Scattering by systems of spheroids in arbitrary configurations

Cooray, M.F.R.; Ciric, I.R.

doi:10.1016/0010-4655(91)90204-x

Cited by 20 publications

(11 citation statements)

References 10 publications

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“…Their first derivatives for the same c are shown in Figure 3. For this size parameter c and range of n, both the original Legendre expansion, Equation (5), and its prolate-type asymptotic expansion, Equations (7)- (11), are accurate expansions to at least five or six decimal places. This is not always the case.…”

Section: Normalizations Of the Asymptotic Expansionsmentioning

confidence: 99%

“…Spheroidal wave functions (SWFs) have become increasingly important in the solution of a variety of different physical problems due to the flexibility afforded by the spheroid's nonspherical yet canonical geometry. The use of SWFs can be found in diverse areas such as light scattering [1][2][3], nuclear modeling [4], signal processing and communication theory [5][6][7][8], electromagnetic modeling [9][10][11][12][13][14], and in finding the electromagnetic induction (EMI) response of canonical objects at magnetoquasistatic frequencies [15,16]. Three classic works on SWFs are those by Stratton [17], Meixner [18], and Flammer [19], with tables of function values provided in [17,19,20].…”

Section: Introductionmentioning

confidence: 99%

“…(a) S mn (c, η) for c = (1 + i)20, m = 0, n = (0, 3, 4) (or (n p = 0, 1, 2)), and 0 ≤ η < 1. (b) Absolute error between derivative of Legendre expansion, S mn (c, η) from Equation(5), and derivative of the prolate-type asymptotic expansion, S (a) mn (c, η) Equations (7)-(11).…”

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confidence: 99%

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On the Asymptotic Expansion of the Spheroidal Wave Function and Its Eigenvalues for Complex Size Parameter

Barrowes¹,

O’Neill²,

Grzegorczyk³

et al. 2004

Stud Appl Math

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We provide a rapid and accurate method for calculating the prolate and oblate spheroidal wave functions (PSWFs and OSWFs), S mn (c, η), and their eigenvalues, λ mn , for arbitrary complex size parameter c in the asymptotic regime of large |c|, m and n fixed. The ability to calculate these SWFs for large and complex size parameters is important for many applications in mathematics, engineering, and physics. For arbitrary arg(c), the PSWFs and their eigenvalues are accurately expressed by established prolate-type or oblate-type asymptotic expansions. However, determining the proper expansion type is dependent upon finding spheroidal branch points, c mn •;r , in the complex c-plane where the PSWF alternates expansion type due to analytic continuation. We implement a numerical search method for tabulating these branch points as a function of spheroidal parameters m, n, and arg(c). The resulting table allows rapid determination of the appropriate asymptotic expansion type of the SWFs. Normalizations, which are dependent on c, are derived for both the prolateand oblate-type asymptotic expansions and for both (n − m) even and odd. The ordering for these expansions is different from the original ordering of the SWFs and is dictated by the location of c mn •;r . We document this ordering for the specific case of arg(c) = π/4, which occurs for the diffusion equation in spheroidal coordinates. Some representative values of λ mn and S mn (c, η) for large, complex c are also given.

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Section: Normalizations Of the Asymptotic Expansionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Asymptotic Expansion of the Spheroidal Wave Function and Its Eigenvalues for Complex Size Parameter

Barrowes¹,

O’Neill²,

Grzegorczyk³

et al. 2004

Stud Appl Math

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“…The spheroidal vector wave functions Mmn are those given in [8], and N mn = is the column matrix of the unknown coefficients and [G] is the system matrix whose elements are independent of the direction and polarization of the incident wave. The calculation of the elements of [G] is given in [11]. The details regarding the calculation of the integrals that appear as a result of applying the orthogonality of the spheroidal wave functions are given in [15] and [11].…”

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confidence: 99%

“…The calculation of the elements of [G] is given in [11]. The details regarding the calculation of the integrals that appear as a result of applying the orthogonality of the spheroidal wave functions are given in [15] and [11]. Once the coefficients a, 0, 7, and b are known, it is possible to calculate the fields outside the spheroidal system, inside the coating, and inside the spheroid by substituting back in the appropriate series expansions of the fields.…”

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confidence: 99%

Scattering of Electromagnetic Waves by a Coated Dielectric Spheroid

Cooray

Ciric

1992

Journal of Electromagnetic Waves and Applications

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The method of separation of variables is used to derive an analytic solution to the problem of electromagnetic scattering by a homogeneous dielectric spheroid with a confocal lossy dielectric coating of arbitrary thickness. The electric and magnetic fields in each different region are expressed in terms of a set of vector spheroidal eigenfunctions, and the solution is obtained by imposing the appropriate boundary conditions at each spheroidal surface. Computed results illustrate the dependence of the scattered field in the far zone on the coating material and its thickness, the size and the material of the spheroid, and on the angle of incidence.

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Basics on Light Scattering by Particles

Onofri¹,

Barbosa²

2012

Laser Metrology in Fluid Mechanics

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Scattering by systems of spheroids in arbitrary configurations

Cited by 20 publications

References 10 publications

On the Asymptotic Expansion of the Spheroidal Wave Function and Its Eigenvalues for Complex Size Parameter

On the Asymptotic Expansion of the Spheroidal Wave Function and Its Eigenvalues for Complex Size Parameter

Scattering of Electromagnetic Waves by a Coated Dielectric Spheroid

Basics on Light Scattering by Particles

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