We present theoretically a type of one-dimensional (1D) structured ultrasonic metamaterial that exhibits a forbidden band where both the effective dynamic density and bulk modulus are simultaneously negative. The material consists of a 1D array of repeated unit cells with shunted Helmholtz resonators. The transmission coefficient, wave vector, negative dynamic density, and modulus are determined by means of the acoustic transmission line method (ATLM). The double negativity in the effective dynamic density and bulk modulus is an acoustic counterpart of negative permittivity and permeability in the electromagnetic metamaterials. The double negative band is ascribed to the local resonance. In order to confirm the ATLM results, we further calculate the field intensity, phase distribution, and transmission coefficient using the finite element method. In addition, the influences of some essential geometric acoustic parameters on the transmission properties, such as periodic constant $L$, are also discussed.

One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus

Inspired by the fractal concept, a miniaturized and fully printed planar, left-handed (LH) material with C band (from 4.89 to 5.55 gigahertz) negative permittivity and permeability is proposed, using the transmission-line (TL) approach. By incorporating four interdigital capacitors in the Sierpinski fractal curves of the second iteration order, the resulting LH-TL material features large inductance and capacitance values in the equivalent circuit model, and thus facilitates an electrically small dimension and a broadband negative magnetic response. Based on the planar LH-TL materials and sophisticated theory, a three-dimensional (3D) free-space LH-TL super lens is designed and fabricated using multiple structures. Both numerical and experimental results illustrate that the 3D super lens exhibits excellent impedance matching to free space and significantly improves the imaging resolution. It is shown that the resolution reaches 0.39 λ0 at 5.35 gigahertz, in which the LH-TL material possesses μ ≈ –μ0 and e ≈ –e0 (μ0 and e0 are free-space permeability and permittivity).

Three‐Dimensional Super Lens Composed of Fractal Left‐Handed Materials

Understanding the impact of order and disorder is of fundamental importance to perceive and to appreciate the functionality of modern photonic metasurfaces. Metasurfaces with disordered and amorphous inner arrangements promise to mitigate problems that arise for their counterparts with strictly periodic lattices of elementary unit cells such as, e.g., spatial dispersion, and allows the use of fabrication techniques that are suitable for large scale and cheap fabrication of metasurfaces. In this study, we analytically, numerically and experimentally investigate metasurfaces with different lattice arrangements and uncover the influence of lattice disorder on their electromagnetic properties. The considered metasurfaces are composed of metal-dielectric-metal elements that sustain both electric and magnetic resonances. Emphasis is placed on understanding the effect of the transition of the lattice symmetry from a periodic to an amorphous state and on studying oblique illumination. For this scenario, we develop a powerful analytical model that yields, for the first time, an adequate description of the scattering properties of amorphous metasurfaces, paving the way for their integration into future applications.

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Resonant metasurfaces at oblique incidence: interplay of order and disorder

In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of regular and random grids and explain recently observed dramatic differences in resonance broadening in the electric and magnetic modes of random arrays. We show that randomness in the particle positioning influences equally on the scattering loss from both electric and magnetic dipoles, however, the observed resonance broadening can be very different depending on the absorption level in different modes as well as on the average electrical distance between the particles. The theory is illustrated by an example of a planar metasurface composed of cut-wire pairs. We show that in this particular case at the magnetic resonance the array response is almost not affected by positioning randomness due to lower frequency and higher absorption losses in that mode. The developed model allows predictions of behavior of random grids based on the knowledge of polarizabilities of single inclusions.

Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state

We report a polarization beam splitter (PBS) utilizing the anomalous reflection and transmission of an anisotropic metamaterial slab. By properly design of the constitutive tensors of the slab, PBS is achieved with little dependence on incident angle and slab thickness. The realization of the proposed PBS in the optical range is achieved by layered metal-dielectric nanostructured system, which could be modeled as an effective anisotropic metamaterial with the desired constitutive tensors. The full-wave electromagnetic simulation has confirmed the optical polarization splitting with an extinction ratio of over 20dB by a slab of an alternating silver and silicon carbide multilayer.

Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure

We propose a complete set of periodic circuit networks which can realize electromagnetic wave propagation in different two-dimensional (2D) isotropic and anisotropic metamaterials (AMMs). We synthesize the periodic circuits with unit cells of series capacitor or inductor in orthogonal directions, together with either capacitor or inductor shunted to ground. The dispersion relations of the periodic circuits are derived by applying Bloch boundary conditions to the unit cell, which show either elliptic or hyperbolic dispersion surface in phase space. The effective constitutive parameters are obtained by choosing different types and values of the impedance elements in the unit cell. The validity of the circuit models is proved by showing examples that the anisotropic $L\text{\ensuremath{-}}C$ circuits could exhibit the wave propagation characteristics of two 2D AMMs with different cutoff properties, called never-cutoff or anti-cutoff medium. We construct interfaces between isotropic normal medium and AMMs with properly designed $L\text{\ensuremath{-}}C$ circuits and analyze the electromagnetic wave propagation using microwave circuit simulations. We demonstrate extraordinary electromagnetic wave reflection and refraction phenomena including negative refraction, total reflection with reversion of the critical angle and anomalous Brewster effect that have good agreements with the theoretical analysis. Furthermore, we show that the $L\text{\ensuremath{-}}C$ circuit models of AMMs could lead to different approach of actual implementation of 2D AMMs through capacitance loaded transmission line metamaterials. The simulation on actual microstrip line structure demonstrates similar wave propagation phenomena of AMMs, and the losses in the structure only affect the magnitude of the propagating energy.

Electromagnetic wave propagation in anisotropic metamaterials created by a set of periodic inductor-capacitor circuit networks

We realize the planar lens of anisotropic compensated bilayer through the implementation of anisotropic metamaterials by periodic transmission-line circuits based on different unit cells of loaded microstrip grids. The electromagnetic wave propagation in such transmission-line circuits has been analyzed using microwave circuit simulations and verified by experiment on fabricated transmission-line circuit structure. Utilizing the compensated bilayer lens, we demonstrate subwavelength imaging at microwave frequency including the consideration of losses in the lens. We also confirm that the spatial resolution of the compensated bilayer lens is less sensitive to material loss than that of an isotropic left-handed metamaterial planar lens.

Subwavelength imaging with compensated anisotropic bilayers realized by transmission-line metamaterials

We have studied the electromagnetic wave propagation in two-dimensional anisotropicmetamaterial (AMM) by realizing the AMM through periodic structure composed of anisotropically loaded transmission line (TL) network. The dispersion relation of the TL metamaterial is analyzed by rigorous periodic TL theory, which shows hyperbolic dispersion surface in phase space below certain critical frequency. Utilizing microstrip line technique, we have constructed an interface between isotropic normal medium and a particular type of AMM with properly designed normal TL mesh and the loaded TL network, respectively. The electromagnetic wave propagation in such system has been analyzed with the consideration of circuit losses using microwave circuit simulations. We directly demonstrate interesting phenomena including the total reflection with inversion of the critical angle at small incident angle as well as the oblique total transmission at large incident angle at the interface, which have good agreement with the theoretical prediction.

Anomalous reflection and refraction in anisotropic metamaterial realized by periodically loaded transmission line network

We have studied the electromagnetic wave propagation in a two-dimensional anisotropic metamaterial (AMM) realized by a periodic structure composed of an anisotropically loaded transmission line (TL) network. The dispersion relation of the TL metamaterial is analysed by rigorous periodic TL theory, which shows hyperbolic dispersion surface in phase space below a certain critical frequency. We have constructed an interface between an isotropic normal medium and an AMM with a properly designed normal TL mesh and the loaded TL network, respectively, and analysed the electromagnetic wave propagation in such a system using microwave circuit simulations. We directly demonstrate the negative refraction of energy flow and the positive refraction of the wave vector, as well as the partial focusing phenomenon in such AMM, have good agreement with the theoretical prediction. When the dissipation is included in the simulation on actual microstrip line structure, we find that the dissipation in the TL metamaterial affects only the magnitude of the propagating energy, not the refraction phenomenon.

https://iopscience.iop.org/article/10.1088/0022-3727/39/1/031/pdf

Negative refraction and partial focusing in an anisotropic metamaterial realized by a loaded transmission line network

Ordinary planar waveguide cannot support electromagnetic (EM) wave propagating at frequency below the cut-off frequency of the waveguide, due to the evanescent wave nature of the EM wave in such waveguide. We have found by theoretical analysis that extraordinary EM wave transmission could occur for transverse-electric modes at frequency below the cut-off frequency of the hollow waveguide by inserting different kinds of anisotropic metamaterials (AMMs) in the hollow waveguide. Such transmission of EM energy has no lower cut-off frequency and is due to the conversion of the evanescent wave into propagating mode inside the AMMs, which is quite different from that in the case of waveguide loaded with an isotropic left-handed material slab. We have verified the extraordinary phenomenon by performing circuit analog of the planar waveguide loaded with different kinds of AMMs through realization with transmission line metamaterials.

Xiaohua Teng

Papers

Electromagnetic wave propagation in anisotropic metamaterials created by a set of periodic inductor-capacitor circuit networks

Subwavelength imaging with compensated anisotropic bilayers realized by transmission-line metamaterials

Anomalous reflection and refraction in anisotropic metamaterial realized by periodically loaded transmission line network

Negative refraction and partial focusing in an anisotropic metamaterial realized by a loaded transmission line network

Extraordinary transmission in planar waveguide loaded with anisotropic metamaterials