scholarly journals Chiral optical fields: a unified formulation of helicity scattered from particles and dichroism enhancement

2017 ◽  
Vol 375 (2090) ◽  
pp. 20160314 ◽  
Author(s):  
Manuel Nieto-Vesperinas
Keyword(s):  
Plane Waves ◽  
Angular Spectrum ◽  
Longitudinal Component ◽  
Optical Theorem ◽  
Extinction Rate ◽  
Weak Signal ◽  
Optical Fields ◽  
New Horizons ◽  
Elliptic Polarization ◽  
Circular Plane

We establish a general unified formulation which, using the optical theorem of electromagnetic helicity, shows that dichorism is a phenomenon arising in any scattering—or diffraction—process, elastic or not, of chiral electromagnetic fields by objects either chiral or achiral. It is shown how this approach paves the way to overcoming well-known limitations of standard circular dichroism, like its weak signal or the difficulties of using it with magnetodielectric particles. Based on the angular spectrum, representation of optical fields with only right circular or left circular plane waves, we introduce beams with transverse elliptic polarization and possessing a longitudinal component. Then, our formulation for general optical fields shows how to enhance the extinction rate of incident helicity (and therefore the dichroism signal) versus that of energy of the light scattered or emitted by a particle, or vice versa. This article is part of the themed issue ‘New horizons for nanophotonics’.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

scholarly journals Spectral dispersion modeling of virtually imaged phased array by using angular spectrum of plane waves

2015 ◽  
Vol 23 (1) ◽  
pp. 1 ◽  
Author(s):  
Xinrong Hu ◽  
Qiang Sun ◽  
Jing Li ◽  
Chun Li ◽  
Ying Liu ◽  
...  
Keyword(s):  
Phased Array ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Dispersion Modeling ◽  
Spectral Dispersion

Phase hologram optimization for the generation of optical fields composed by an arbitrary number of plane waves

2013 ◽  
Vol 311 ◽  
pp. 248-255
Author(s):  
Alfonso Fernandez-Vazquez ◽  
Guadalupe Méndez ◽  
Rafael Páez López
Keyword(s):  
Arbitrary Number ◽  
Plane Waves ◽  
Optical Fields ◽  
Phase Hologram

Electromagnetic diffraction in optical systems - I. An integral representation of the image field

1959 ◽  
Vol 253 (1274) ◽  
pp. 349-357 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Integral Representation ◽  
Optical System ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Optical Systems ◽  
Angular Aperture ◽  
Spherical Waves ◽  
Simple Physical Interpretation ◽  
Electromagnetic Diffraction

An integral representation is obtained for the electromagnetic field in the image space of an optical system . This representation, which is not restricted to systems of low angular aperture, is in the form of an angular spectrum of plane waves, and is closely related to that introduced by Luneberg (1944) as a vector generalization of well-known formulae of Debye (1909) and Picht (1925). It is shown that the representation has a simple physical interpretation in terms of a modified Huygens—Fresnel principle which operates with secondary plane waves rather than with secondary spherical waves.

DIFFRACTION BY A CONDUCTING HALF-PLANE IN AN ANISOTROPIC PLASMA

1964 ◽  
Vol 42 (8) ◽  
pp. 1455-1468 ◽  
Author(s):  
E. V. Jull
Keyword(s):  
Magnetic Field ◽  
Half Plane ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Anisotropic Plasma ◽  
Angle Of Incidence ◽  
Dual Integral Equations ◽  
Magnetostatic Field

The diffraction of a plane electromagnetic wave by a perfectly conducting half-plane in an anisotropic plasma is considered. The plasma is characterized by a permittivity tensor and the wave is assumed to propagate in a direction normal to the magnetostatic field and the diffracting edge, but its angle of incidence is otherwise arbitrary. Only the H-polarized wave of the incident field, which has a single magnetic field component parallel to the edge, is affected by the anisotropy and the analysis is restricted accordingly. Representing the scattered field as an angular spectrum of plane waves leads to dual integral equations from which an expression for the scattered field is obtained. The total field is then reduced to Fresnel integrals and its far-field behavior is investigated. Agreement with Seshadri and Rajagopal's result for a wave normally incident on the conductor, which was obtained by using the Wiener–Hopf technique, is found. The differences between isotropic and anisotropic solutions to this problem, which arise from the differing boundary conditions on the tangential magnetic field, are examined.

