Christian Sohl

Physical limitations on antennas of arbitrary shape

In this paper, physical limitations on bandwidth, realized gain, Q-factor and directivity are derived for antennas of arbitrary shape. The product of bandwidth and realizable gain is shown to be bounded from above by the eigenvalues of the long-wavelength, high-contrast polarizability dyadics. These dyadics are proportional to the antenna volume and are easily determined for an arbitrary geometry. Ellipsoidal antenna volumes are analysed in detail, and numerical results for some generic geometries are presented. The theory is verified against the classical Chu limitations for spherical geometries and shown to yield sharper bounds for the ratio of the directivity and the Q-factor for non-spherical geometries.

Illustrations of New Physical Bounds on Linearly Polarized Antennas

A recent approach to physical bounds on antennas of arbitrary shape is numerically illustrated. In particular, physical bounds for antennas circumscribed by the rectangular parallelepiped, finite cylinders, and planar rectangles are presented. The bounds are verified against numerical results for various small antennas with excellent agreement.

Physical limitations on metamaterials: restrictions on scattering and absorption over a frequency interval

A limitation on the extinction cross section, valid for all scatterers satisfying some basic physical assumptions, is investigated. The physical limitation is obtained from the holomorphic properties of the forward scattering dyadic. The analysis focuses on the consequences for materials with negative permittivity and permeability, i.e. metamaterials. From a broadband point of view, the limitations imply that there is no fundamental difference between metamaterials and ordinary materials with respect to scattering and absorption. The analysis is illustrated by three numerical examples of metamaterials modelled by temporal dispersion. (Some figures in this article are in colour only in the electronic version)

A scattering and absorption identity for metamaterials: experimental results and comparison with theory

A dispersion relation for the combined effect of scattering and absorption of electromagnetic waves is presented for a large class of linear and passive material models. By invoking the optical theorem, the result states that the extinction cross section integrated over all frequencies is equal to the static limit of the extinction volume. The present paper focuses on an attempt to experimentally verify this sum rule by measuring the monostatic radar cross section of a fabricated sample of metamaterial. In particular, the paper utilizes the idea that, for a specific class of targets, the scattered fields in the forward and backward directions are identical. It is concluded that the theoretical findings are in good agreement with measurements performed in the frequency range [3.2,19.5] GHz. (Less)

Physical bounds on the all-spectrum transmission through periodic arrays

We show that the blockage in transmission of a screen with a periodic microstructure integrated over all wavelengths is bounded by the static polarizability per unit area of the screen. Physical bounds on the co-polarized transmission coefficient over a wavelength interval are presented using only information from the zero-frequency properties of the microstructure. The theoretical results are compared to and verified by measurements on a screen composed of a large number of split ring resonators printed on a dielectric substrate.

The integrated extinction for broadband scattering of acoustic waves.

In this paper, physical bounds on scattering of acoustic waves over a frequency interval are discussed based on the holomorphic properties of the scattering amplitude in the forward direction. The result is given by a dispersion relation for the extinction cross section which yields an upper bound on the product of the extinction cross section and the associated bandwidth of any frequency interval. The upper bound is shown to depend only on the geometry and the material properties of the scatterer in the static or low-frequency limit. The results are exemplified by permeable and impermeable scatterers with homogeneous and isotropic material properties.

