Bianisotropic Metamaterials Research Articles

Bianisotropic metamaterials based on twisted asymmetric crosses

The effective bianisotropic response of 3D periodic metal-dielectric structures, composed of crosses with asymmetrically-cut wires, is investigated within a general homogenization theory using the Fourier formalism and the form-factor division approach. It is found that the frequency dependence of the effective permittivity for a system of periodically-repeated layers of metal crosses exhibits two strong resonances, whose separation is due to the cross asymmetry. Besides, bianisotropic metamaterials, having a base of four twisted asymmetric crosses, are proposed. The designed metamaterials possess negative refractive index at frequencies determined by the cross asymmetry, the gap between the arms of adjacent crosses lying on the same plane, and the type of Bravais lattice.

Power analysis of multilayer structures composed of conventional materials and bi-anisotropic metamaterial slabs

In this paper, we analyze wave propagation properties (transmitted, reflected, and absorbed powers) of composite multilayer structures consisting of bi-anisotropic metamaterial (MM) slabs and conventional isotropic materials. We also separately investigate the propagation properties of bi-anisotropic MM slabs and conventional materials to better interpret the results. We consider two different bi-anisotropic MM slab structures composed of only split-ring-resonators (SRRs) and composing SRRs and a rod. In the analysis, we apply the well-known transfer matrix method to obtain transmitted, reflected, and absorbed powers of the composite structures. From the analysis, we note the following three important results. First, while the transmitted powers from forward and backward directions of the multilayer structure are identical (reciprocal feature), reflected (and absorbed) powers from forward and backward directions of the multilayer structure are different. This difference arises from reflection asymmetric nature of the bi-anisotropic MM slabs. Second, whereas the conventional material loss influences propagation characteristics aside resonance frequencies of bi-anisotropic MM slabs, bi-anisotropic MM loss worsens propagation properties of the multilayer structure at resonance frequencies of these slabs. Third, variations in (or determination of) electromagnetic properties of low-loss thin conventional materials in between two bi-anisotropic MM slabs can be realized at frequencies in which conventional materials demonstrate thickness-resonance effect.

Importance of Mueller matrix characterization of bianisotropic metamaterials

We present a study on the optical properties of metamaterial layers containing U-shaped resonators. Using Finite Element Methods, we show that the description of the optical properties on one isolated resonator requires taking into account permittivity, permeability and magneto-electric tensors. The effect of weak spatial dispersion in arrays of resonators can be reproduced by adding two elements in the permittivity and magneto-electric coupling tensors. We show how the symmetries of the Mueller matrix of the sample can be used to discriminate the contributions of the different tensor elements. Generalized ellipsometry measurements made on a sample realized by e-beam lithography confirm the qualitative findings of the theoretical study. A quantitative determination of the different elements of permittivity, permeability and magneto-electric coupling is obtained by using oscillators with Lorentzian lineshape, to fit to the measurements.

Stepwise technique for accurate and unique retrieval of electromagnetic properties of bianisotropic metamaterials

Metamaterials (MMs) are artificial materials that have received attention recently because their built-in features create collective electromagnetic effects that are otherwise impossible, such as negative refraction, and because of their exotic electromagnetic applications, namely, perfect lens and invisibility cloaks. Depending on wave propagation characteristics, MMs possessing normally weak magneto-electric coupling coefficients start to exhibit stronger bianisotropic effects. Therefore, accurate electromagnetic characterization of these MMs is important. In this study, we adapt a stepwise method based on the Nicolson–Ross–Weir technique for accurate and unique retrieval of electromagnetic properties of bianisotropic MM slabs. For this goal, we have derived explicit expressions for unique retrieval of electromagnetic properties of these slabs and compared these expressions with those in the literature in the retrieval process. From the comparison, we note that derived expressions are appropriate for unique determination of electromagnetic properties of bianisotropic MM slabs. In the performance analysis of the stepwise method for different measurement scenarios, we considered different bianisotropic MM cell configurations (split-ring and Omega-shaped resonators as well as the same resonators with wire strips) and extracted their electromagnetic properties when measured/simulated scattering parameters have some thermal noise. We note that for most of the frequencies, the stepwise method retrieves correct electromagnetic properties even when a relatively higher normally distributed noise with zero mean value and with standard deviations of 0.015 is present. In addition to the influence of thermal noise on performance of the stepwise method, we also analyzed the effect of both increasing length slab and the frequency band on retrieved electromagnetic properties of the analyzed various bianisotropic MM slabs.