Radio propagation over a flat Earth across a boundary separating two different media

1953 ◽  
Vol 246 (905) ◽  
pp. 1-55 ◽  
Keyword(s):  
Plane Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Dipole Source ◽  
Radio Waves ◽  
Dual Integral Equations ◽  
Plane Wave Incident ◽  
General Complex ◽  
Infinite Conductivity ◽  
New Feature

A theoretical investigation is given of the phenomena arising when vertically polarized radio waves are propagated across a boundary between two homogeneous sections of the earth’s surface which have different complex permittivities. The problem is treated in a two-dimensional form, but the results, when suitably interpreted, are valid for a dipole source. The earth’s surface is assumed to be flat. In the first part of the paper one section of the earth is taken to have infinite conductivity and is represented by an infinitely thin, perfectly conducting half-plane lying in the surface of an otherwise homogeneous earth. The resulting boundary-value problem is initially solved for a plane wave incident at an arbitrary angle; the scattered field due to surface currents induced in the perfectly conducting sheet is expressed as an angular spectrum of plane waves, and this formulation leads to dual integral equations which are treated rigorously by the methods of contour integration. The solution for a line-source is then derived by integration of the plane-wave solutions over an appropriate range of angles of incidence, and is reduced to a form in which the new feature is an integral of the type missing text where a and b are in general complex within a certain range of argument.

Acoustic Scattering

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Acoustic Waves ◽  
Acoustic Radiation ◽  
Scattering Amplitude ◽  
Medical Physics ◽  
Plane Waves ◽  
Acoustic Scattering ◽  
Radiation Condition ◽  
Optical Theorem ◽  
Rigid Sphere ◽  
Symmetric Geometry

This chapter focuses on the mathematics underlying the scattering of acoustic waves. Scattering of waves and/or particles is a common phenomenon. The scattering of plane waves from spheres is applied in a wide array of fields, from optics and acoustics to meteorology, elasticity, seismology, medical physics, quantum mechanics, and biochemistry. With respect to the problem of electromagnetic wave scattering from a sphere, Lorenz found the complete mathematical solution in 1890 in terms of an infinite series of so-called partial waves. The solution is known as the Mie or Debye-Mie solution. The chapter first considers scattering by a cylinder and time-averaged energy flux before discussing spherically symmetric geometry, taking into account the scattering amplitude, the optical theorem, and the Sommerfeld radiation condition. It also examines the case of a rigid sphere, acoustic radiation from a rigid pulsating sphere, the sound of mountain streams, and mathematical bubbles.

The propagation of magneto-thermo-viscoelastic plane waves in a parallel union of the Kelvin and Maxwell bodies

1971 ◽  
Vol 70 (2) ◽  
pp. 343-350 ◽  
Author(s):  
D. S. Chandrasekhariah
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Wave Propagation ◽  
Thermal Field ◽  
Plane Waves ◽  
Viscoelastic Body ◽  
Longitudinal Component ◽  
Transverse Component ◽  
Wave Travel

AbstractThe propagation of plane waves in a viscoelastic body representing a parallel union of the Kelvin and Maxwell bodies placed in a magneto-thermal field is investigated. It is shown that the longitudinal component of the wave is in general coupled with a transverse component and the wave travels in two families. In particular if the primary magnetic field is either parallel or perpendicular to the direction of wave propagation, the three components of the wave travel unlinked, with either the longitudinal component or the transverse components unaffected by the presence of the electromagnetic field. If the electrical conductivity of the solid is infinite the effect of the primary magnetic field is to increase the values of the material constants. The effect of wave propagation on magnetic permeability is equivalent to an anisotropic rescaling of the primary magnetic field. Some of the results obtained in the earlier works are obtained as particular cases of the more general results derived here.

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