Lossy Metamaterials Research Articles

Poles and residues of lossy and dispersive electromagnetic metamaterials

This paper proposes a system-based pole-residue approach to describe loss and dispersion in double-positive (DPS), epsilon-negative (ENG), and epsilon-near-zero (ENZ) isotropic metamaterials. The matrix pencil (MP) method extracts the poles and residues from the damped sinusoids of the singular expansion (SEM) of the impulse responses of the transmitted and reflected waves. The complex values of poles and residues serve as a basis for a computational tool to discriminate between lossless, lossy, and dispersive materials. The extracted poles and residues can also be used to classify the material under test as a DPS, an ENG, or an ENZ metamaterial. The proposed method delivers reliable results even with noisy transmission and reflection data.

Effects of Defect Layers and Loss Factors on Transmission Spectrum for One-dimensional Lossy Metamaterial Photonic Crystal

Effects of Defect Layers and Loss Factors on Transmission Spectrum for One-dimensional Lossy Metamaterial Photonic Crystal

Analysis and Modeling of Wideband Common-Mode Absorption With Lossy Complementary Split-Ring Resonator Chain in Resistor-Free Differential Microstrip Lines

Novel resistor-free differential microstrip lines prototype loaded with lossy metamaterial is proposed to achieve wideband common-mode (CM) absorption. The metamaterial is constructed by a chain of lossy complementary split-ring resonators (CSRRs), which are etched on the ground plane. Different from the CM absorption realized by lumped resistors, this work utilizes the inherent dielectric and conductor losses introduced by the differential microstrip lines and CSRRs to absorb CM energy. Furthermore, CSRRs are designed with gradual perturbation to broaden the CM absorption band. The lossy even-mode equivalent circuit models are established and analyzed to reveal the CM absorption mechanism. In order to verify the proposed strategy to design resistor-free differential microstrip lines with CM absorption, a sample was fabricated and measured. The measured <inline-formula> <tex-math notation="LaTeX">$S_{\mathrm {cc21}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$S_{\mathrm {cc11}}$ </tex-math></inline-formula> are kept below &#x2212;10 dB simultaneously from 4.3 to 5.65 GHz with 27.4&#x0025; fractional bandwidth, where the CM energy is absorbed over 80&#x0025; by the dielectric and conductor losses. Meanwhile, the low insertion loss of <inline-formula> <tex-math notation="LaTeX">$S_{\mathrm {dd21}}$ </tex-math></inline-formula> below 6 GHz as well as the good differential-mode eye diagrams demonstrates that good signal integrity of differential signals is kept.

Acoustic wave propagation in permeable lossy metamaterials

This paper investigates acoustic wave propagation in gas-saturated permeable lossy metamaterials, which have different types of resonators, namely, acoustic and elastic resonators, as building-block elements. By using the two-scale asymptotic homogenization method, the macroscopic equations that govern sound propagation in such metamaterials are established. These equations show that the metamaterials can be modeled as equivalent fluids with unconventional effective density and compressibility. Analysis of these frequency-dependent and complex-valued parameters shows that the real parts of both can take negative values within frequency bands determined by inner resonances. The upscaled theory is exemplified with the case of a permeable lossy metamaterial having a unit cell comprising two unconnected fluid networks and a solid frame. One of these fluid networks is loaded with acoustic resonators (e.g., quarter-wavelength, Helmholtz resonators), while thin elastic films are present in the other one. It is shown that the propagation of acoustic waves in permeable lossy metamaterials is determined by both classical visco-thermal dissipation and local elasto-inertial resonances. The results are expected to lead to judicious designs of acoustic materials with peculiar properties including negative phase velocity and phase constant characteristic for regressive waves, very slow phase velocity, and wide sub-wavelength bandgaps.