Polarizability Matrix Extraction of a Bianisotropic Metamaterial from the Scattering Parameters of Normally Incident Plane Waves

In this paper, a polarizability matrix retrieval method for bianisotropic metamaterials is presented. Assuming that scatterers can be modeled by electric and magnetic pointdipoles located at their centers, the induced dipole moments are analytically related to the normally incident fields, while the scattered fields are also analytically obtained for two individual cases of normal wave incidence. The latter can be combined with the incident fields, to express the desired polarizabilities, with regard to the measured or simulated scattering parameters. In this way, the polarizability matrix can be extracted by solving the resulting non-linear system of equations. The proposed technique is applied to two different split-ring resonator structures and reveals very good agreement with previously reported techniques.

Regularity of time-harmonic electromagnetic fields in the interior of bianisotropic materials and metamaterials

The regularity of the four time-harmonic vector fields composing any strong solution of the system obtained from Maxwell's curl equations and the constitutive relations in the interior of an inhomogeneous bianisotropic material are investigated. The results are given as interior Sobolev or Holder regularity. Possible local C ∞ regularity or local analyticity of the four vector fields are discussed, too. Each of these regularity results is obtained under specific conditions on the impressed current densities and on the constitutive parameters of the bianisotropic material considered, but it is shown that such conditions do not significantly limit the coverage of our analysis in terms of applications.

APPLICATION OF A USEFUL UNCERTAINTY ANALYSIS AS A METRIC TOOL FOR ASSESSING THE PERFORMANCE OF ELECTROMAGNETIC PROPERTIES RETRIEVAL METHODS OF BIANISOTROPIC METAMATERIALS

We applied a useful uncertainty model, ignored in most metamaterials retrieval studies, to monitor the accuracy of retrieved electromagnetic properties of bianisotropic metamaterial (MM) slabs composed of split-ring resonators and cut wires. Two difierent MM slab structures are considered to make the analysis complete. As uncertainty-making factors, we took into consideration of uncertainties in scattering (S-) parameters of bianisotropic MM slabs as well as the length of these slabs. The applied uncertainty model is based upon considering the efiect of minute change (difierential) in uncertainty factors on the retrieved electromagnetic properties of bianisotropic MM slabs. The signiflcant results concluded from the analysis are: 1) any abrupt changes in the phase of S-parameters of bianisotropic MM slabs remarkably in∞uence the retrieved electromagnetic properties; 2) any small-scale loss (i.e., the loss of the substrate) in the bianisotropic MM slabs improves the accuracy of the retrieved electromagnetic properties of these slabs; and 3) precise knowledge of bianisotropic MM slab lengths are required for correct analysis of exotic properties

Twisted optical metamaterials for planarized ultrathin broadband circular polarizers

Optical metamaterials are usually based on planarized, complex-shaped, resonant nano-inclusions. Three-dimensional geometries may provide a wider set of functionalities, including broadband chirality to manipulate circular polarization at the nanoscale, but their fabrication becomes challenging as their dimensions get smaller. Here we introduce a new paradigm for the realization of optical metamaterials, showing that three-dimensional effects may be obtained without complicated inclusions, but instead by tailoring the relative orientation within the lattice. We apply this concept to realize planarized, broadband bianisotropic metamaterials as stacked nanorod arrays with a tailored rotational twist. Because of the coupling among closely spaced twisted plasmonic metasurfaces, metamaterials realized with conventional lithography may effectively operate as three-dimensional helical structures with broadband bianisotropic optical response. The proposed concept is also shown to relax alignment requirements common in three-dimensional metamaterial designs. The realized sample constitutes an ultrathin, broadband circular polarizer that may be directly integrated within nanophotonic systems.

Retrieval of effective parameters for bianisotropic metamaterials with omega shaped metallic inclusions

Bianisotropic metamaterials including Ω-shaped metallic elements are investigated experimentally and theoretically. A passband is observed for a composite metamaterial (CMM) based on an Ω-medium below the plasmonic frequency of the corresponding closed CMM. The effective parameters (refractive index, impedances, permittivity, permeability, and magnetoelectric coupling coefficient) are retrieved for the Ω-medium and the CMM based on it. Our retrieval results show that the passband observed for the CMM is a band with positive refractive indices. Our retrieval results confirm the deductions of our previous reports.

