Time domain Green's function for an infinite sequentially excited periodic planar array of dipoles

F Capolino,L.B Felsen

doi:10.1109/aps.2000.874897

Abstract

Periodic arrays of radiating or scattering elements play an important role in phased array antennas, frequency selective surfaces and related applications. To gain an understanding of the sparsely explored time domain (TD) behavior of such structures, we have initiated a systematic investigation of relevant canonical TD dipole-excited Green's functions (GF), which so far include those for infinite and truncated line periodic arrays, parameterized in terms of TD-Floquet waves (FW) and truncation-induced TD-FW-modulated tip diffractions. Such waves on semi-infinite and finite square arrays of dipoles have been investigated in the frequency domain, and shown to be useful in practical array applications. This article extends our TD studies to an infinite periodic sequentially pulsed planar array. Like the predecessor GFs, this canonical prototype is simple enough to admit closed form exact solutions, whose interpretation is discussed phenomenologically aided by asymptotic parameterization in terms of instantaneous frequencies. Preliminary numerical results demonstrate the efficiency of the TD-FW algorithms.

Highlights

T HIS paper represents the third in a series of prototype studies [1], [2] of the time-domain (TD) behavior of sequentially excited periodic dipole array configurations, motivated by similar investigations in the frequency domain (FD) [3]–[6], which have already been applied effectively and efficiently to finite practical array antennas [7]–[10]
The FD-Floquet wave (FW) and TD–FW wavefields, i.e., the Floquet plane waves, radiated by these FW-modulated aperture distributions are developed in Sections III and IV, respectively, with emphasis in the TD on the new phenomenologies exhibited by the planar array, as well as on similarities with the previously investigated TD-infinite line dipole array [1]
In the frequency domain, Poisson summation converts the effect of the infinite periodic array of individual phased -indexeddipole radiators collectively into an infinite superposition of linearly smoothly phased -indexed equivalent planar distributions that furnish the initial conditions for propagating PFW and evanescent EFW Floquet-type waves

Summary

INTRODUCTION

T HIS paper represents the third in a series of prototype studies [1], [2] of the time-domain (TD) behavior of sequentially excited periodic dipole array configurations, motivated by similar investigations in the frequency domain (FD) [3]–[6], which have already been applied effectively and efficiently to finite practical array antennas [7]–[10]. Referring to the more detailed introduction in [1] for background, we proceed in Section II to the formulation of the problem in terms of the frequency-domain (FD) and time-domain (TD) fields excited by the individual phased dipole radiators. The FD-FW and TD–FW wavefields, i.e., the Floquet plane waves, radiated by these FW-modulated aperture distributions are developed in Sections III and IV, respectively, with emphasis in the TD on the new phenomenologies exhibited by the planar array, as well as on similarities with the previously investigated TD-infinite line dipole array [1].

Element-by-Element Formulation

FLOQUET WAVES

Spatial Synthesis of TD–FWs Via Poisson Summation

Asymptotic Inversion From the FD

Band-Limited Asymptotics

Illustrative Examples

CONCLUSION