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.

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Physical limitations on antennas of arbitrary shape

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.

Illustrations of New Physical Bounds on Linearly Polarized Antennas

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In this paper, new physical limitations on the extinction cross section and broadband scattering are investigated. A measure of broadband scattering in terms of the integrated extinction is derived for a large class of scatterers based on the holomorphic properties of the forward scattering dyadic. Closed-form expressions of the integrated extinction are given for the homogeneous ellipsoids, and theoretical bounds are discussed for arbitrary heterogeneous scatterers. Finally, the theoretical results are illustrated by numerical computations for a series of generic scatterers.

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Physical limitations on broadband scattering by heterogeneous obstacles

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Christian Sohl

Papers

Physical limitations on antennas of arbitrary shape

Illustrations of New Physical Bounds on Linearly Polarized Antennas

Physical limitations on antennas of arbitrary shape

Physical limitations on broadband scattering by heterogeneous obstacles

Physical limitations on broadband scattering by heterogeneous obstacles