On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays

A useful procedure, that has been described previously in the literature, employs the Poisson sum formula to represent the solution to the fields of a three-dimensional (3D) large periodically spaced finite planar array problem configuration as a convolution of the infinite planar periodic array solution and the Fourier transform of the equivalent aperture distribution over the finite array. It is shown here that the Poisson sum formula utilized by Felsen and Carin (see J. Opt. Soc. Am. A, vol.11, no.4, p.1291-1306, 1994) and by Felsen and Ribas (see IEEE Trans. Antennas Propagat., vo1.44, no.3, p.375-82, 1996) is exact, hence the use of the less complete Poisson sum formula of Ishimaru (1962), Ishimaru et al. (1985) and Skrivervik et al. (1992, 1993) in finite array problems provides somewhat less accurate results particularly for the wide angle radiation/scattering directions while it provides results in the stronger main beam region that are essentially as accurate as those predicted by the use of the exact Poisson sum formula of Felsen et al.


On the Poisson sum formula for the analysis of wave radiation and scattering from large finite arrays
Aydın Çivi, Hatice Özlem; Chou, HT (1999-05-01)
Poisson sum formulas have been previously presented and utilized in the literature [1]-[8] for converting a finite element-by-element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation/scattering from electrically large finite periodic arrays. However, different authors [1]-[6] appear to use two different versions of the Poisson sum formula; one of these explicitly shows the end-point discontinui...
Applications of hybrid discrete Fourier transform-moment method to the fast analysis of large rectangular dipole arrays printed on a thin grounded dielectric substrate
Chou, HT; Ko, HK; Aydın Çivi, Hatice Özlem; ERTÜRK, VAKUR BEHÇET (2002-08-05)
Recently a discrete Fourier transform-method of moments (DFT-MoM) scheme was developed for fast analysis of electrically large rectangular planar dipole arrays, which has been shown to be very efficient in terms of number reduction of unknown variables and computational complexity. The applications of this DFT-MoM to treat dipole arrays printed on a grounded dielectric substrate are examined in this Letter. Numerical results are presented to validate its efficiency and accuracy. (C) 2002 Wiley Periodicals, ...
A Non-iterative Domain Decomposition Method for Finite Element Analysis of 3D Electromagnetic Scattering Problems
Ozgun, Ozlem; Kuzuoğlu, Mustafa (2008-07-11)
In this paper, we generalize this algorithm to 3D scattering problems, and we demonstrate that the algorithm is actually non-iterative in problems involving smooth convex geometries (such as sphere, cube, missile, cone, plate, etc.) and some special geometries (such as inlet). The most distinguished feature of the algorithm is the utilization of the locally-conformal perfectly matched layer (PML) method along the boundaries of the subdomains. In this algorithm, the original computational domain is partition...
Modified Superformula Contours Optimized via Genetic Algorithms for Exponentially Converging 2D Solutions of MFIE
Guler, Sadri; Onol, Can; Ergül, Özgür Salih; Sever, Emrah; Dikmen, Fatih; Tuchkin, Yury A. (2017-05-25)
An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of magnetic field integral equation (MFIE) in 2D either for TM or TE polarized excitations. A version of superformula modified for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the MFIE kernel and convergence of the solution ...
YAVUZ, H; BUYUKDURA, OM (1994-04-14)
A rigorous integral equation formulation for the analysis of a phased array of flangemounted waveguide apertures is given for a finite number of elements and nonuniform spacings. The resulting set of ihtegrd equations is reduced to a matrix equation called the coupling matrix which relates the coefficients of all the modes in all the waveguides to one another. The solution then yields the dominant mode reflection coefficient, coefficients of scattered modes and hence the field in each waveguide. The blockTo...
Citation Formats
H. Ö. Aydın Çivi and H. Chou, “On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays,” 1998, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42882.