Bounds on metamaterials: theoretical and experimental results

Preface. General Aspects Of Metamaterials And Plasmonics. Handedness in Plasmonics: Electrical Engineers Perspective A. Sihvola, S. Zouhdi.- Bounds on Metamaterials - Theoretical and Experimental Results G. Kristensson et al.- Transformation Media And Cloaking. Plasmonic Cloaks A. Alu and N. Engheta.- Geometrical Transformations for Numerical Modelling and for New Material Design in Photonics A. Nicolet et al.- Transformation and Moving Media: A Unified Approach Using Geometric Algebra M A. Ribeiro and C. R. Paiva.- Effective Medium Modeling. Homogenization of Split-Ring Arrays, Seen as the Exploitation of Translational Symmetry A. Bossavit.- Mixing Formulas and Plasmonic Composites H. Wallen et al.- Applications: Antennas, Absorbers. Applications of EBG in Low Profile Antenna Designs: What Have We Learned? Y. Rahmat-Samii and F. Yang.- Negative Index Metamaterial Lens for the Scanning Angle Enhancement of Phased-Array Antennas T. Lam et al.- Application of Wire Media in Antenna Technology S.Hrabar.- Optimization of Radar Absorber Structures using Genetic Algorithms N. Lassouaoui et al.- Design of Metamaterial-Based Resonant Microwave Absorbers with Reduced Thickness and Absence of a Metallic Backing F Bilotti and L. Vegni.- Metamaterial Elements And Components. Dual-Mode Metamaterial-Based Microwave Components D. S. Goshi et al.- Chiral Swiss Rolls M C. K. Wiltshire.- Trapped-Mode Resonances in Planar Metamaterials with High Structural Symmetry S. Prosvirnin et al.- Fabricating Plasmonic Components for Nano- and Meta-Photonics A. Boltasseva et al.- Line Source Excitation ofan Array of Circular Metamaterial Cylinders: Boundary Value Solution and Applications B. H. Henin et al.- Surfaces And Planar Structures. Analytical Modeling of Surface Waves on High Impedance Surfaces A. B. Yakovlev et al.- Migration and Collision of Magnetoplasmon Modes in Magnetised Planar Semiconductor-Dielectric Layered Structures A. G.Schuchinsky and X. Yan.- Transmission Lines And Waveguides. Dispersion Engineering in Resonant Type Metamaterial Transmission Lines and Applications J. Bonache et al.- Compact Dual-band Rat-Race Coupler Based on a Composite Right/Left Handed Transmission Line X. Hu and S.He.- Dispersion and Losses in Metamaterial DNG H-Guides A. L. Topa et al.- List of Contributors.

Scattering measurements in a parallel plate waveguide — First results

This paper describes a parallel plate waveguide designed for scattering and material measurements. The experimental setup can for certain scatterers be considered as a two dimensional radar cross section range. Measurements on metallic circular cylinders of finite length are performed, and the forward radar cross section and the extinction cross section are determined. Two different calibration methods are used, and it is found that the method employing a calibration object is the most accurate. It is concluded that the two dimensional radar cross section in the forward direction can be measured with ±1 dB accuracy at the level of 10cm and the accuracy at the level of 1 cm is estimated to ±3 dB.

On the Relation Between Optimal Wideband Matching and Scattering of Spherical Waves

Using an exact circuit analogy for the scattering of vector spherical waves, it is shown how the problem of determining the optimal scattering bounds for a homogeneous sphere in its high-contrast limit is identical to the closely related, and yet very different problem of finding the broadband tuning limits of the spherical waves. Using integral relations similar to Fanos broadband matching bounds, the optimal scattering limitations are determined by the static response as well as the high-frequency asymptotics of the reflection coefficient. The scattering view of the matching problem yields explicitly the necessary low-frequency asymptotics of the reflection coefficient that is used with Fanos broadband matching bounds for spherical waves, something that appears to be non-trivial to derive from the classical network point of view.

Physical bounds on the antenna scattering matrix

The antenna scattering matrix is based on a spherical vector wave expansion and contains a complete description of the matching, transmission, receiving, and scattering properties of an antenna. It is commonly utilized in near-field measurements and it can also be used to model MIMO antennas. Here, an approach based on the holomorphic properties of the antenna scattering matrix is used to derive physical bounds on the bandwidth of lossless antennas. The resulting bounds are expressed in the radius of the smallest circumscribing sphere and the polarizability dyadics of the antenna. The derivation and final results resemble both the classical work by Chu (1948) and a recently developed theory based on the forward scattering. However, instead of estimating the Q-factor through the stored energy, the low-frequency expansion of the scattering matrix is used to obtain a set of summation rules from which bounds on the bandwidth are derived. The use of Cauchy integrals and the low-frequency expansion in terms of the polarizability dyadics are similar with the approach in (Chu, 1948 and Gustafsson et al., 2007).