## 1. Introduction

[2] The prototype study of short-pulse radiation by a semi-infinite sequentially pulsed planar periodic array of dipoles (Figure 1) plays an important role in the efficient modeling of time-dependent radiation from, or scattering by, actual rectangular phased array antennas, frequency selective surfaces and related applications. Impulsive (delta function) excitations of the array elements, leading to the time domain (TD) Green's functions (GF), are analyzed here, as well as band-limited short-pulse excitations to model more realistic signals.

[3] Our approach is based on the exact equivalence between summation over the contributions from individual sequentially pulsed elements in an array and their collective treatment (via Poisson summation) in terms of infinite series of time domain (TD) Floquet waves (FW). We have already investigated the basic canonical TD-GFs for infinite [*Felsen and Capolino*, 2000] and truncated [*Capolino and Felsen*, 2002] periodic line arrays, and that for an infinite periodic planar array [*Capolino and Felsen*, 2003]. These cases have been parameterized, respectively, in terms of nontruncated or truncated conical TD-FWs [*Felsen and Capolino*, 2000; *Capolino and Felsen*, 2002], truncation-induced TD FW-modulated tip diffractions [*Capolino and Felsen*, 2002], and nontruncated planar TD-FWs [*Capolino and Felsen*, 2003], which furnish understanding of the corresponding FW critical parameters and phenomenologies pertaining to time domain analysis of spatial periodicity. The present contribution extends the investigation of *Capolino and Felsen* [2003] to a semi-infinite periodic sequentially pulsed planar array, which introduces new truncation-induced TD phenomena.

[4] We proceed by accessing the time domain through asymptotic inversion of the frequency domain (FD) semi-infinite array results of *Capolino et al.* [2000b, 2000c], and obtain thereby the instantaneous frequencies that parameterize the behavior of the constituent TD-FWs. The problem is formulated in section 2. Section 3 contains a summary of the relevant FD results from *Capolino et al.* [2000b], prepared so as to facilitate the inversion to the TD, which is carried out in sections 4 and 5. Section 4 summarizes the TD-FW behavior for the infinite planar array investigated by *Capolino and Felsen* [2003] because these FWs play an essential role in building up the behavior for the semi-infinite case. Here emphasis is on the distinction between the nondispersive lowest-order, and the dispersive higher-order TD-FWs. The TD-FW behavior for the semi-infinite array is developed in section 5, using the infinite array results in section 4 to parameterize and interpret truncation-induced phenomena affecting the bulk TD-FWs as well as giving rise to TD-FW-modulated diffractions from the array edge. Explaining these new TD results in section 5 in terms of band-limited (BL) problem-matched asymptotics implemented on the inversion integral (4) from the FD constitutes the main contribution in this paper. Preliminary numerical examples of radiation from a two-edged strip array with pulsed band-limited excitation in section 6 demonstrate the accuracy of the TD-FW algorithm and illustrate the rapid convergence of the (TD-FW)-based field representation since only a few terms are required for describing the off-surface field radiated by the truncated planar array. Conclusions are presented in section 7. Refinement and future calibration of these preliminary results through a systematic series of numerical experiments over broad ranges of parameters is reserved for a future publication.