Absorption and Diffusion Enabled Ultrathin Broadband Metamaterial Absorber Designed by Deep Neural Network and PSO

With absorption and interference cancellation, lossy metamaterials can achieve broadband electromagnetic wave absorption. However, the design of such metamaterial absorbers (MMAs) is very complicate, because tremendous meta-atoms and their configuration parameters need to be determined. The conventional methods, such as parameter sweep and adjoint-based optimization, suffer from slow convergence and local minimum problem. In this letter, a deep neural network (DNN) is used to map the configuration parameters of a type of meta-atom onto its reflection coefficients. The DNN well predicts the reflection coefficients and is applied to design the MMA under the demand of −10 dB backscattering reduction (BSR) covering the microwave S to Ku bands with the smallest thickness. By globally searching the configuration parameter space using particle swarm optimization (PSO) algorithm, which automatically cooperates the absorption and phase cancelation (or diffusion) of meta-atoms, we obtain the optimized configuration of the meta-atoms and corresponding filling ratios. The designed MMA realizes −10 dB absorption bandwidth covering 2.2–18 GHz with the thickness only 4 mm, which is further verified by experiments. The performance of our absorber is better than other similar absorbers reported. Our letter provides a useful method for ultrathin broadband MMA design, which can also be applied to other functional devices based on metamaterials.

Multi-scale integrated design and fabrication of ultrathin broadband microwave absorption utilizing carbon fiber/Prussian blue/Fe3O4-based lossy lattice metamaterial

Microwave absorption materials (MAMs) are specialist kinds of composites applied in stealth technology and electromagnetic interference (EMI).

Fine manipulation of sound via lossy metamaterials with independent and arbitrary reflection amplitude and phase

The fine manipulation of sound fields is critical in acoustics yet is restricted by the coupled amplitude and phase modulations in existing wave-steering metamaterials. Commonly, unavoidable losses make it difficult to control coupling, thereby limiting device performance. Here we show the possibility of tailoring the loss in metamaterials to realize fine control of sound in three-dimensional (3D) space. Quantitative studies on the parameter dependence of reflection amplitude and phase identify quasi-decoupled points in the structural parameter space, allowing arbitrary amplitude-phase combinations for reflected sound. We further demonstrate the significance of our approach for sound manipulation by producing self-bending beams, multifocal focusing, and a single-plane two-dimensional hologram, as well as a multi-plane 3D hologram with quality better than the previous phase-controlled approach. Our work provides a route for harnessing sound via engineering the loss, enabling promising device applications in acoustics and related fields.

Stored and absorbed energy of fields in lossy chiral single-component metamaterials

Here we present theoretical results for estimation of electromagnetic field energy density and absorbed energy in dispersive lossy chiral single-component metamaterials which consist of an ensemble of identical helical resonators as inclusions. The shape of the helical resonator can vary over a wide range, from a straight wire to a flat split ring. An interaction of the inclusions with harmonic circularly polarized electromagnetic plane waves is studied. We focus on how the inclusion shape influences the mentioned metamaterial properties. The derived general solution for the problem is in good agreement with previous partial and alternative solutions obtained for split ring resonators, straight wires, and helices. The study reveals the optimal geometry of helical lossy resonators for their strongest selectivity of interaction with circularly polarized radiation.

E-B Eigenmode Formulation for the Analysis of Lossy and Evanescent Modes in Periodic Structures and Metamaterials

We present here a 3-D E-B linear eigenmode formulation for the analysis of periodic structures, including lossy periodic waveguides, photonic crystals, and metamaterials. The proposed finite-element formulation utilizes proper H (curl) vector basis functions for the electric field and H (div) vector basis functions for magnetic flux density. The resulting eigenmode problem is linear, and it enforces periodic boundary conditions in a simple manner via appropriate field transformations and does not exhibit spurious modes. Moreover, it can provide accurate complex-k dispersion diagrams, in terms of both propagation and attenuation constant, while it is also able to deal with either propagating or evanescent modes, including those with oblique propagation directions.

Periodic Structure Containing Lossy Metamaterial and Defect Mode

Periodic Structure Containing Lossy Metamaterial and Defect Mode

A Generalized Reaction Theorem That Eliminates Internal Resonances in the Electric and Magnetic Field Integral Equations

This paper presents stable magnetic-field and electric-field integral equation formulations for exterior electromagnetic scattering by either penetrable or perfectly conducting closed bodies of general shape. The development relies on an extension of the conventional reciprocity theorem allowing the fields produced by some combination of sources in one environment to be connected with the fields generated by another combination of sources in a different environment. By the use of lossy metamaterials, the internal-resonance problem inherent to the original versions is eliminated, and thus the new formulations are amenable to a unique, highly accurate, and well-conditioned solution.

