Michael Zedler

Anisotropic Transmission-Line Metamaterials for 2-D Transformation Optics Applications

In this contribution, we present a two-dimensional metamaterial unit cell which synthesizes effective material parameters needed for “transformation optics” applications. The metamaterial consists of a grid of reactively loaded transmission-line segments and is a generalization of a previously presented unit cell in that it also synthesizes off-diagonal elements of the permeability tensor. We apply this unit cell to two “transformation optics” applications, a retro-directive reflector, and a cloak. This cloak is different from the so-far reported split-ring-resonator/wire structures in that it not only synthesizes the required μρ and εz distribution but also the μφ one. For the cloak, detailed radar cross-section (RCS) and bandwidth results are presented. It is shown that the total RCS bandwidth is 33.5%, and that losses influence the cloaking performance not critically, pointing to the possibility of practical “transformation optics” designs using the proposed unit cell. Full-wave simulation results of a transmission-line metamaterial cloak in microstrip technology are presented, verifying that the unit cell presented in this paper synthesizes the effective material parameters needed for “transformation optics” or applications that require effective material parameters with off-diagonal tensor elements.

2D transformation optics using anisotropic transmission-line metamaterials

In this contribution we propose a two-dimensional metamaterial unit cell which synthesizes equivalent material parameters needed for ‘transformation optics’, as introduced in [1]. The proposed metamaterial consists of a grid of reactively loaded transmission-line segments and is a variation of the unit cell presented in [2], [3], synthesizing also the required off-diagonal elements of the permeability tensor. The application of cloaking of the ‘transformation optics’ approach is taken as a test case for the novel metamaterial. The cloak we present is different from the structure presented in [4] in that it synthesizes not only µ<inf>ρ</inf> and ∈<inf>z</inf> but also µ<inf>ø</inf>.

Modal Analysis and Wave Propagation in Finite 2D Transmission-Line Metamaterials

In this paper we examine the propagation of plane waves and Gaussian beams in 2D periodic grids constructed with lumped reactive immitances. We demonstrate the equivalence between the Bloch/Floquet modal description and the multiple coupled-line modal analysis of finite-sized periodic grids. This establishes that the Floquet analysis of 2D metamaterial negative-refractive-index grids and the associated exotic wave propagation/refraction/focusing phenomena, can be deduced from traditional analysis of M coupled lines (and hence M eigenmodes), albeit with considerable algebraic complexity. We present simulation results of Gaussian beams through these grids to demonstrate that they can be analyzed using simple geometrical optics along with the index of refraction associated with Bloch/Floquet analysis.

Circuital and Experimental Demonstration of a 3D Isotropic LH Metamaterial based on the rotated TLM scheme

In this contribution the rotated TLM LH metamaterial is analyzed algebraically, circuit simulations verifying the predicted behaviour are carried out, a possible realization is proposed and verified experimentally.

3D Composite Right-Left Handed Metamaterials with Lorentz-type Dispersive Elements

In this paper the 3D rotated TLM (RTLM) model is extended to the general case of metamaterial cells with arbitrary number of poles in the series and parallel elements of the metamaterial cells. The (RTLM) 3D metamaterial model is a general model for 3D metamaterials based on symmetry considerations. The possibility to account for general Lorentzian dispersion behavior allows the application of the RTLM model to distributed metamaterial cells as long as the symmetry relations are fulfilled. For the first time, a transmission line representation of the mixed Lorentz-Drude ring-wire metamaterial is presented, and reveals that this structure may be analyzed and synthesized by efficient approaches such as the TLM.

Spatial Harmonics and Homogenization of Negative-Refractive-Index Transmission-Line Structures

In this paper, we discuss negative-refractive-index transmission-line (NRI-TL) metamaterial structures with respect to spatial harmonics. The power in the fundamental spatial harmonic is shown to yield a measure that relates to the homogeneity of the metamaterial. It is shown that NRI-TL metamaterials yield highly homogeneous field distributions if both the unit cell is short compared to the guided wavelength, and if the unloaded unit cell is short compared to the “free space” wavelength. Based on the homogeneity, we provide practical design choices for NRI-TL metamaterial unit cells. Under the restriction of a high homogeneity we derive expressions for extracting an effective permittivity and permeability. Circuit theory results and full-wave eigenmode simulations of two NRI-TL structures are presented.

Three-dimensional isotropic scalar metamaterial with Drude dispersion for the permittivity and permeability

In this contribution we present a topological analysis of metamaterials, which can describe one-, two-, and three-dimensional structures. Using this approach a novel three-dimensional metamaterial scalar structure is deduced, i.e., it supports one polarisation having left-handed operation. Its physical realisation has Drude dispersion for ∈eff, μeff and obeys Th symmetry, ensuring isotropy. Full-wave eigenmode simulations show a 30% relative bandwidth of left-handed operation.

Analysis of a planarized 3D isotropic LH metamaterial based on the rotated TLM scheme

In this contribution a planar fabrication technique for the rotated TLM LH metamaterial is presented. This realization of the metamaterial cell preserves the electrical topology, thus maintaining isotropic LH behaviour. An evaluation of unwanted coupling effects is carried out leading to design considerations for the planar fabrication.

Circuit theory approach to the design of metamaterials

In this contribution we show that space-discretising numerical schemes can be considered the unifying framework behind metamaterials. Physical implementations of these schemes which obey the condition that the unit cell is small compared to the wavelength lead to either Drude or Lorentz dispersion with their immanent properties and hence limitations. This perspective on metamaterials as being physical implementations of space-discretising schemes is formulated for 1D, 2D, 3D supporting one polarisation and 3D supporting two polarisations. Two isotropic three-dimensional metamaterials are presented which are derived using this approach. Approaches to mass fabrication of maximally-symmetric 3D metamaterials are presented.

Numerical Analysis of a Planarized 3D Isotropic LH Metamaterial based on the rotated TLM scheme

In this contribution a planar fabrication technique for the rotated TLM LH metamaterial is presented. Such a realization of the metamaterial cell preserves the electrical topology, thus maintaining isotropic LH behaviour. Numerical simulations of the dispersion relation are carried out proving LH behaviour.