Some remarks on green's dyadic for infinite space

Bladel, J. Van

doi:10.1109/tap.1961.1145064

Cited by 209 publications

(74 citation statements)

References 5 publications

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“…jωµ zẑ are the well-known electric and magnetic field depolarizing dyads resulting from the longitudinal current densities and are mathematically and physically consistent with prior well-documented findings [25][26][27][28][29][30][31][32][33][34][35]. In these findings, it is discussed that the source region of volume V is split into two subregions V − V δ and V δ , where V δ is a small cavity excavated around the source point (in the limit as δ → 0).…”

Section: Prior Uniaxial Anisotropic Scalar Potential Formulationsupporting

confidence: 84%

“…In the work considered here in which the z axis is the principal axis, the source excluding region is a slice gap as shown in Figure 1. Also shown are the expected electric and magnetic surface charges due to the longitudinal (i.e., z-directed) current densities J ez , J hz and the corresponding gap fields E g , H g and In a similar manner, an examination of (6) and (7) in conjunction with (16) and (18) reveals that (25) where ∇ t u e and ∇ t u h are identified as, with the aid of (8) and (9), the curl-free contributions of the transverse electric and magnetic current densities, respectively. Analogous with the previous results in (22) and (23), it appears that based on (24) and (25), there exists transverse electric and magnetic depolarizing dyad fields implicated by the transverse current densities, namely − 1 jωε t ∇ t u e and − 1 jωµt ∇ t u h .…”

Section: Prior Uniaxial Anisotropic Scalar Potential Formulationmentioning

confidence: 92%

“…Thus gap and depolarizing fields are not anticipated. Note, it is this physical picture that prompted the author to explore the mathematical derivation that demonstrates the cancelation of the apparent transverse depolarizing dyad fields in (24)- (25). This observation, which represents the second salient point, will be further discussed in Section 3.…”

Section: Prior Uniaxial Anisotropic Scalar Potential Formulationmentioning

confidence: 93%

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Scalar Potential Depolarizing Dyad Artifact for a Uniaxial Medium

Havrilla¹

2013

PIER

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Abstract-A scalar potential formulation for a uniaxial anisotropic medium is succinctly derived through the exclusive use of Helmholtz's theorem and subsequent identification of operator orthogonality. The resulting formulation is shown to be identical to prior published research, with the notable exception that certain scalar potential fields not considered in previous work are rigorously demonstrated to be unimportant in the field recovery process, thus ensuring uniqueness. In addition, it is revealed that both a physically expected and unexpected depolarizing dyad contribution appears in the development. Using a Green's function spectral domain analysis and subsequent careful application of Leibnitz's rule it is shown that, for an unbounded homogeneous uniaxial medium, the unexpected depolarizing dyad term is canceled, leading to a mathematically and physically consistent and correct theory.

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Section: Prior Uniaxial Anisotropic Scalar Potential Formulationsupporting

confidence: 84%

Section: Prior Uniaxial Anisotropic Scalar Potential Formulationmentioning

confidence: 92%

Section: Prior Uniaxial Anisotropic Scalar Potential Formulationmentioning

confidence: 93%

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Scalar Potential Depolarizing Dyad Artifact for a Uniaxial Medium

Havrilla¹

2013

PIER

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“…The study of dyadic Green's functions has attracted numerous researchers in the EM community [1][2][3][4][5][6][7][8]. Dyadic Green's functions can be classified into a spatial representation, in which the function is written in terms of simple algebraic expressions in the coordinate space r, and an eigenfunction representation, in which the function is written in terms of vector wave functions or eigenfunctions suitable for the assumed geometry [1].…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the dyadic Green's function can be derived in closed form using vector and scalar potential theory [2]. A fundamental feature of the dyadic Green's function is the singularity in the source region.…”

Section: Introductionmentioning

confidence: 99%

Analytical Techniques to Evaluate the Integrals of 3d and 2d Spatial Dyadic Green's Functions

Gao¹,

Torres‐Verdín²,

Habashy³

2005

PIER

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Abstract-The Dyadic Green's function is in general viewed as a generalized, or distribution function. A commonly used procedure to evaluate its volume integral is the principal-volume method, in which an infinitesimal volume around the singularity is excluded from the integration volume. In this paper, we develop a general analytical technique to evaluate the integral of the dyadic Green's function without the need to specify an exclusion volume.The newly derived expressions accurately integrate the singularity and can be used for integration over any shape of spatial discretization cell. We derive explicit expressions for the integral of the 3D dyadic Green's function over a sphere and over a general rectangular block. Similar expressions are obtained for the 2D dyadic Green's function over a cylinder and over a general rectangular cell. It is shown that using the integration technique described in this paper for spherical/circular cells, simple analytical expressions can be derived, and these expressions are exactly the same as those obtained using the principal-volume method. Furthermore, the analytical expressions for the integral of the dyadic Green's function are valid regardless of the location of the observation point, both inside and outside the integration domain. Because the expressions only involve surface integrals/line integrals, their evaluation can be performed very efficiently with a high degree of accuracy. We compare our expressions against the equivalent volume approximation for a wide 48 Gao, Torres-Verdín, and Habashy range of frequencies and cell sizes. These comparisons clearly show the efficiency and accuracy of our technique.It is also shown that the cubic cell (3D) and the square cell (2D) can be approximated with an equivalent spherical cell and circular cell, respectively, over a wide range of frequencies. The approximation can be performed analytically, and the results can be written as the value of the dyadic Green's function at the center multiplying a "geometric factor". We describe analytical procedures to derive the corresponding geometric factors.

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