Metamaterial-based model of the Alcubierre warp drive

Electromagnetic metamaterials are capable of emulating many exotic space-time geometries, such as black holes, rotating cosmic strings, and the big bang singularity. Here we present a metamaterial-based model of the Alcubierre warp drive, and study its limitations due to available range of material parameters. It appears that the material parameter range introduces strong limitations on the achievable "warp speed", so that ordinary magnetoelectric materials cannot be used. On the other hand, newly developed "perfect" bi-anisotropic non-reciprocal magnetoelectric metamaterials should be capable of emulating the physics of warp drive gradually accelerating up to 1/4c.

RETRIEVAL APPROACH FOR DETERMINATION OF FORWARD AND BACKWARD WAVE IMPEDANCES OF BIANISOTROPIC METAMATERIALS

A simple approach is proposed for retrieving the forward and backward wave impedances of lossless and lossy bianisotropic metamaterials. Compared with other methods in the literature, its main advantage is that forward and backward wave impedances can be uniquely and noniteratively extracted. It has been validated for both lossless and lossy bianisotropic metamaterials by performing a numerical analysis. The proposed approach can be applied for checking whether the metamaterial structure shows the bianisotropic property by monitoring forward and backward wave impedances, since the forward and backward wave impedances of a metamaterial structure depend on difierent polarizations of the incident wave.

A Cloaking Metamaterial Based on an Inhomogeneous Linear Field Transformation

A new type of bianisotropic metamaterial is theoretically investigated on the basis of a linear inhomogeneous field transformation applied to an arbitrary free-space Maxwellian field. This transformation does not include any space compression as predicted by transformation optics, and consists of a linear combination with space-dependent coefficients of the electric and magnetic incident fields. Duality conditions are applied to select an appropriate shape of the constituent dyads, thus resulting in a metamaterial completely defined by two real differentiable functions of space ¿ and ¿. When these functions satisfy the condition ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + ¿ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = constant on the medium contour, the medium becomes globally lossless, and when imposing ¿ = 0 and ¿ = 1 at the same boundary, the medium does not scatter for any arbitrary incident field, that is, it becomes invisible. When an additional internal boundary is introduced with boundary conditions ¿ = 0 and ¿ = 0, the medium becomes a perfect cloak. Explicit analytical results are given for an invisible sphere and for a spherical cloak to provide additional physical insight.

Bianisotropic Photonic Metamaterials

In metamaterials, electric (magnetic) dipoles can be excited by the electric (magnetic) component of the incident light field. Moreover, in the description of bianisotropic metamaterials, cross terms occur, i.e., magnetic dipoles can also be excited by the electric-field component of the incident light and vice versa. For the cross terms, in the general bianisotropic case, the exciting field and dipole vectors include an arbitrary angle. For the special case of chirality, the angle is zero. In the spirit of a brief tutorial, a very simple electric-circuit description of the split-ring resonator is used to give a basic introduction to the cross terms. Mathematical details of the effective parameter retrieval are presented. Furthermore, we briefly review recent experiments on bianisotropic metamaterials operating at optical frequencies.

WELL-POSEDNESS AND FINITE ELEMENT APPROXIMABILITY OF TIME-HARMONIC ELECTROMAGNETIC BOUNDARY VALUE PROBLEMS INVOLVING BIANISOTROPIC MATERIALS AND METAMATERIALS

A boundary value problem for the time harmonic Maxwell system is investigated through a variational formulation which is shown to be equivalent to it and well-posed if and only if the original problem is. Different bianisotropic materials and metamaterials filling subregions of the problem domain with Lipschitz continuous boundaries are allowed. Well-posedness and finite element approximability of the variational problem are proved by Lax–Milgram and Strang lemmas for a class of material configurations involving bianisotropic materials and metamaterials. Belonging to this class is not necessary, yet, for well-posedness and finite element approximability. Nevertheless, the material configurations of many radiation or scattering problems and many models of microwave components involving bianisotropic materials or metamaterials belong to the above class. Moreover, none of the other available tools commonly used to prove well-posedness seems to be able to cope with the material configurations left out by our treatment.

