2D array in the x and y directions, and composed of vertically aligned SiNW suspended in air. Hexagonal fractal-like geometry is adapted in arranging cylindrical SiNW in these arrays. Full-wave finite element method 3D simulation is used to compute reflectance, transmittance and absorptance of the array for a normal incidence plane wave. The proposed fractal-like distribution of SiNW arrays yield broad absorption spectrum and enhanced efficiency while using less material. The efficiency of the proposed fractal-like SiNW arrays achieve ∼100% enhancement over that of the equivalent thickness flat c-Si film, and ∼18% enhancement over an equivalent height hexagonal array. The proposed optimized structures achieved a filling ratio ∼25%, which is ∼33% less than the corresponding hexagonal array.

Theoretical and Experimental Investigation of a 60-GHz Off-Body Propagation Model

A fast computation and accurate analytical model for off-body propagation is derived in this paper. The paper discusses the off-body model propagation from an external source to a receiver located on the body. The model is developed for normal incident plane wave by describing the human body with a circular cylinder. We show that the total received electric field around the human body can be written as a creeping wave in the shadow region and as a geometrical optics result for the lit region. It is also shown that at 60 GHz, the shadow boundary width is negligible. The model shows perfect agreement with the experimental results conducted on a perfectly conducting cylinder. Measurements of the creeping wave path gain have been also conducted on a real body to assess the validity of the cylinder assumption. The results have shown a path gain of about 5 dB/cm for the TM case and 3 dB/cm for the TE case. The standard deviation between the measurements and the cylindrical model is about 3.5 dB for both TM and TE cases.

Transmission of a spherical sound wave through a single-leaf wall: Mass law for spherical wave incidence

This paper examines the sound insulation of a single-leaf wall driven by a spherical wave. The transmitted sound field of an infinite elastic plate under a spherical wave incidence is theoretically analyzed and insulation mechanisms are considered. The displacement of the plate is formulated using the Hankel transform in wavenumber space and the transmitted sound pressure in the far-field is obtained by Rayleigh’s formula in an explicit closed form. Moreover, a reduction index is also derived in a closed form by introducing an approximation into the vibration characteristics of the plate. Deterioration of the insulation performance under the spherical wave incidence is caused by an apparent decrease of wall impedance that depends on the directivity of the transmitted sound wave. The mass law for a spherical wave incidence is different from that for a normal plane wave incidence: doubling the weight of the wall or the frequency gives an increase of 3dB (c.f. 6dB for a normal plane wave incidence), which is also smaller than the field incidence mass law.

Acoustic properties of low growing plants

The plane wave normal incidence acoustic absorption coefficient of five types of low growing plants is measured in the presence and absence of soil. These plants are generally used in green living walls and flower beds. Two types of soil are considered in this work: a light-density, man-made soil and a heavy-density natural clay base soil. The absorption coefficient data are obtained in the frequency range of 50-1600 Hz using a standard impedance tube of diameter 100 mm. The equivalent fluid model for sound propagation in rigid frame porous media proposed by Miki [J. Acoust. Soc. Jpn. (E) 11, 25-28 (1990)] is used to predict the experimentally observed behavior of the absorption coefficient spectra of soils, plants, and their combinations. Optimization analysis is employed to deduce the effective flow resistivity and tortuosity of plants which are assumed to behave acoustically as an equivalent fluid in a rigid frame porous medium. It is shown that the leaf area density and dominant angle of leaf orientation are two key morphological characteristics which can be used to predict accurately the effective flow resistivity and tortuosity of plants.

An X-Band Reflectarray With Novel Elements and Enhanced Bandwidth

A novel single-layer reflectarray element with an I-shaped dipole encompassed by a circular ring, showing smooth phase-frequency response, is proposed in this letter. Based on this element, an optimization method is adopted to match the desired phase delays at two edge frequencies so as to get fixed phase difference between two adjacent elements in the optimized band. A low-profile X-band 6 × 10-element reflectarray with a scattering angle of 30° for normal incidence of plane waves is designed and fabricated. Simulations and measurements show that a bandwidth of 22.3% for 3 dB directivity dropping and 15.2% for -10 dB sidelobe level (SLL) can be achieved.