There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

by J. Biggs and C. Tang, Maidenhead, England,
Open University Press, 2007, 360 pp., £29.99, ISBN-13: 978-0-335-22126-4

Teaching for quality learning at university

This book presents the separation-of-variables and T-matrix methods of calculating the scattering of electromagnetic waves by particles. Analytical details and computer programs are provided for determining the scattering and absorption characteristics of the finite-thickness slab, infinite circular cylinder (normal incidence), general axisymmetric particle, and sphere.The computer programs are designed to generate data that is easy to graph and visualize, and test cases in the book illustrate the capabilities of the programs. The connection between the theory and the computer programs is reinforced by references in the computer programs to equations in the text. This cross-referencing will help the reader understand the computer programs, and, if necessary, modify them for other purposes.

Light scattering by particles: Computational methods

In recent years we have learned to fabricate structures smaller than electromagnetic wavelengths, and to assemble them into metamaterials with exotic optical properties for previously unimaginable applications. One such property is perfect absorption of incident light, with no reflection or transmission, across many wavelengths. The authors review the physics, design principles, and classification of thin perfect absorbers, and outline avenues for progress.

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Thin perfect absorbers for electromagnetic waves: Theory, design, and realizations

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.

/pdf/physical-limitations-on-antennas-of-arbitrary-shape-1m02gyih6t.pdf

Physical limitations on antennas of arbitrary shape

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.

/pdf/physical-limitations-on-metamaterials-restrictions-on-3hds33r6rx.pdf

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

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.

/pdf/a-scattering-and-absorption-identity-for-metamaterials-1j0mpymsqo.pdf

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

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.

Physical bounds on the all-spectrum transmission through periodic arrays

A sum rule valid for a large class of linear and reciprocal antennas is presented in terms of the electric and magnetic polarizability dyadics. The identity is based on the holomorphic properties of the forward scattering dyadic and includes arbitrarily shaped antennas modelled by linear and time-translational invariant constitutive relations. In particular, a priori estimates on the partial realized gain are introduced, and lower bounds on the onset frequency are derived for two important archetypes of ultra-wideband antennas: those with a constant partial realized gain and those with a constant effective antenna aperture. The theoretical findings are illustrated by an equiangular spiral antenna, and comparison with numerical simulations show great potential for future applications in antenna design.

A priori estimates on the partial realized gain of ultra-wideband (UWB) antennas

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)

/pdf/physical-limitations-on-metamaterials-restrictions-on-47e5qbmdwb.pdf

Christian Sohl

Papers

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

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

Physical bounds on the all-spectrum transmission through periodic arrays

A priori estimates on the partial realized gain of ultra-wideband (UWB) antennas

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