A broadband sound absorber based on lossy acoustic rainbow trapping metamaterials

Acoustic rainbow trapping (ART) metamaterials offer spatial-spectral modulation and intensive trapping of broadband sound, with strong acoustic dispersion that is absent in naturally occurring materials. However, thermal and viscous losses stemming from the acoustic boundary layers within narrow resonance regions of ART metamaterials has not been thoroughly studied and effectively utilized. Here, we would like to propose a lossy model of ART metamaterials. By taking advantage of the thermal and viscous losses, such lossy metamaterials can effectively work as a broadband sound absorber. A rigid surface perforated with very narrow subwavelength holes that can provide boundary-layer losses and have gradient depth along the propagation direction is constructed to mimic the lossy ART model. Full wave numerical simulation results indicate that the system's thermal and viscous losses are governed by the geometry of the resonance unit cells. Together with the intrinsic trapping effect, this lossy ART metamaterials function as a high performance broadband sound absorber. It may contribute to the optimization of sound absorption materials and wedge design of anechoic chambers.

Negative refractive index and negative refraction of waves in lossy metamaterials

An experimental study of the conditions for negative energy refraction and negative phase refraction in lossy metamaterials is provided. In hypothetical non-lossy metamaterials, the angles of phase and energy refraction are one and the same. Using measured S-parameters of split ring resonator–wire metamaterial samples, it is shown that negative refractive index is not a requirement for negative energy refraction in lossy metamaterials. It was assumed that the sample is effectively homogeneous and isotropic in the direction of wave propagation. For transverse-electric polarisation, negative energy refraction with a positive refractive index was demonstrated.

Loss-induced localized field enhancement and optical bistable state in heterostructure containing single-negative materials

Permittivity depends on the electric field intensity in a nonlinear material, and it changes with the incident intensity of the electromagnetic wave. This phenomenon leads to the occurrence of optical bistability. The optical bistable threshold value depends on the localized degree of electromagnetic field in the nonlinear material, and the stronger the localized field, the lower the threshold value is. However, the loss of material is one of the important factors influencing the strength of the local field. It is commonly believed that the loss is not conducible to reducing the threshold value because increased loss can weaken the localized degree of fields. For the lossy single-negative metamaterial, the transmission is nonmonotonic as the loss varies. That is to say, the transmission first decreases and then increases in the lossy single-negative metamaterial. Therefore, the nonlinear transmission in the lossy single-negative metamaterial may lead to novel physical phenomena. Permeability-negative material and permittivity-negative material are two kinds of different single-negative metamaterials. In this paper, the optical bistable phenomena in the heterostructure of permeability-negative material and permittivity-negative material are studied by using the transfer matrix method. Here, the permittivity-negative material is nonlinear material. The results show that the optical bistable threshold value first increases and then falls down as the loss increases. The variance of the localized electromagnetic field at the interface between the permeability-negative layer and the permittivity-negative layer at the discussed frequency is discussed in the present paper to understand the nonmonotonic phenomenon. Further studies indicate that the nonmonotonic localized electromagnetic field is also presented at the interface between the permeability-negative layer and permittivity-negative layer. That is to say, the enhancement of the localized field can be obtained when the loss is increased, which results in the nonmonotonic optical bistable threshold value in the heterosturcture composed of the single-negative metamaterials. In the final analysis, the abnormal phenomenon is induced by the loss in the single-negative metamaterial, which is the special property of single-negative metamaterial.

Perfect Lensing by a Single Interface: Defying Loss and Bandwidth Limitations of Metamaterials.

Loss is known to be detrimental for achieving perfect focusing with the passive perfect lens designs suggested thus far, and it is believed to pose a fundamental barrier. We show that perfect lensing can be achieved with actual lossy left-handed metamaterials, without a need for gain or nonlinearity. The proposed loss-immune perfect lens is composed of a single interface between a conventional dielectric material on the source side and a lossy left-handed material on the image side. Its immunity to material loss was derived analytically using three complementary methodologies, confirming perfect lensing with point-to-point accuracy and shedding light on the underlying focusing mechanism. This result provides a new road map for practical realization of a near-field camera based on the single-interface lens design.

