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Waves and Fields in Inhomogeneous Media
28 Jun 1990-
TL;DR: Inverse scattering problems in planar and spherically layered media have been studied in this article, where Dyadic Green's functions have been applied to the mode matching method to solve the problem.
Abstract: Preface. Acknowledgements. 1: Preliminary background. 2: Planarly layered media. 3: Cylindrically and spherically layered media. 4: Transients. 5: Variational methods. 6: Mode matching method. 7: Dyadic Green's functions. 8: Integral equations. 9: Inverse scattering problems. Appendixes A, B, C, & D. Index
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06 May 2002
TL;DR: Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli which govern the macroscopic behavior as mentioned in this paper.
Abstract: Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades (and particularly in the last three decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which govern the macroscopic behavior This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification This 2002 book surveys these exciting developments at the frontier of mathematics
2,455 citations
TL;DR: In this paper, an exact solution for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals.
Abstract: An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally thin, local, and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green’s functions represented as Sommerfeld integrals. The solution of plane wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity σ=σ′+jσ″, a proper transverse-electric surface wave exists if and only if σ″>0 (associated with interband conductivity), and a proper transverse-magnetic surface wave exists for σ″<0 (associated with intraband conductivity). By tuning the chemical potential at infrared frequencies, the sign of σ″ can be varied, allowing for some control over surface wave properties.
2,304 citations
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TL;DR: This paper gives a basic review and a summary of recent developments for leaky-wave antennas (LWAs), a guiding structure that supports wave propagation along the length of the structure, with the wave radiating or “leaking” continuously along the structure.
Abstract: This paper gives a basic review and a summary of recent developments for leaky-wave antennas (LWAs). An LWA uses a guiding structure that supports wave propagation along the length of the structure, with the wave radiating or “leaking” continuously along the structure. Such antennas may be uniform, quasi-uniform, or periodic. After reviewing the basic physics and operating principles, a summary of some recent advances for these types of structures is given. Recent advances include structures that can scan to endfire, structures that can scan through broadside, structures that are conformal to surfaces, and structures that incorporate power recycling or include active elements. Some of these novel structures are inspired by recent advances in the metamaterials area.
988 citations
Cites methods from "Waves and Fields in Inhomogeneous M..."
...From a more mathematical point of view, the use of the steepest-descent method of asymptotic evaluation [24] provides a convenient means to recognize the physical significance of a leakywave pole....
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TL;DR: In this paper, a compact representation of the electric and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification is given.
Abstract: A compact representation is given of the electric- and magnetic-type dyadic Green's functions for plane-stratified, multilayered, uniaxial media based on the transmission-line network analog along the aids normal to the stratification. Furthermore, mixed-potential integral equations are derived within the framework of this transmission-line formalism for arbitrarily shaped, conducting or penetrable objects embedded in the multilayered medium. The development emphasizes laterally unbounded environments, but an extension to the case of a medium enclosed by a rectangular shield is also included.
774 citations
TL;DR: In this paper, Dyadic Green's functions are presented for an anisotropic surface conductivity model of biased graphene, where the graphene surface can be biased using either a perpendicular static electric field or by a static magnetic field via the Hall effect.
Abstract: Dyadic Green's functions are presented for an anisotropic surface conductivity model of biased graphene. The graphene surface can be biased using either a perpendicular static electric field, or by a static magnetic field via the Hall effect. The graphene is represented by an infinitesimally-thin, two-sided, non-local anisotropic conductivity surface, and the field is obtained in terms of Sommerfeld integrals. The role of spatial dispersion is accessed, and the effect of various static bias fields on electromagnetic field behavior is examined. It is shown that by varying the bias one can exert significant control over graphene's electromagnetic propagation characteristics, including guided surface wave phenomena, which may be useful for future electronic and photonic device applications.
738 citations
Cites background or methods from "Waves and Fields in Inhomogeneous M..."
...With parallel to the interface normal, the principle Greens dyadic can be written as [14]...
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...The value of the wavenumbers and govern the size of , and to access upper limits for the wavenumbers it is worthwhile to represent the spectral integrals (27) as a sum of branch cuts and residues [14], [15], [18]....
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...For any planarly layered, piecewise-constant medium, the electric and magnetic fields in region due to an electric current can be obtained as [14], [15]...
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...Surface Waves Guided by Graphene Pole singularities in the Sommerfeld integrals represent discrete surface waves guided by the medium [14], [15]....
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