Green's function for an unbounded biaxial medium in cylindrical coordinates

Cottis, Panayotis G.; Vazouras, C.N.; Spyrou, C.

doi:10.1109/8.753010

Cited by 23 publications

(28 citation statements)

References 16 publications

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“…The depolarization dyadics degenerate to simple forms in these limits, as has been demonstrated in earlier works by a direct analysis of Eq. (6) [28] or by considering the corresponding eigenfunction expansion cast in cylindrical coordinates [29]. These simplified forms for the depolarization dyadics render the dyadic Bruggeman equation (4) more amenable to analysis.…”

Section: Limits To Anisotropymentioning

confidence: 99%

Towards metamaterials with giant dielectric anisotropy via homogenization: An analytical study

Mackay

2015

Photonics and Nanostructures - Fundamentals and Applications

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A random mixture of two isotropic dielectric materials, one composed of oriented spheroidal particles of relative permittivity a and the other composed of oriented spheroidal particles of relative permittivity b , was considered in the long wavelength regime. The permittivity dyadic of the resulting homogenized composite material (HCM) was estimated using the Bruggeman homogenization formalism. The HCM was an orthorhombic biaxial material if the symmetry axes of the two populations of spheroids were mutually perpendicular and a uniaxial material if these two axes were mutually aligned. The degree of anisotropy of the HCM, as gauged by the ratio of the eigenvalues of the HCM's permittivity dyadic, increased as the shape of the constituent particles became more eccentric. The greatest degrees of HCM anisotropy were achieved for the limiting cases wherein the constituent particles were shaped as needles or discs. In these instances explicit formulas for the HCM anisotropy were derived from the dyadic Bruggeman equation. Using these formulas it was found that the degrees of HCM anisotropy are proportional to √ b or b , at fixed values of volume fraction and a , for b > a . Thus, in principle, metamaterials can be conceptualized via homogenization with extremely large degrees of anisotropy, by controlling the geometries and orientations of remarkably simple constituent particles. In practice, the degree of anisotropy would be limited by the available value of b (and/or a ).

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Section: Limits To Anisotropymentioning

confidence: 99%

Towards metamaterials with giant dielectric anisotropy via homogenization: An analytical study

Mackay

2015

Photonics and Nanostructures - Fundamentals and Applications

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“…The radiated power ([20, (5-58)]), found by integrating over a large sphere, therefore equals , with the more general integral defined by (42) The reason for the more general notation will be explained in the next section. Once the radiated power is found, the directivity and radiation resistance easily follow ([20, §5.3.2]).…”

Section: A Constant-current Circular-loop Antennasmentioning

confidence: 99%

“…Change the variable in (42) to obtain the more suitable expression (44) which is (31) with for , and for . To avoid unnecessary complications, let us assume that the complex quantities and have nonnegative real parts.…”

Section: Integral Evaluationmentioning

confidence: 99%

“…One treats the region between patch and ground plane as a cavity bounded above and below by electric conductors and by a magnetic conductor along the patch's perimeter. Within this model, the radiated power can be shown to be proportional to the quantity ( [20, (14-75) and (14-72)]) (43) where was defined in (42), and where is the "effective radius" ([20, (14-67)]) of the patch. Details of the derivation of (43) are provided in [20, §14.3], [21], and [22].…”

Section: B Circular-patch Microstrip Antennas; Cavity Modelmentioning

confidence: 99%

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Integral Evaluation Using the Mellin Transform and Generalized Hypergeometric Functions: Tutorial and Applications to Antenna Problems

Fikioris

2006

IEEE Trans. Antennas Propagat.

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This is a tutorial presentation of the Mellin-transform (MT) method for the exact calculation of one-dimensional definite integrals, and an illustration of the application of this method to antenna/electromagnetics problems. Once the basics have been mastered, one quickly realizes that the MT-method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the MT-method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. In fact, the MT-method is used by Mathematica to symbolically calculate definite integrals. The first part of this paper is a step-by-step tutorial, proceeding from first principles. It includes basic information on Mellin-Barnes integrals and generalized hypergeometric functions, and summarizes the key ideas of the MT-method. In the remaining parts, the MT-method is applied to three examples from the antenna area. The results here are believed to be new, at least in the antenna/electromagnetics literature. In our first example, we obtain a closed-form expression, as a generalized hypergeometric function, for the power radiated by a constant-current circular-loop antenna; this quantity has been extensively discussed recently. Our second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In our third example, finally, we obtain a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media.

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“…Theoretical studies of such mediums have focused on Green functions (Kaklamani & Vzunoglu, 1992Cottis & Kondylis, 1995;Cottis, Vazouras, & Spyrou, 1999;Weiglhofer & Lakhtakia, 1995). 1 Other work has concentrated on the explicit evaluation of depolarization dyadics (Weiglhofer, 1998a) and on classification and general wave propagation .…”

Section: Introductionmentioning

confidence: 99%

Homogenization of Biaxial Composite Materials: Nondissipative Dielectric Properties

Mackay

2001

Electromagnetics

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A homogenized composite medium (HCM) that is biaxial with respect to its dielectric constitutive properties can arise even though its components have electromagnetic properties less complex than biaxial. We investigate a variety of means of realizing biaxial HCMs and consider how their biaxial nature depends on the geometry, orientation, and composition of their constituents. We demonstrate that biaxiality in a composite medium may be achieved when the component mediums collectively present two noncollinear distinguished axes; these axes can have either an electromagnetic or topological origin.

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Green's function for an unbounded biaxial medium in cylindrical coordinates

Cited by 23 publications

References 16 publications

Towards metamaterials with giant dielectric anisotropy via homogenization: An analytical study

Towards metamaterials with giant dielectric anisotropy via homogenization: An analytical study

Integral Evaluation Using the Mellin Transform and Generalized Hypergeometric Functions: Tutorial and Applications to Antenna Problems

Homogenization of Biaxial Composite Materials: Nondissipative Dielectric Properties

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