Dyakonov surface waves in lossy metamaterials

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.

Negative-index metamaterials: is double negativity a real issue for dissipative media?

One way to obtain materials with a negative index is to achieve media with doubly negative constitutive parameters. We show that the double negativity required for perfect (non-dissipative) media is not necessary for real passive (lossy) metamaterials, for which single negativity of one of the two constitutive parameters may be sufficient. The analysis is presented through original diagrammatic representations involving both the real and imaginary parts of the dynamic constitutive parameters for isotropic media. A valid demonstration for acoustic and electromagnetic metamaterials is supported by considering an actual soft 3D locally-resonant ultrasonic metafluid having a negative acoustic index while being a single-negative medium. The crucial role of the imaginary parts of the constitutive parameters is then discussed through its impact on the figure of merit. Finally, the analysis is extended to an example of an electromagnetic negative-index metamaterial exhibiting both single and double negativity.

An automated phase correction algorithm for retrieving permittivity and permeability of electromagnetic metamaterials

To retrieve complex-valued effective permittivity and permeability of electromagnetic metamaterials (EMMs) based on resonant effect from scattering parameters using a complex logarithmic function is not inevitable. When complex values are expressed in terms of magnitude and phase, an infinite number of permissible phase angles is permissible due to the multi-valued property of complex logarithmic functions. Special attention needs to be paid to ensure continuity of the effective permittivity and permeability of lossy metamaterials as frequency sweeps. In this paper, an automated phase correction (APC) algorithm is proposed to properly trace and compensate phase angles of the complex logarithmic function which may experience abrupt phase jumps near the resonant frequency region of the concerned EMMs, and hence the continuity of the effective optical properties of lossy metamaterials is ensured. The algorithm is then verified to extract effective optical properties from the simulated scattering parameters of the four different types of metamaterial media: a cut-wire cell array, a split ring resonator (SRR) cell array, an electric-LC (E-LC) resonator cell array, and a combined SRR and wire cell array respectively. The results demonstrate that the proposed algorithm is highly accurate and effective.

ROLE OF THE LINEAR LOSSES AND NONLINEAR MAGNETIC SUSCEPTIBILITY IN THE MODULATIONAL INSTABILITY IN NONLINEAR METAMATERIALS

We analyze modulation instability (MI) in lossy metamaterials (MMs) with both nonlinear polarization and nonlinear magnetization. A detailed discussion on the role of the nonlinear electric polarization, nonlinear magnetic susceptibility and linear loss on the MI is presented. It is found that the nonlinear magnetization and linear loss play an important role in determining the MI in nonlinear MMs. Linear stability analysis predicts that MI may occur in the MMs with self-defocusing nonlinearity due to the negative-index of MMs. In particular, the nonlinear magnetic susceptibility changes the generation condition of MI seriously, it can be used to enhance or depress the MI depending on the sign of the nonlinear magnetic susceptibility. Finally, the influence of the loss in MMs on the MI is discussed.

Investigation of one-dimensional photonic bandgap structures containing lossy double-negative metamaterials through the Bloch impedance

The Bloch impedance is studied and used to understand the properties of the absorption loss in one-dimensional photonic crystals (PCs) composed of air and metal-based double-negative metamaterials. We find that as the frequency increases across the zero-¯ n gap of the considered structures, the modulus of the Bloch impedance always decreases from a maximum to a minimum value. On the other hand, the frequency dependence of the phase angle of the Bloch impedance is greatly influenced by the ratio of the electric to the magnetic damping coefficient γe∕γm of the metamaterials. When the phase angle of the Bloch impedance reaches maximum inside the zero-¯ n gap, the impedance mismatch between the incident medium and the considered PC becomes greatest, the reflection will be strongest and a minimum absorption will be observed. As γe∕γm increases, the frequency corresponding to the minimum absorption shifts from the lower to the upper gap edge. We also show that the main characteristics of both the Bloch impedance and the absorption loss are insensitive to the geometrical parameters. Our study offers a valuable reference in the designs of zero-¯ n gap with optimized properties. © 2013 Optical Society of America