Multiple scattering of EM waves by dielectric spheres located in the near field of a source of radiation
TL;DR: In this paper, an analysis of multiple scattering of electromagnetic (EM) waves by two loss-free dielectric spheres with radii greater than a wavelength and located in the bear field of a source of radiation is presented.
Abstract: An analysis of multiple scattering of electromagnetic (EM) waves by two loss-free dielectric spheres with radii greater than a wavelength and located in the bear field of a source of radiation is presented. The incident field is expressed in terms of spherical vector wave functions (SVWF). Translational and rotational addition theorems are employed to express the SVWF of the incident field in the coordinate system associated with the dielectric scatterer. Numerical computations are performed for obtaining the amplitude and phase patterns of fields multiply scattered by two loss-free dielectric spheres, whose centers are located on the boresight axis and in the nearfield of an open-ended circular cylindrical waveguide excited in its dominant mode. Numerically computed results show good agreement with measured results obtained from a systematic experimental study on forward scatter performed in the X -band.
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TL;DR: The electric dyadic Green's function of a cluster of spheres is obtained by application of the superposition principle, dyadic algebra, and the indirect mode-matching method, which results in a set of linear equations for the unknown, vector, wave amplitudes of the dGf.
Abstract: The electric dyadic Green's function (dGf) of a cluster of spheres is obtained by application of the superposition principle, dyadic algebra, and the indirect mode-matching method. The analysis results in a set of linear equations for the unknown, vector, wave amplitudes of the dGf; that set is solved by truncation and matrix inversion. The theory is exact in the sense that no simplifying assumptions are made in the analytical steps leading to the dGf, and it is general in the sense that any number, position, size and electrical properties can be considered for the spheres that cluster together. The point source can be anywhere, even within one of the spheres. Energy conservation, reciprocity, and other tests prove that this solution is correct. Numerical results are presented for an electric Hertz dipole radiating in the presence of an array of rexolite spheres, which manifests lensing and beam-forming capabilities.
22 citations
TL;DR: A straightforward dipole array model of the more complicated antenna structure is justified by the accuracy of the results obtained and an experimental example is presented to show that this antenna in a GPR system application is effective in detecting even small plastic targets.
Abstract: A double-sided broadband antenna for applications including ground-penetrating radar for detecting buried target is described. When compared with traditional coplanar-strip antennas, a better performance is achieved with a more practical design for construction. The steps in the design procedure are demonstrated herein. In addition, using incremental segments of current elements, a distributed dipole array model is derived and presented for determining S11 in the time domain and for determining the radiation pattern of this antenna. By comparing measured results and HFSS simulations, our straightforward dipole array model of the more complicated antenna structure is justified by the accuracy of the results obtained. Finally, an experimental example is presented to show that this antenna in a GPR system application is effective in detecting even small plastic targets
12 citations
07 Mar 2005
TL;DR: In this paper, the authors presented an accurate analytical formulation based on spherical modal expansion (SME) of the near fields of small apertures radiating in the presence of a shaped dielectric lens.
Abstract: Dielectric lens antennas are inherently broadband and cost effective at producing highly shaped beams critical to mobile broadband applications (MBS). The paper presents an accurate analytical formulation based on spherical modal expansion (SME) of the near fields of small apertures radiating in the presence of a shaped dielectric lens. The analysis treats the lens as a scatterer. It utilizes techniques for radial translation and coordinate rotation of the small aperture spherical modal coefficients to align them to the phase center of the dielectric lens. The spherical modal coefficients of the scattered fields due to the lens are then obtained by application of boundary conditions. A sample computation is performed to demonstrate the approach and supported by an experimental result. The analysis is flexible enough to accommodate different types of small radiating apertures and different shapes for the dielectric lenses.
5 citations
Proceedings Article•
12 Apr 2010TL;DR: In this article, the authors present an analytical formulation of a patch array radiating in the presence of a hemispherical dielectric lens based on spherical modal expansion (SME) and experimentally demonstrate an increase in directive gain due to lens collimation.
