Bianisotropic Metamaterial Slabs Research Articles

Parameter extraction method for reflection-asymmetric bianisotropic metamaterial slabs using one-port measurements

An effective microwave method is developed for extracting electromagnetic properties of bianisotropic metamaterial (MM) slabs. As a non-iterative method, it utilizes only the one-port (air-backed and metal-backed MM slab) scattering (S-) parameter measurements. This is a useful feature especially for vector network analyzers, such as MS46131A, MS46121B, and R60, performing only one-port S-parameter measurements. Electromagnetic properties of a bianisotropic MM slab formed by C-shaped resonators are measured by an X-band (8.2–12.4 GHz) rectangular waveguide setup. The effect of any gap between the short-circuit termination for metal-backed measurements and the end of the MM slab on extracted electromagnetic properties is also examined for evaluating the possible error for proposed method.

Artificial Neural Network Model for Evaluating Parameters of Reflection-Asymmetric Samples From Reference-Plane-Invariant Measurements

A technique based on artificial neural network (ANN) is proposed to extract electromagnetic properties of reflection-asymmetric samples from reference-plane-invariant scattering parameter measurements. It first determines reference plane transformation distances and then extract material properties. The number of neurons in the hidden layer of the ANN model was evaluated subject to accuracy and time constraints. We examined the conformity of the dataset of the ANN model and the required time for the training process by considering different number of neurons in the selected hidden layer. S-parameter waveguide measurements at X-band (8.2-12.4 GHz) of two bianisotropic metamaterial slabs, as reflection-asymmetric samples, composed of square-shaped split-ring-resonators and asymmetrically positioned into their measurement cells were used to validate the ANN model and evaluate the effectiveness of the proposed method in extracting the electromagnetic properties.

Parameter Retrieval of Bianisotropic Metamaterials Without Application of the Passivity Principle

In this article, a microwave method has been proposed for accurate parameter retrieval of bianisotropic metamaterial (MM) slabs without enforcing the passivity principle. Thanks to the introduced asymmetrical even and odd reflection coefficients, not only is our method free from singularity-point problem (the argument of a square-root function crosses the negative real axis) explicit expressions for electromagnetic properties but it is also resistant to random noises more than the conventional method that strictly requires the application of the passivity principle. Our new method has been validated by measured and simulated scattering parameters of a fabricated Omega-type bianisotropic MM slab with C-shaped rings.

Sign-ambiguity-free retrieval of electromagnetic properties of bianisotropic metamaterials

We propose a retrieval procedure for extraction of electromagnetic properties of bianisotropic metamaterial (MM) slabs involving no sign-ambiguity. Toward this end, as different from the studies in the literature, we derive a closed-form expression for the intermediate variable T (propagation factor) and use it to obtain sign-ambiguity-free electromagnetic properties of bianisotropic MM slabs. We utilized 3D CST Microwave Studio to simulate scattering parameters of a bianisotropic MM slab composed of circular split-ring-resonators and to validate the derived closed-form expressions. The effects of substrate loss, geometrical parameters, and noise in S-parameters were examined to assess the capability of the proposed method.

Determination of Constitutive Parameters of Strong-Coupled Bianisotropic Metamaterials Using Oblique Incidence Scattering Parameters

An attractive extraction method has been proposed to determine all constitutive parameters of diagonal permittivity and permeability tensors in addition to the coupling term (a total of seven quantities) of omega-type bianisotropic metamaterial (MM) slabs. Noniterative (no need to use any numerical method) and less-requirement (scattering parameters of two modes only) features put our method to the forefront over other similar methods in the literature. A bianisotropic MM slab synthesized by the Drude and Lorentz models and another bianisotropic MM slab constructed by split-ring resonators are considered to validate and examine the accuracy of our method. Finally, additional analyses are performed to test dependencies of our method on incidence angle and the number of cells and to investigate whether it retrieves a unique solution.

Determination of Effective Constitutive Parameters of Inhomogeneous Metamaterials With Bianisotropy

A recursive algorithm is proposed to accurately extract the electromagnetic parameters of isotropic/bianisotropic metamaterial (MM) slabs of inhomogeneous structures. The algorithm is based on the recursive calculations of measured/ simulated forward and backward scattering (S-) parameters from previously extracted wave impedances and refractive indices of each homogeneous layer (except the analyzed intermediate layer) by a suitable retrieval method. There are two main advantages of our proposed method over existing extraction algorithms. First, it could retrieve the electromagnetic parameters of both isotropic and bianisotropic MM slabs. Second, it is applicable for electromagnetic parameter extraction of inhomogeneous structures. For validation of our method and assessing its accuracy over existing extraction methods, we used the simulation results of various inhomogeneous structures constructed by different isotropic/bianisotropic MM slabs (split-ring-resonator (SRR), SRR-wire, omega, and omega-wire). For completeness, the effects of noise present in S-parameters and iterative error (by increasing the value of iteration numbers) are examined to test the robustness of the proposed algorithm.

