Far-Field Patterns for Electromagnetic Waves in an Inhomogeneous Medium

1990 ◽  
Vol 21 (6) ◽  
pp. 1537-1549 ◽  
Author(s):  
David Colton ◽  
Lassi Päivärinta
Keyword(s):  
Inhomogeneous Medium ◽  
Electromagnetic Waves ◽  
Far Field ◽  
Field Patterns

Far field patterns and the inverse scattering problem for electromagnetic waves in an inhomogeneous medium

1988 ◽  
Vol 103 (3) ◽  
pp. 561-575 ◽  
Author(s):  
David Colton ◽  
Lassi Päivärinta
Keyword(s):  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Integral Identity ◽  
Electromagnetic Waves ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Optimal Solution ◽  
Far Field ◽  
Field Patterns

AbstractWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support. It is first shown that the set of far field patterns of the electric fields corresponding to incident plane waves propagating in arbitrary directions is complete in the space of square-integrable tangential vector fields defined on the unit sphere. We then show that under certain conditions the electric far field patterns satisfy an integral identity involving the unique solution of a new class of boundary value problems for Maxwell's equations called the interior transmission problem for electromagnetic waves. Finally, it is indicated how this integral identity can be used to formulate an optimization scheme yielding an optimal solution of the inverse scattering problem for electromagnetic waves.

Transmissive 2-bit anisotropic coding metasurface

2022 ◽  
Author(s):  
Pengtao Lai ◽  
Zenglin Li ◽  
Wei Wang ◽  
Jia Qu ◽  
Liang Wei Wu ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Electromagnetic Wave ◽  
Circular Polarization ◽  
Orbital Angular Momentum ◽  
Electromagnetic Waves ◽  
Beam Splitter ◽  
Far Field ◽  
Polarization Conversion ◽  
Field Patterns ◽  
Phase Profile

Abstract Coding metasurfaces have attracted tremendous interests due to unique capabilities of manipulating electromagnetic wave. However, archiving transmissive coding metasurface is still challenging. Here we propose a transmissive anisotropic coding metasurface that enables the independent control of two orthogonal polarizations. The polarization beam splitter and the OAM generator have been studied as typical applications of anisotropic 2-bit coding metasurface. The simulated far field patterns illustrate that the x and y polarized electromagnetic waves are deflected into two different directions, respectively. The anisotropic coding metasurface has been experimentally verified to realize an orbital angular momentum (OAM) beam with l = 2 of right-handed polarized wave, resulting from both contributions from linear-to-circular polarization conversion and the phase profile modulation. This work is beneficial to enrich the polarization manipulation field and develop transmissive coding metasurfaces.

SCATTERING OF ELECTROMAGNETIC WAVES BY A MOVING CYLINDER IN FREE SPACE

1967 ◽  
Vol 45 (9) ◽  
pp. 2999-3007 ◽  
Author(s):  
S. W. Lee ◽  
R. Mittra
Keyword(s):  
Angular Dependence ◽  
Lorentz Transformation ◽  
Doppler Shift ◽  
Free Space ◽  
Electromagnetic Waves ◽  
Stationary Problem ◽  
Small Radius ◽  
Far Field ◽  
Field Patterns ◽  
Moving Cylinder

Scattering of electromagnetic waves by a moving cylinder in free space is studied by an application of Lorentz transformation. It is shown that the solution in the transformed coordinates can be derived readily from a knowledge of the solution of the corresponding stationary problem. Several important characteristics of the scattered far-fields are investigated in detail for a cylinder of small radius. These include the calculation of the far-field patterns and the angular dependence of the Doppler shift.

Dense sets and far field patterns for acoustic waves in an inhomogeneous medium

1988 ◽  
Vol 31 (3) ◽  
pp. 401-407 ◽  
Author(s):  
David Colton
Keyword(s):  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Acoustic Waves ◽  
Scattering Problem ◽  
Plane Waves ◽  
Related Result ◽  
Wave Number ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic

In this paper, we shall obtain two results on the class of far field patterns corresponding to the scattering of time harmonic acoustic plane waves by an inhomogeneous medium of compact support. Although the problem of characterizing the class of far field patterns is of basic importance in inverse scattering theory, very little is known about this class other than the fact that the far field patterns are entire functions of their independent (complex) variables for each positive fixed value of the wave number. In particular, the class of far field patterns is not all of L2(∂Ω) where ∂Ω is the unit sphere and this implies that the inverse scattering problem is improperly posed since the far field patterns are, in practice, determined from inexact measurements. The purpose of this paper is to show that while the class of far field patterns corresponding to the scattering of time harmonic plane waves by an inhomogeneous medium is not all of L2(∂Ω), it is dense in L2(∂Ω) for sufficiently small values of the wave number. In addition, a related result will be obtained for a special translation of the class of far field patterns. Analogous results for the scattering of time harmonic acoustic waves by a homogeneous scattering obstacle have recently been obtained by Colton [1], Colton and Kirsch [2], Colton and Monk [3, 4] and Kirsch [8].

Far-Field Patterns for Acoustic Waves in an Inhomogeneous Medium

1989 ◽  
Vol 20 (6) ◽  
pp. 1472-1483 ◽  
Author(s):  
David Colton ◽  
Andreas Kirsch ◽  
Lassi Päivärinta
Keyword(s):  
Inhomogeneous Medium ◽  
Acoustic Waves ◽  
Far Field ◽  
Field Patterns

scholarly journals Axial localization and tracking of self-interference nanoparticles by lateral point spread functions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yongtao Liu ◽  
Zhiguang Zhou ◽  
Fan Wang ◽  
Günter Kewes ◽  
Shihui Wen ◽  
...  
Keyword(s):  
Mirror Image ◽  
Excitation Wavelength ◽  
Far Field ◽  
Point Spread Functions ◽  
Microscopy Imaging ◽  
Localization Accuracy ◽  
Field Patterns ◽  
Atomic Force ◽  
Point Spread ◽  
Sensing Technology

AbstractSub-diffraction limited localization of fluorescent emitters is a key goal of microscopy imaging. Here, we report that single upconversion nanoparticles, containing multiple emission centres with random orientations, can generate a series of unique, bright and position-sensitive patterns in the spatial domain when placed on top of a mirror. Supported by our numerical simulation, we attribute this effect to the sum of each single emitter’s interference with its own mirror image. As a result, this configuration generates a series of sophisticated far-field point spread functions (PSFs), e.g. in Gaussian, doughnut and archery target shapes, strongly dependent on the phase difference between the emitter and its image. In this way, the axial locations of nanoparticles are transferred into far-field patterns. We demonstrate a real-time distance sensing technology with a localization accuracy of 2.8 nm, according to the atomic force microscope (AFM) characterization values, smaller than 1/350 of the excitation wavelength.

Sign in / Sign up

Export Citation Format

Share Document