Constitutive relations and adiabatic invariants for electromagnetic waves in a dynamic Lorentz medium

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenisation, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

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Electromagnetic Waves in Variable Media

Zeitschrift für Naturforschung A ◽

10.5560/zna.2011-0069 ◽

2012 ◽

Vol 67 (3-4) ◽

pp. 111-131

Author(s):

Ulrich Brosa

Keyword(s):

Material Properties ◽

Electromagnetic Waves ◽

Maxwell's Equations ◽

Constitutive Relations ◽

Electromagnetic Energy ◽

General Solutions ◽

Optical Instruments ◽

Dielectric Mirrors ◽

New Foundations ◽

Invisibility Cloaks

Two methods are explained to exactly solve Maxwell’s equations where permittivity, permeability, and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one coordinate, general solutions are derived. If the properties depend on two coordinates, geometrically restricted solutions are obtained. Applications to graded reflectors, especially to dielectric mirrors, to filters, polarizers, and to waveguides, plain and cylindrical, are indicated. New foundations for the design of optical instruments, which are centered around an axis, and for the design of invisibility cloaks, plain and spherical, are proposed. The variability of material properties makes possible effects which cannot happen in constant media, e.g. stopping the flux of electromagnetic energy without loss. As a consequence, spherical devices can be constructed which bind electromagnetic waves

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Adiabatic invariants for electromagnetic waves guided by time-varying plasma structures

Conference Proceedings 2000 International Conference on Mathematical Methods in Electromagnetic Theory (Cat. No.00EX413) ◽

10.1109/mmet.2000.888525 ◽

2002 ◽

Author(s):

M.I. Bakunov ◽

V.B. Gildenburg ◽

N.A. Zharova ◽

S.N. Zhukov

Keyword(s):

Electromagnetic Waves ◽

Adiabatic Invariants ◽

Time Varying

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Effective constitutive relations for waves in composites and metamaterials

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2010.0620 ◽

2011 ◽

Vol 467 (2131) ◽

pp. 1865-1879 ◽

Cited By ~ 61

Author(s):

J. R. Willis

Keyword(s):

Electromagnetic Waves ◽

Random Media ◽

Original Problem ◽

Effective Properties ◽

Local Level ◽

Constitutive Relations ◽

Equations Of Motion ◽

Attractive Feature ◽

Weighted Averages ◽

Special Case

Definitions of ‘effective fields’ for a randomly inhomogeneous material are offered, which guarantee automatic satisfaction of the equations of motion. The important case of a medium with periodic microstructure is included. In this special case, the definitions are completely explicit and can be applied without reference to random media. The presentation is mostly expressed in terms of electromagnetic waves. The reasoning is applicable also to other types of waves and its realization for elastodynamics is briefly outlined towards the end. Some of the effective fields are defined directly as ensemble averages, ensuring the exact satisfaction of the equations of motion, but the effective ‘kinematic’ fields to which they are related are defined more generally, as weighted averages. The main result of this work is an explicit formula for the tensor of effective properties. The important issue of uniqueness (or not) of the effective properties is explained and resolved. Self-adjointness of the original problem is not assumed. An attractive feature of the formulation is that self-adjointness at the local level implies self-adjointness at the level of the ‘effective medium’.

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Crystal optics

Properties of Materials ◽

10.1093/oso/9780198520757.003.0027 ◽

2004 ◽

Author(s):

Robert E. Newnham

Keyword(s):

Dielectric Constant ◽

Refractive Index ◽

Acoustic Waves ◽

Electromagnetic Waves ◽

Constitutive Relations ◽

Dielectric Anisotropy ◽

Refractive Indices ◽

Double Refraction ◽

Light Waves ◽

Wave Normal

Calcite (CaCO3) is a beautiful transparent mineral that readily cleaves into rhombohedra. Images viewed through a thin slice of a cleaved calcite crystal are split into two images, an effect known as double refraction, or birefringence. Birefringence is the most obvious manifestation of optical anisotropy in crystals. For any given wave normal, there are two light waves, transversely polarized in mutually perpendicular directions, traveling with different velocities, and consequently different refractive indices. Double refraction is caused by dielectric anisotropy. For transparent crystals like calcite, the magnetic susceptibility is small and the permeability μ ≌ μ0, the permeability of free space. In this class of materials the refractive index n = c/v = where c is the speed of light in vacuum, v the velocity of light in the crystal, and K is the dielectric constant measured at optical frequencies. Refractive indices of transparent materials lie between 1 and 3. Electromagnetic waves differ from acoustic waves in that there are, for a given wave normal, two waves rather than three. In the acoustic case there are, in general, two quasitransverse waves and a quasilongitudinal wave. Starting with Maxwell’s Equations and the material constitutive relations, the propagation of electromagnetic waves through transparent crystals are described in terms of the refractive indices, wave normals, and polarization directions.

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Seti Space Missions

International Astronomical Union Colloquium ◽

10.1017/s0252921100015372 ◽

1997 ◽

Vol 161 ◽

pp. 761-776 ◽

Cited By ~ 1

Author(s):

Claudio Maccone

Keyword(s):

Electromagnetic Waves ◽

Space Missions ◽

Gravitational Lens ◽

The Sun ◽

Space Antenna ◽

Focal Distance ◽

Large Space ◽

The Earth ◽

Space Antennas ◽

New Space

AbstractSETI from space is currently envisaged in three ways: i) by large space antennas orbiting the Earth that could be used for both VLBI and SETI (VSOP and RadioAstron missions), ii) by a radiotelescope inside the Saha far side Moon crater and an Earth-link antenna on the Mare Smythii near side plain. Such SETIMOON mission would require no astronaut work since a Tether, deployed in Moon orbit until the two antennas landed softly, would also be the cable connecting them. Alternatively, a data relay satellite orbiting the Earth-Moon Lagrangian pointL2would avoid the Earthlink antenna, iii) by a large space antenna put at the foci of the Sun gravitational lens: 1) for electromagnetic waves, the minimal focal distance is 550 Astronomical Units (AU) or 14 times beyond Pluto. One could use the huge radio magnifications of sources aligned to the Sun and spacecraft; 2) for gravitational waves and neutrinos, the focus lies between 22.45 and 29.59 AU (Uranus and Neptune orbits), with a flight time of less than 30 years. Two new space missions, of SETI interest if ET’s use neutrinos for communications, are proposed.

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Microwaves: Application in Electron Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100158248 ◽

1990 ◽

Vol 48 (3) ◽

pp. 140-141

Author(s):

Anthony S-Y Leong ◽

David W Gove

Keyword(s):

Electron Microscopy ◽

Light Microscopy ◽

Chemical Reactions ◽

Electromagnetic Waves ◽

Tissue Fixation ◽

Primary Method ◽

Dipolar Molecules ◽

Wide Range ◽

Time Required ◽

Cryostat Sections

Microwaves (MW) are electromagnetic waves which are commonly generated at a frequency of 2.45 GHz. When dipolar molecules such as water, the polar side chains of proteins and other molecules with an uneven distribution of electrical charge are exposed to such non-ionizing radiation, they oscillate through 180° at a rate of 2,450 million cycles/s. This rapid kinetic movement results in accelerated chemical reactions and produces instantaneous heat. MWs have recently been applied to a wide range of procedures for light microscopy. MWs generated by domestic ovens have been used as a primary method of tissue fixation, it has been applied to the various stages of tissue processing as well as to a wide variety of staining procedures. This use of MWs has not only resulted in drastic reductions in the time required for tissue fixation, processing and staining, but have also produced better cytologic images in cryostat sections, and more importantly, have resulted in better preservation of cellular antigens.

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