Finite periodic structure approach to large scanning array problems

Ishimaru, Akira; Coe, Ryan L.; Miller, Gary E.; Geren, Preston

doi:10.1109/aps.1984.1149206

Cited by 29 publications

(54 citation statements)

References 2 publications

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“…Methods by which solutions to infinite array scattering problems can be applied to shed light on associated large finite array problems have been applied previously in the design of large phased array antennas, early examples using a Fourier windowing approach [13,24], in which some fairly crude assumptions are made about the field near each scatterer. Recently, methods based on integral equations have been devised in which the basic idea is to formulate an integral equation for the difference between the infinite array and finite array solutions; see [26,21], for example.…”

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confidence: 99%

Semi-Infinite Arrays of Isotropic Point Scatterers. A Unified Approach

Linton¹,

Martin²

2004

SIAM J. Appl. Math.

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Abstract. We solve the two-dimensional problem of acoustic scattering by a semi-infinite periodic array of identical isotropic point scatterers, i.e., objects whose size is negligible compared to the incident wavelength and which are assumed to scatter incident waves uniformly in all directions. This model is appropriate for scatterers on which Dirichlet boundary conditions are applied in the limit as the ratio of wavelength to body size tends to infinity. The problem is also relevant to the scattering of an E-polarized electromagnetic wave by an array of highly conducting wires. The actual geometry of each scatterer is characterized by a single parameter in the equations, related to the single-body scattering problem and determined from a harmonic boundary-value problem. Using a mixture of analytical and numerical techniques, we confirm that a number of phenomena reported for specific geometries are in fact present in the general case (such as the presence of shadow boundaries in the far field and the vanishing of the circular wave scattered by the end of the array in certain specific directions). We show that the semi-infinite array problem is equivalent to that of inverting an infinite Toeplitz matrix, which in turn can be formulated as a discrete Wiener-Hopf problem. Numerical results are presented which compare the amplitude of the wave diffracted by the end of the array for scatterers having different shapes.

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mentioning

confidence: 99%

Semi-Infinite Arrays of Isotropic Point Scatterers. A Unified Approach

Linton¹,

Martin²

2004

SIAM J. Appl. Math.

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“…For large argument it is approximated by erfc(z) ∼ e −z 2 /( √ πz), which highlights the Gaussian n-convergence of (20). The spectral term (19) instead is slowly converging as 1/n, since the original series (9) converges as 1/n, and requires the use of the Poisson transformation to accelerate its convergence.…”

Section: The Ewald Transformationmentioning

confidence: 99%

“…Ishimaru solves for the active impedance of a finite array of dipole elements with progressive phasing by assuming that the current on each array element is identical except for a weighting coefficient [19]. The current on the elements are weighted by an aperture distribution function across the entire array.…”

Section: Work Pertaining To Seamsmentioning

confidence: 99%

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Johnson¹,

Warne²,

Jorgenson³

et al. 2006

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In this LDRD we examine techniques to analyze the electromagnetic scattering from structures that are nearly periodic. Nearly periodic could mean that one of the structure's unit cells is different from all the others -a defect. It could also mean that the structure is truncated, or butted up against another periodic structure to form a seam. Straightforward electromagnetic analysis of these nearly periodic structures requires us to grid the entire structure, which would overwhelm today's computers and the computers in the foreseeable future. In this report we will examine various approximations that allow us to continue to exploit some aspects of the structure's periodicity and thereby reduce the number of unknowns required for analysis. We will use the Green's Function Interpolation with a Fast Fourier Transform (GIFFT) to examine isolated defects both in the form of a source dipole over a meta-material slab and as a rotated dipole in a finite array of dipoles. We will look at the numerically exact solution of a one-dimensional seam. In order to solve a two-dimensional seam, we formulate an efficient way to calculate the Green's function of a 1d array of point sources. We next formulate ways of calculating the far-field due to a seam and due to array truncation based on both array theory and high-frequency asymptotic methods. We compare the high-frequency and GIFFT results. Finally, we use GIFFT to solve a simple, two-dimensional seam problem.3

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“…This fact increases the complexity of the problem of the investigated problem and fitting the modal analysis of the periodic structure being excited [2,13,15,16]. This study shows some fundamental properties of the impressed electromagnetic fields in arbitrary located sources for periodic structures and introduces the periodic Fourier transform to approach the scattering problem of periodic structures in the spectral-domain [8,11,14].…”

Section: Introductionmentioning

confidence: 99%

“…Several articles show that it is impossible to get rigorous result when dealing with the mutual coupling problems: element-by-element method and infinite periodic structure method [2,16]. To take coupling effects into account, a new modal analysis is necessary [10].…”

Section: Introductionmentioning

confidence: 99%

Calculation of the Mutual Coupling Parameters and Their Effects in 1-D Planar Almost Periodic Structures

Hamdi¹,

Aguili²,

Raveu³

et al. 2014

PIER B

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Abstract-This paper proposes a new modal analysis based on Floquet's theorem which is needful for the study of a 1-D periodic phased array antenna excited by arbitrary located sources. This analysis requires an accurate estimation for calculation of the mutual coupling parameters (for example: mutual impedances or admittances . . . ) between the array elements and their effects integrating a large planar radiating structure. Two different formulations are suggested, in spectral and spatial domains, to solve the problem and to calculate the coupling coefficients between the neighbouring elements in a periodic environment. Important gain in the running time and used memory is obtained using Floquet analysis. One numerical method is used for modeling the proposed structures: the moment method combined with Generalized Equivalent Circuit (MoM-GEC).

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Finite periodic structure approach to large scanning array problems

Cited by 29 publications

References 2 publications

Semi-Infinite Arrays of Isotropic Point Scatterers. A Unified Approach

Semi-Infinite Arrays of Isotropic Point Scatterers. A Unified Approach

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Calculation of the Mutual Coupling Parameters and Their Effects in 1-D Planar Almost Periodic Structures

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