Matrix formulation of electromagnetic scattering

Waterman, P. C.

doi:10.1109/proc.1965.4058

Cited by 934 publications

(482 citation statements)

References 9 publications

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“…Owing to the linearity of Maxwell's equations and boundary conditions, the linear relation between the scattered field coefficientsā sca and the incident field coefficientsā inc can be related by a system transfer operator called T-matrix as follows [11]:ā sca =Tā inc .…”

Section: T-matrix Approachmentioning

confidence: 99%

“…On the other hand, a semi-analytical method called the T-matrix approach [11] is based on the extended boundary condition method (EBCM), with the T matrix being used to relate the exciting field and scattered field, where the exciting field is assumed to be inside the inscribing sphere and the scattered field outside the circumscribing sphere, respectively. The T-matrix approach is gaining popularity due to its rigor and powerfulness and has been applied to scattering from objects of various shapes, such as spheroids, finite cylinders, Chebyshev particles, cubes, clusters of spheres, and so on [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Yan¹,

et al. 2009

PIER

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Abstract-The T-matrix approach is effective in analyzing electromagnetic scattering from finite scatterers. Yet for scatterers with extreme geometry, this approach may fail. One example is its inability to analyze scattering from dielectric cylinders with large aspect ratios. To deal with such difficulty, recently we proposed a method based on an extension of the T-matrix approach, where a long cylinder is hypothetically divided into a cluster of identical sub-cylinders, for each the T matrix can be numerically stably calculated. Special care was paid to fulfill the boundary conditions at the hypothetic surface of any two neighboring sub-cylinders. The resultant coupled equations are different from that of multi-scatterer theory. The model results were in good agreement with experiment data available in the literature. However, the validity region of the proposed method was not fully characterized. Now we have developed and validated a method of moment (MoM) code, and are in a position to carry on the task of characterizing the validity region. The proposed method is found to be applicable to dielectric cylinders of arbitrary length as long as the T matrix is attainable for the elementary sub-cylinder. The conditions for the T matrix to be numerically stably calculated in terms of the equivalent volumetric radius and relative dielectric constant are also empirically obtained.

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Section: T-matrix Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Yan¹,

et al. 2009

PIER

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“…Numerical analysis of a set of such deformed bodies may be done by the transition matrix method [22]. The Yasuura method would be effective as well, including out-going and in-coming wave functions, which is a spherical coordinate version of the deep grating case [23] where up-and down-going waves are considered.…”

Section: Resultsmentioning

confidence: 99%

“…(8) by their approximate expressions of Eq. (22). Then the solution is written in the closed form as…”

Section: Effect Of Multiple Scatteringmentioning

confidence: 99%

Effect of Temperature and Multiple Scattering on Rain Attenuation of Electromagnetic Waves by a Simple Spherical Model

Setijadi¹,

Matsushima

Tanaka³

et al. 2009

PIER

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Abstract-Specific rain attenuation is discussed from the viewpoint of numerical solution for scattering and absorption of electromagnetic waves related to dielectric spheres. Special attention is paid to the quantitative evaluations considering the change of temperature and the existence of multiple scattering effect. The analysis is based on the set of Stratton's vector spherical wave functions and its addition theorem, which lead to the simultaneous linear equations for the expansion coefficients with adaptively selected truncation numbers. Computed extinction cross sections lead directly to the specific rain attenuation, where the Weibull raindrop distribution model is used. It is discussed how the dependence of the permittivity of water on temperature and frequency affects the attenuation property. Furthermore, the effect of multiple scattering is evaluated in terms of the root mean square of attenuation deviation from the simple superposition of single scattering (Mie's) coefficients. Contrary to general belief, this deviation is the highest at around the boundary between microwave and millimeter wave bands.

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“…Waterman [2] reviewed the process of using electric fields to improve coalescence and found these techniques to be quite effective in the removal of water from oil. Williams and Bailey [3] examined coalescence of poorly conducting drops in the presence of an elec-trical field both theoretically and experimentally.…”

Section: Introductionmentioning

confidence: 99%

Electrohydrodynamic Dispersion of Deformable Aerosols in the Presence of an Electric Field and Chemical Reaction Using Taylor Dispersion Model

Rudraiah

Devaraju²,

2011

J Hydrodyn

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Under the effects of electric field and chemical reaction, the problem of dispersion of aerosols in a poorly conducting fluid in a channel is solved analytically using the mixture theory together with a regular perturbation technique. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, called the Taylor dispersion coefficient. This coefficient is numerically computed and the results reveal that it increases with an increase in the electric number, but decreases with increasing porous parameter. The physical explanations for the phenomena are given in this article.

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Matrix formulation of electromagnetic scattering

Cited by 934 publications

References 9 publications

Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Characterization of the Validity Region of the Extended T-Matrix Method for Scattering From Dielectric Cylinders With Finite Length

Effect of Temperature and Multiple Scattering on Rain Attenuation of Electromagnetic Waves by a Simple Spherical Model

Electrohydrodynamic Dispersion of Deformable Aerosols in the Presence of an Electric Field and Chemical Reaction Using Taylor Dispersion Model

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