Journal ArticleDOI
Efficient calculation of the free-space periodic Green's function
R.E. Jorgenson,Raj Mittra +1 more
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TLDR
In this article, a method is discussed to overcome the slow convergence by using the Poisson summation formula and summing in a combination of spectral and spatial domains, and a parameter study is performed to determine an optimum way to weigh the combination of domains.Abstract:
Electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic Green's function. The periodic Green's function can be derived as a response to an array of line/point sources (spatial domain) or as a response to series of current sheets (spectral domain). These responses are a Fourier transform pair and are slowly convergent summations. The convergence problems in each domain arise from unavoidable singularities in the reciprocal domain. A method is discussed to overcome the slow convergence by using the Poisson summation formula and summing in a combination of spectral and spatial domains. A parameter study is performed to determine an optimum way to weigh the combination of domains. simple examples of scattering from a one-dimensional array of strips and two-dimensional array of plates are used to illustrate the concepts. >read more
Citations
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Journal ArticleDOI
The Green's Function for the Two-Dimensional Helmholtz Equation in Periodic Domains
TL;DR: In this paper, analytical techniques for transforming the Green's function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of images into forms more suitable for computation are described.
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Layer Potential Techniques in Spectral Analysis
TL;DR: In this paper, a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals.
Journal ArticleDOI
Lattice Sums for the Helmholtz Equation
TL;DR: A survey of different representations for lattice sums for the Helmholtz equation is made to show how the various forms depend on the dimension$d$ of the underlying space and the lattice dimension $d_\Lambda$.
Journal ArticleDOI
Efficient calculation of lattice sums for free-space periodic Green's function
TL;DR: In this paper, an efficient method to calculate the lattice sums for a one-dimensional (1-D) periodic array of line sources is presented, based on the recurrence relations for Hankel functions and the Fourier integral representation of the zeroth-order Hankel function.
Journal ArticleDOI
A review on array mutual coupling analysis
TL;DR: An overview of mutual coupling analysis in antenna arrays is given in this paper, where the relationships between array impedance matrix and embedded element patterns, including beam coupling factors, are reviewed while considering general-type antennas; approximations resulting from single-mode assumptions are pointed out.
References
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TL;DR: This first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis.
Journal ArticleDOI
Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces
TL;DR: In this paper, a simple and efficient numerical method is developed for treating electromagnetic problems of scattering and radiation from surfaces, where special consideration is given to the treatment of edges so that rather arbitrary geometrical configurations may be handled.
Journal ArticleDOI
Spectral-domain analysis of frequency selective surfaces comprised of periodic arrays of cross dipoles and Jerusalem crosses
Chich-Hsing Tsao,Raj Mittra +1 more
TL;DR: In this paper, a full-wave analysis for the problem of scattering frequency selective surfaces from (FSS) comprised of periodic arrays of cross dipoles and Jerusalem crosses is presented, where the formulation is carried out in the spectral domain where the convolution form of the integral equation for the induced current is reduced to an algebraic one.
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Signals and linear systems
TL;DR: This book discusses linear Systems, Discrete-Time Systems, and Continuous-Time systems, and an Introduction to the Design of Digital Filters.
Journal ArticleDOI
Integral Transforms Useful for the Accelerated Summation of Periodic, Free-Space Green's Functions (Short Paper)
TL;DR: The Poisson summation formulas for two-and three-dimensional, periodic, free-space Green's functions of the Helmholtz and Laplace equations are described in this paper.