scholarly journals A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 315-342
Author(s):  
Masud Mansuripur
Keyword(s):  
Cross Section ◽  
Electromagnetic Scattering ◽  
Final Section ◽  
Scattering Amplitude ◽  
Plane Waves ◽  
Homogeneous Medium ◽  
Far Field ◽  
Scalar Diffraction ◽  
Optical Cross Section ◽  
Section Theorem

AbstractStarting with Maxwell’s equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector electromagnetic fields. The famous Sommerfeld solution to the problem of diffraction from a perfectly conducting half-plane is elaborated. Far-field scattering of plane waves from obstacles is treated in some detail, and the well-known optical cross-section theorem, which relates the scattering cross-section of an obstacle to its forward scattering amplitude, is derived. Also examined is the case of scattering from mild inhomogeneities within an otherwise homogeneous medium, where, in the first Born approximation, a fairly simple formula is found to relate the far-field scattering amplitude to the host medium’s optical properties. The related problem of neutron scattering from ferromagnetic materials is treated in the final section of the paper.

The low frequency scalar diffraction by an elliptic disc

1967 ◽  
Vol 63 (4) ◽  
pp. 1273-1280 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Scattered Field ◽  
Low Frequency ◽  
Field Amplitude ◽  
Wave Number ◽  
Series Expansions ◽  
Far Field ◽  
Scalar Diffraction ◽  
Scattering Cross

SummaryThe problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

scholarly journals Uniqueness in inverse electromagnetic scattering problem with phaseless far-field data at a fixed frequency

2020 ◽  
Author(s):  
Xiaoxu Xu ◽  
Bo Zhang ◽  
Haiwen Zhang
Keyword(s):  
Electromagnetic Scattering ◽  
Field Data ◽  
Scattering Problem ◽  
Plane Waves ◽  
Index Of Refraction ◽  
Field Pattern ◽  
Far Field ◽  
Fixed Frequency ◽  
Uniqueness Results ◽  
Far Field Pattern

Abstract This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work (2018,SIAM J. Appl. Math. 78, 3024–3039), by adding a known reference ball into the acoustic scattering system, it was proved that the impenetrable obstacle and the index of refraction of an inhomogeneous medium can be uniquely determined by the acoustic phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency. In this paper, we extend these uniqueness results to the inverse electromagnetic scattering case. The phaseless far-field data are the modulus of the tangential component in the orientations ${\boldsymbol{e}}_\phi $ and ${\boldsymbol{e}}_\theta $, respectively, of the electric far-field pattern measured on the unit sphere and generated by infinitely many sets of superpositions of two electromagnetic plane waves with different directions and polarizations. Our proof is mainly based on Rellich’s lemma and the Stratton–Chu formula for radiating solutions to the Maxwell equations.

Electromagnetic scattering by a perfectly conducting elliptic disk

1987 ◽  
Vol 65 (7) ◽  
pp. 723-734 ◽  
Author(s):  
Jonas Björkberg ◽  
Gerhard Kristensson
Keyword(s):  
Total Cross Section ◽  
Cross Section ◽  
Electromagnetic Scattering ◽  
Recurrence Relations ◽  
Scattering Amplitude ◽  
Azimuthal Angle ◽  
Low Frequency ◽  
Prolate Spheroid ◽  
Numerical Computations ◽  
Theoretical Results

Electromagnetic scattering from a perfectly conducting elliptic disk is treated by means of the null-field approach. The disk is obtained as the zero-thickness limit of an ellipsoid. It is shown that in this limit all relevant matrix elements have a well-defined limit. Owing to the lack of axial symmetry, an integral that can not be solved analytically remains in the azimuthal angle. In an appendix, an efficient algorithm to solve these integrals by means of recurrence relations is presented. The formalism is attractive for numerical computations, and stable results for very eccentric disks have been obtained. The first few terms in the low-frequency expansion of the total cross section are derived. Numerical computations of the scattering amplitude and the total cross section illustrate the theoretical results. In a final appendix, the thin wire limit of the elliptic disk is discussed, and a comparison with corresponding results of a prolate spheroid is presented.

The scattering cross-section of an obstacle in an elastic solid for plane harmonic waves

1965 ◽  
Vol 61 (4) ◽  
pp. 969-981 ◽  
Author(s):  
P. J. Barratt ◽  
W. D. Collins
Keyword(s):  
Cross Section ◽  
Scattering Amplitude ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Scattering Cross Section ◽  
Harmonic Waves ◽  
Far Field ◽  
Scattering Cross ◽  
Plane Harmonic Waves

AbstractIt is shown that, when a plane harmonic P or S wave is incident upon a two-or three-dimensional obstacle in an infinite elastic solid, the scattering cross-section of the obstacle can be calculated from an appropriate far-field scattering amplitude.

scholarly journals Elusive Pure Anapole Excitation in Homogenous Spherical Nanoparticles with Radial Anisotropy

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Liu ◽  
Bing Lei ◽  
Jianhua Shi ◽  
Haojun Hu ◽  
Andrey E. Miroshnichenko
Keyword(s):  
Cross Section ◽  
Plane Waves ◽  
Far Field ◽  
Spherical Nanoparticles ◽  
Magnetic Dipoles ◽  
Anisotropic Dielectric ◽  
Scattered Power ◽  
Incident Plane ◽  
Total Scattering Cross Section ◽  
Radial Anisotropy

For homogenous isotropic dielectric nanospheres with incident plane waves, Cartesian electric and toroidal dipoles can be tunned to cancel each other in terms of far-field scattering, leading to the effective anopole excitation. At the same time however, other multipoles such as magnetic dipoles with comparable scattered power are simultanesouly excited, mixing with the anopole and leading to a nonnegligible total scattering cross-section. Here, we show that, for homogenous dielectric nanospheres, radial anisotropy can be employed to significantly suppress the other multipole excitation, which at the same time does not compromise the property of complete scattering cancallation between Cartesian electric and toroidal dipoles. This enables an elusivepure anopoleexcitation within radially anisotropic dielectric nanospheres, which may shed new light on many scattering related fundamental researches and applications.

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