Surface waves guided by a plate made from a bianisotropic resonance metamaterial

The dispersion characteristics, the distribution of energy fluxes, and the polarization of the magnetic field of surface waves formed in free space by a bianisotropic-material layer with resonance and anisotropic chirality, permittivity, and permeability are studied theoretically. The transmission and reflection spectra for lattices of resonance planar elements exhibiting magnetoelectric interaction are investigated experimentally. The nonreciprocity of microwave transmission in structures consisting of a lattice and a transversely magnetized ferrite plate is also investigated experimentally. The qualitative agreement of experimental results and theoretical predictions is established.

Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials

The planewave response of a linear passive material generally cannot be characterized by a single scalar refractive index, as directionality of energy flow and multiple wave vectors may need to be considered. This is especially significant for materials which support negative refraction, negative phase velocity, and counterposition. By means of a numerical example based on a commonly studied bianisotropic material, our theoretical investigation revealed that (i) negative (positive) refraction can arise even though the phase velocity is positive (negative), (ii) counterposition can arise in instances of positive and negative refraction, (iii) the phase velocity and time-averaged Poynting vectors can be mutually orthogonal, and (iv) whether or not negative refraction occurs can depend on the state of polarization and angle of incidence. A further numerical example revealed that negative phase velocity and positive refraction can coexist even in a simple isotropic dielectric material.

Fundamental modal properties of SRR metamaterials and metamaterial based waveguiding structures

A rigorous full wave analysis of bianisotropic split ring resonator (SRR) metamaterials is presented for different electromagnetic field polarization and propagation directions. An alternative physical explanation is gained by revealing the fact that imaginary wave number leads to the SRR resonance. Metamaterial based parallel plate waveguide and rectangular waveguide are then examined to explore the resonance response to transverse magnetic and transverse electric waves. It is shown that different dispersion properties, such as non-cutoff frequency mode propagation and enhanced bandwidth of single mode operation, become into existence under certain circumstances. In addition, salient dispersion properties are imparted to non-radiative dielectric waveguides and H waveguides by uniaxial bianisotropic SRR metamaterials. Both longitudinal-section magnetic and longitudinal-section electric modes are capable of propagating very slowly due to metamaterial bianisotropic effects. Particularly, the abnormal falling behavior of some higher-order modes, eventually leading to the leakage, may appear when metamaterials are double negative. Fortunately, for other modes, leakage can be reduced due to the magnetoelectric coupling. When the metamaterials are of single negative parameters, leakage elimination can be achieved.

Determination of the effective constitutive parameters of bianisotropic metamaterials from reflection and transmission coefficients

We propose a method to retrieve the effective constitutive parameters of a slab of bianisotropic metamaterial from reflection and transmission coefficients (or scattering parameters). In our retrieval method, only the scattering parameters in one propagation direction are used. Analytical inversion equations are derived in order to retrieve the effective parameters of the permittivity, permeability, and magnetoelectric coupling coefficient of the bianisotropic metamaterial. To demonstrate the validity of the method, we used it to retrieve the parameters of four different metamaterials, among which two were normal media without bianisotropy and the other two were bianisotropic media. In using our retrieval method, including bianisotropy, the intrinsic differences between a normal medium and a bianisotropic medium were illustrated clearly. Our simulation and retrieval results also corroborate the conclusions of the previously published literature.

Slow wave propagation in nonradiative dielectric waveguides with bianisotropic split ring resonator metamaterials

Different dispersion properties are imparted to nonradiative dielectric (NRD) waveguides by split ring resonator metamaterials. Both longitudinal section magnetic and longitudinal section electric modes are capable of propagating very slowly due to the metamaterial bianisotropic effects, and can even approach zero velocity under certain condition. Enhanced energy flow in the considered structure is also demonstrated. Finally, miniaturization of NRD waveguide based on these unusual properties is proposed.

Free space measurement of the cross-polarized transmission band of a bianisotropic left-handed metamaterial

A left-handed metamaterial based on a bianisotropic S-ring resonator is fabricated. By shorting some of the horizontal arms of the paired S-rings, net electric (magnetic) dipoles accumulate under certain magnetic (electric) field induction, which results in a magnetoelectric coupling effect. Free space experimental measurements are carried out and the experimental results demonstrate the cross polarization effect around the left-handed pass band of the metamaterial. The simple planar configuration of the structure also indicates the superiority of this inclusion in the realization of bianisotropic left-handed metamaterials.