Christine Letrou

A phase-space beam summation formulation for ultrawide-band radiation

A new discrete phase space Gaussian beam (GB) summation representation for ultrawide-band (UWB) radiation from an aperture source distribution is presented. The formulation is based on the theory of the windowed Fourier transform (WFT) frames, wherein we introduce a novel relation between the frequency and the frame overcompleteness. With this procedure, the discrete lattice of beams that are emitted by the aperture satisfies the main requirement of being frequency independent, so that only a single set of beams needs to be traced through the medium for all the frequencies in the band. It is also shown that a properly tuned class of iso-diffracting (ID) Gaussian-windows provides the snuggest frame representation for all frequencies, thus generating stable and localized expansion coefficients. Furthermore, due to the ID property, the resulting GBs propagators are fully described by frequency independent matrices whose calculation in the ambient environment need to be done only once for all frequencies. Consequently, the theory may also be expressed directly in the time-domain as will be presented elsewhere. The localization implied by the new formulation is demonstrated numerically for an UWB focused aperture. It is shown that the algorithm extracts the local radiation properties of the aperture source and enhances only those beams that conform with these properties, i.e., those residing near the phase space Lagrange manifold. Further localization is due to the fact the algorithm accounts only for beams that pass within a few beamwidths vicinity of the observation point. It is thus shown that the total number of beams is much smaller than the Landau Pollak bound on the apertures degrees of freedom.

Frame‐based Gaussian beam summation method: Theory and applications

[1]xa0A discrete phase-space Gaussian beam summation representation for electromagnetic radiation from a planar source is presented. The formulation is based on the theory of frames and removes the inherent difficulties of the Gabor representation for both monochromatic and ultra wideband (UWB) fields. For monochromatic fields the frame-based representation leads to an efficient and flexible discrete Gaussian beam representation with local and stable expansion coefficients. For UWB fields a novel scaling of the frame overcompleteness parameter is introduced, leading to a new expansion that utilizes a discrete frequency-independent set of beams over the entire relevant spectrum. It is demonstrated that the isodiffracting Gaussian beams provide the snuggest frame representation over the entire spectrum. The rules for choosing the “optimal” frame and beam parameters for a given problem are discussed and demonstrated on application examples.

Fast radiation pattern evaluation for lens and reflector antennas

A novel algorithm referred to as the fast physical optics (FPO) for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The computation is performed in the framework of the conventional physical optics approximation appropriate for the high frequency regime. The proposed algorithm is directly applicable to reflector and lens antennas as well as to radomes. The method comprises two steps. First, a decomposition of the aperture into subdomains and computation of the pertinent radiation pattern of each subdomain. Second, interpolation, phase-correction and aggregation of the radiation patterns into the final pattern of the whole aperture. A multilevel algorithm is formulated via a recursive application of the domain decomposition and aggregation steps. The computational structure of the multilevel algorithm resembles that of the FFT while avoiding its limitations.

Multilevel fast physical optics algorithm for radiation from non-planar apertures

A novel multilevel algorithm for computing the radiation patterns of nonplanar aperture antennas over a range of observation angles is presented. The proposed technique is directly applicable to reflector and lens antennas as well as to radomes. The multilevel computational sequence is based on a hierarchical decomposition of the radiating aperture and comprises two main steps. First, computation of the radiation patterns of all subapertures of the finest level over a very coarse angular grid. Second, multilevel aggregation of the radiation patterns of neighboring subapertures into the final pattern of the whole aperture via a phase compensated interpolation. The multilevel algorithm attains computational complexity comparable to that of the fast Fourier transform based techniques while avoiding their limitations.

Printed antennas analysis by a Gabor frame-based method of moments

Gabor frame-based discretization is proposed for the first time as a fully rigorous and flexible tool in the context of antenna analysis. A rigorous discretization procedure based on frame theory is presented and applied to integral equations solution through a method of moments (MoM). In this approach, the unknown field or current is expanded in a set of spatially and spectrally translated elementary functions. The use of a Gaussian window function as basis element allows for the representation of radiated fields as a superposition of shifted and rotated Gaussian beams. By exploiting the well understood propagation and transformation features of Gaussian beams, the fields can be evaluated by summations of analytic terms, at any observation point. This method seems well suited to model antennas embedded in complex systems including arbitrary interfaces. Numerical results are presented for slot antennas at the interface between two dielectric half spaces and compared to a standard MoM to validate the approach and illustrate its attractive characteristics.

Generalized Multilevel Physical Optics (MLPO) for Comprehensive Analysis of Reflector Antennas

Recent developments of the multilevel physical optics (MLPO) algorithm aiming at the comprehensive analysis of complex reflector antenna systems are presented. The physical theory of diffraction (PTD) line integral along the rim of a reflector is combined with the physical optics (PO) surface integral within the multilevel algorithm. The multilevel scheme is also generalized to combine fields radiated by various components of different sizes, as encountered in complex antenna systems with multiple feeds and/or reflectors. Comparison with published results demonstrates the ability of the MLPO algorithm to cope accurately and efficiently with realistic reflector antenna problems.

Frame based Gaussian beam bouncing

A general formulation based on frame re-expansions of Gaussian beam fields in the course of Gaussian beam shooting algorithms will be outlined, and closed form expressions used for frame decomposition of incident beam fields and frame change will be given. The algorithm will be tested on a specific 3d problem chosen with a view toward ground-based Radar application in semi-urban environments. The range of validity of closed form expressions for frame re-expansion coefficients will be discussed, and the accuracy of Gaussian beam summations after such re-expansions will be compared to reference solutions in cases involving diffraction.

Optical and diffraction simulation techniques for large multibeam reflector

Geometrical optics (GO) based methods are widely used for modeling and parameters determination of big reflector antennas in the millimeter wave band, when the diffraction effects are small enough, and computations using methods that are more precise would take excessively long time. The main features of the ray tracing technique we used in our work are described in [1].

Spectral Ray Tracking: An Alternative Method for Guided Propagation Modeling

An original ray tube launching and tracking technique, based on the discretized plane-wave spectrum of source fields is proposed. This technique is well suited to compute fields in contexts where multiple reflections have to be taken into account. The validity of the method is demonstrated in the case of wave propagation in open-ended waveguides and cavities

Gaussian beams representation based on periodic frames for radiation from cylindrical apertures

A formulation is introduced for periodic windowed Fourier transform (WFT) frames. Such frames are then used to represent fields on cylindrical surfaces. Through phase matching at the surface, fields radiated from localized Gaussian windows are expressed in the form of general Gaussian beams, leading to a representation of radiated fields as sums of beam propagators. Such representations are presented on test cases, and can be most useful in representing fields in complex environments, around linear sources or obstacles.