Abstract: Steered Patch arrays with a dielectric lens for collimation are well suited for mobile applications due to their small form factor and effective sealing ability. In this paper we present an accurate analytical formulation of a patch array radiating in the presence of a hemispherical Dielectric lens based on spherical modal expansion (SME) and experimentally demonstrate an increase in directive gain due to lens collimation. The analysis treats the lens as a scatterer, and utilizes techniques for radial translation and coordinate rotation of the patch array SME coefficients to align them to the phase center of the Lens. The SME coefficients of the scattered fields are then obtained by application of boundary conditions. A sample computation using this approach shows a good match with experimental results. The analysis is flexible enough to accommodate different types of small radiating apertures with different shapes of dielectric lenses that are inherently broadband.
5 citations
Patent•
16 Jan 2004TL;DR: In this paper, a low cost antenna in a base station suitable for deployment where high density of wireless users are present in specific directions (e.g., cross roads in urban areas) is used associated with antenna elements to collimate the beam for a longer distance in the desired directions.
Abstract: A low cost antenna in a base station suitable for deployment where high density of wireless users are present in specific directions (e.g., cross roads in urban areas). A lens is used associated with antenna elements to collimate the beam for a longer distance in the desired directions. By using the lens, the need for complex electronics is minimized, thereby reducing the cost of a base station. Another aspect of the present invention enables the lens to be designed precisely by first determining the radiation pattern of each array element according to a corresponding coordinate system, transforming the radiation pattern to a common coordinate system, and determining a composite radiation pattern using the value determined for the common coordinate system. Inverse scattering technique is applied using the composite radiation pattern and the desired collimation pattern to determine the precise shape of the lens.
3 citations
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TL;DR: In this article, the authors derived translation theorems for spherical vector wave functions in a reduced form by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions.
Abstract: : Translational addition theorems for spherical vector wave functions are derived in a reduced form. The reduction is accomplished by the use of formulas relating the coefficients that arise in expansion of the product of two associated Legendre functions. These addition theorems should be useful in those cases in which spherical vector wave functions are used where the distances of bodies and sources are separated by the order of a few wavelengths.
413 citations
TL;DR: In this paper, the vector wave function addition theorems are based on corresponding theorem for the spherical scalar wave functions, which are the characteristic solutions in spherical coordinates of vector wave equation, such as occurs in electromagnetic problems.
Abstract: Addition theorems are described for spherical vector wave functions, under both rotations and translations of the coordinate system. These functions are the characteristic solutions in spherical coordinates of the vector wave equation, such as occurs in electromagnetic problems. The vector wave function addition theorems are based on corresponding theorems for the spherical scalar wave functions. The latter are reviewed and discussed. (auth)
363 citations
TL;DR: In this article, a new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10 λ in radius at a spacing as small as two spheres in contact becomes feasible.
Abstract: Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as 10\lambda in radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small as \lambda/4 in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.
306 citations
TL;DR: In this paper, the first appearance of reliable results for the scattered field from two spheres of radii larger than one wavelength and as large as ten or more was presented. But these results were only applied to three collinear spheres of various materials.
Abstract: In [8], both low- and high-frequency solutions to the two-sphere problem were presented in a form suitable for efficient computer solution, Here, numerical results are presented using a method which has enabled the first appearance of reliable results for the scattered field from two spheres of radii larger than one wavelength and as large as ten or more. Radar cross sections (RCS) are computed for numerous configurations of two spheres of various materials. Results for scattering by three collinear spheres are also given. An experimental program was undertaken and is briefly described. Whenever possible, these results are compared with the theory. In all cases the agreement is excellent. Depolarization due to multiple scattering is also investigated, revealing some interesting effects and practical applications to scattering range calibration.
105 citations
TL;DR: In this paper, the effects of placing a dielectric sphere over the aperture of a circular waveguide were investigated, and the results of an experimental and theoretical study were presented.
Abstract: The results of an experimental and theoretical study of the effects of placing a dielectric sphere over the aperture of a circular waveguide are presented. A dielectric sphere excited by a Huygens' source is used us the theoretical model to interpret the experimental results. Calculations based on this model show good overall agreement with experimental patterns and directivity measurements. It is concluded that dielectric loaded antennas such as the dielectric sphere excited by a waveguide can produce directivities in excess of that obtained by a uniformly illuminated aperture of the same cross section, particularly for dielectric objects with dimensions of two wavelengths or less. Measurements of the coupling between these antennas show that they, in general, are not as closely coupled as plain apertures without dielectric object loading.
17 citations