Propagation Constant Measurement of Microwave Networks With Symmetric/Asymmetric Reflections

We proposed a Line-Line (LL) method for complex propagation constant $\gamma $ determination of uniform transmission lines or uniform lines loaded by samples having symmetric or asymmetric reflections using calibration-free scattering (S-) parameter measurements. To achieve our goal, we first derived pseudo wave-cascading-matrix (WCM) presentation of a network modeling a uniform line with asymmetric reflections ( $S_{11} \ne S_{22}$ ). Then, we proved that such a network can be represented by the product of three matrices: two matrices for impedance transitions and one matrix for phase and amplitude changes. While the first impedance transition matrix is a $2\times 2$ square matrix with unity values at diagonal entries and two different reflection coefficient values at off-diagonal entries, the second one is the inverse of the first one. Besides, the phase-amplitude change matrix is a diagonal matrix with diagonal entries corresponding to phase and amplitude changes. Next, using such representation of the pseudo WCM, we implemented the LL method to determine $\gamma $ of a network with asymmetric (or symmetric) reflections by a simple trace operation (summation of the diagonal terms in a square matrix) without resorting to ascertaining the reflection coefficient corresponding to an impedance transition. The method was validated by $\gamma $ measurements of an empty waveguide section with length 7.70 mm, the same section loaded by a polyethylene sample, and another waveguide section with length 10.16 mm loaded by bianisotropic metamaterial slabs in C-shape form.

Reflection/transmission calculation of complex particle slabs for normal incidence through dipole approximation

The computation of the reflection/transmission coefficients from normally illuminated bianisotropic metamaterial slabs through a rigorous method is presented in this paper. The bianisotropic particles that compose finite slabs are approximated as electric and magnetic dipoles. Modeling these slabs as a succession of 2D arrays, the interaction of all dipoles is described via Green’s function series, for a given wave illumination on each array, and the excited dipole moments are obtained by the resulting linear system. Finally, the reflection/transmission coefficients are derived in terms of summing the scattering from the equivalent surfaces that comprise the slab. The new algorithm is applied to a bianisotropic and a complicated chiral particle, while all results are compared to numerically simulated ones.

Semi-Infinite Reflection Coefficients of Bi-Anisotropic Metamaterial Slabs Including Boundary Effects

We analyzed semi-infinite reflection coefficients at an interface formed by a bi-anisotropic metamaterial (MM) slab and an air region by considering boundary effects. Corresponding expressions for reflection coefficients are derived using the ray-tracing technique. Derivations are validated by simulated S-parameters of a bi-anisotropic MM slab composed of circular split-ring-resonators. It is noted that while reflection coefficients at left and right interfaces of the analyzed bi-anisotropic MM slab are closely linked to one another aside from the resonance, they are different from one another especially around resonance.

Scattering parameter analysis of cascaded bi-anisotropic metamaterials

Forward and backward reflection and transmission scattering (S-) parameters of a metamaterial (MM) structure of bi-anisotropic slabs in cascade are analyzed. Signal flow graph technique is applied in this analysis for a cascaded connection of two and three bi-anisotropic MM slabs with different orientations. We also investigated effects of geometrical parameters (fabrication tolerances) of individual MM cells on forward and backward reflection and transmission S-parameters of cascade connection of MM cells. We note from our analysis the following important points. First, forward and backward reflection S-parameters become equal to one another for a MM structure composed of an even number of bi-anisotropic MM slabs (individually characterized by non-identical forward and backward reflection S-parameters) with proper orientations only if there exists symmetry of the structure in the propagation direction. Second, it is noted that it is not possible to obtain identical forward and backward reflection S-parameters of a MM structure composed of an odd number of bi-anisotropic MM slabs. Finally, reflection asymmetry (bi-anisotropy) of cascade connection of MM cells generally is enhanced for a change in geometrical parameters of individual MM cells.

Investigation of transmitted, reflected, and absorbed powers of periodic and aperiodic multilayered structures composed of bi-anisotropic metamaterial slab and conventional material

In this study, we investigate transmitted, reflected, and absorbed powers in forward and backward directions of periodic and aperiodic multilayered structures composed of bi-anisotropic metamaterial (MM) slab and conventional material. Aperiodic multilayered structure is realized by a change in thickness of any bi-anisotropic MM slab or of any conventional material. From this analysis, we note the following key results. First, identical (non-identical) forward and backward transmitted (reflected and absorbed) powers are observed for the analyzed periodic and aperiodic multilayered structures due to reciprocity (reflection-asymmetry) of bi-anisotropic MM slabs. Second, thickness-resonance phenomenon of conventional materials produces some peaks in the transmitted powers of periodic multilayered structures aside from the resonance frequency region of bi-anisotropic MM slabs. Third, each thickness-resonance frequency splits into many frequencies upon increasing the number of sections of periodic multilayered structures (no splitting when number of periods is one). Fourth, while the effect of changing the thickness of any bi-anisotropic MM slab within the aperiodic multilayered structure has no considerable effect around the resonance region of bi-anisotropic MM slabs (resonance of resonating structures such as MM slabs does not change with thickness), the same change in thickness of the conventional material drastically alters forward/backward reflected and absorbed powers aside from the resonance region of bi-anisotropic MM slabs (thickness-resonance totally depends on the value of thickness of conventional materials). The outcomes presented here can be particularly useful for propagation-related applications requiring cascade connection of various MM slabs.

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.

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