## 1. Introduction

[2] The efficient and accurate numerical calculation of wave interaction with large scale complex environments poses a major challenge in diverse forward and inverse wave propagation and scattering scenarios. It is widely acknowledged that analytic physics-based problem-matched modeling plays an important role in the construction of the relevant working algorithms. In a sequence of prototype studies [*Maciel and Felsen*, 1989, 1990a, 1990b, 2002a, 2002b; *Galdi et al.*, 2001; *Felsen and Galdi*, 2001], we have explored a class of problems wherein the excitation is a specified frequency or time domain planar aperture distribution; the excitation due to any other given source distribution can generally be projected onto such a reference plane. For parameterization of the aperture-generated radiated fields which impinge on a complex propagation or scattering environment, we have explored a Gabor-based discretized superposition of narrow-waisted (NW) Gaussian beams (GBs), both in the high-frequency time-harmonic and short-pulse transient regimes. Although each individualized ray-like NW beam emits wide-angle radiation, these wave objects, when acting collectively, are found to have only a paraxial domain of influence, and they synthesize ray optically parameterized wave fields without the failure of conventional ray theory in shadow boundary and other transition regions. In two recent publications [*Maciel and Felsen*, 2002a, 2002b], we have formulated and validated the frequency domain Gabor-based NW GB algorithm for the calculation of the 3D vector electromagnetic fields radiated by coordinate-separable truncated 2D vector aperture field distributions. In the present paper, such fields are allowed to impinge on arbitrarily shaped 3D dielectric layers, with subsequent specific application to the performance of rotationally symmetric hemispherical and ogival missile radomes covering an arbitrarily placed truncated planar aperture platform.

[3] Recently, two new rigorous beam-based algorithms have emerged which avoid the biorthogonality difficulties associated with evaluation of the amplitude coefficients in the rigorous conventional Gabor expansion [*Maciel and Felsen*, 2002a], on which our NW GB scheme is based: the orthogonal Wilson-based beam expansion [*Arnold*, 2001], and the frame-based beam expansion [*Letrou and Lugara*, 2001]. The appearance of these new formulations suggests that our pragmatic approximate (but calibrated) NW GB procedure, which avoids the conventional Gabor biorthogonality problem for the relevant expansion coefficients through Gabor sampling of the aperture field profile in the NW beam limit [*Maciel and Felsen*, 2002b], should be reexamined from the perspective of these new rigorous orthogonal schemes. To do this will require passage to the NW limit in these new algorithms since our algorithm (which works well and efficiently in our cited problem scenarios of interest) is specifically restricted to the NW beam regime. We shall look forward to meaningful comparisons after the NW limit of the new schemes will have been established.

[4] The layout of this paper is as follows. Section 2 deals with previous results [*Maciel and Felsen*, 2002a, 2002b] required for the NW GB parameterization of the vector aperture and radiated fields. In section 3, the individual GBs are tracked through an arbitrarily shaped dielectric layer, with full account taken of the polarization-dependent 3D vector field characteristics. The tracking algorithm is structured around slightly complex paraxial ray and beam shooting methods. It is used in section 4 to synthesize the 3D vector fields transmitted from an off center, rotated rectangular aperture distribution through a hemispherical dielectric layer radome, and also from non rotated centered circular aperture distributions through two different ogival dielectric layer radomes. No independent reference solutions are available for these complex 3D propagation scenarios. Therefore, we assumed that field synthesis based on our thoroughly calibrated beam lattice “scrambling” criteria for stable and accurate 2D beam tracing from 1D aperture distributions through 2D complex environments [see *Maciel and Felsen*, 1990a, 1990b] can be applied locally, via the algorithm in section 3, to the 3D field/2D aperture problem for 3D complex environments. The numerical beam tracking results presented in these three examples have been verified to be stable according to the scrambling criteria, with explicit listing of the number of beams employed. These analytic predictions have been compared with experimental data for various performance measures (boresight error, power transmission) in practical missile radome configurations. Conclusions are presented in section 5.