Abstract
This paper deals with the derivation and physical interpretation of a uniform high‐frequency Green's function for a planar right‐angle sectoral phased array of dipoles. This high‐frequency Green's function represents the basic constituent for the full‐wave description of electromagnetic radiation from rectangular periodic arrays and scattering from rectangular periodic structures. The field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high‐frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW‐modulated diffracted fields, which arise from FW scattering at the array edges and vertex. Emphasis is given to the analysis and physical interpretation of the vertex diffracted rays. The locally uniform asymptotics governing this phenomenology is physically appealing, numerically accurate, and efficient, owing to the rapid convergence of both the FW series and the series of corresponding FW‐modulated diffracted fields away from the array plane. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm.
Highlights
In the electromagneticmodelingof large phased al. [1998]
Often prohibitivenumericaleffort that accompanies that is truncatedat the array edges,plusFW-moduan element-by-elementfull-wave analysisbased on lated diffracted contributionsfrom the edgesand integral equationswhich are structuredaround the vertexesof the array.The asymptoticresultscan be ordinaryfree-spaceGreen'sfunction;when applied castin the formatof a generalizedgeometricaltheory to a periodic array, this array Green's function is of diffraction(GTD) ray theorywhichincludespericomposedof the sum over the individual dipole odicity-inducednonspecularreflectionsas well as radiationsA. s an alternativew, e explorereplacement multipleconicaledgediffractionsandsphericavlertex of the element-by-elementGreen's function by the diffractions
The analysiscan be carried out via the "windowing method"[Ishimaruet al., 1985;Skrivervikand Mosig, 1992]or, moreaccuratelyv,iathemethodof moments [Netoet al., 1998;seealsoCivi et al, 1998].In each case, the canonical AGF is used in the integral equation for the actual array so as to isolate the noncanonicalvariations near the array edges and Figure1
Summary
In the electromagneticmodelingof large phased al. [1998]. With this representation,the radiation arrays,whichisa topicof currentinterest[Ishirnaruet from, or scatteringby, finite phasedarraysis interal., 1985;SkrivervikandMosig,1992;Felsenand Carin, pretedas the radiationfrom a superpositionof con-. 1996;Capolinoetal., 1998;Netoetal., 1998;Civietal., extendingover the entire finite array aperture.The. 1998],one objective[Ishirnaruet al., 1985;Skrivervik asymptotictreatmentof eachFW sectoralaperture and Mosig,1992;Neto et al, 1998]is to reducethe distributionfor a rectangulararray leadsto an FW often prohibitivenumericaleffort that accompanies that is truncatedat the array edges,plusFW-moduan element-by-elementfull-wave analysisbased on lated diffracted contributionsfrom the edgesand integral equationswhich are structuredaround the vertexesof the array.The asymptoticresultscan be ordinaryfree-spaceGreen'sfunction;when applied castin the formatof a generalizedgeometricaltheory to a periodic array, this array Green's function is of diffraction(GTD) ray theorywhichincludespericomposedof the sum over the individual dipole odicity-inducednonspecularreflectionsas well as radiationsA. (Im(k) = 0-) whichare eventuallyremoved[Capolinoetal., 2000a].,we substitute(3) into (2) and whichhaveuncoupledq- andp-indexedpolesin the interchangethe sequenceof the m-sumand spectral (kzl, kz2) plane,locatedat integrationoperations,followedby summingthe resultingrn seriesinto closedform. Letting -->0 in the belowthe kzl- andkz2-integrationpathsin Figure, result leadsto right (clockwise)indentationof the and their residuesaccountcollectivelyfor the effects of untruncatedperiodicityalongthe z1 andz coor- where dinates,respectively. It is convenientto introducethe FW propagation vector.
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