Scattering from a slit in a biisotropic medium

2003 ◽  
Vol 81 (10) ◽  
pp. 1193-1204 ◽  
Author(s):  
T Hayat ◽  
S Asghar ◽  
K Hutter
Keyword(s):  
Scalar Field ◽  
Diffraction Problem ◽  
Normal Component ◽  
Spherical Wave ◽  
Left Handed ◽  
Biisotropic Medium ◽  
Beltrami Field ◽  
Vector Diffraction ◽  
The Fourier Transform ◽  
Conducting Sheet

An analytical solution is developed for spherical wave scattering by a slit in an infinitely perfectly conducting sheet in a homogeneous biisotropic medium. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left-handed or a right-handed Beltrami field. The point source is assumed to be far from the slit so that the incident spherical wave is locally plane. The slit is wide and the sheet thin, both with respect to wavelength. By using the Fourier transform technique the boundary-value problem is transformed into Wiener–Hopf equation that is solved approximately. The diffracted wave field is studied in the far field of the slit. The diffracted field is the sum of the wave fields produced by the two edges of the slit and an interaction wave field.PACS Nos.: 41.20.q, 41.20.Jb, 52.35.Hr

scholarly journals Quantum Vacuum Effects in Braneworlds on AdS Bulk

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 181
Author(s):  
Aram A. Saharian
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Normal Component ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Curvature Radius ◽  
Perfect Conductor ◽  
Quantum Vacuum ◽  
Local Properties

We review the results of investigations for brane-induced effects on the local properties of quantum vacuum in background of AdS spacetime. Two geometries are considered: a brane parallel to the AdS boundary and a brane intersecting the AdS boundary. For both cases, the contribution in the vacuum expectation value (VEV) of the energy–momentum tensor is separated explicitly and its behavior in various asymptotic regions of the parameters is studied. It is shown that the influence of the gravitational field on the local properties of the quantum vacuum is essential at distance from the brane larger than the AdS curvature radius. In the geometry with a brane parallel to the AdS boundary, the VEV of the energy–momentum tensor is considered for scalar field with the Robin boundary condition, for Dirac field with the bag boundary condition and for the electromagnetic field. In the latter case, two types of boundary conditions are discussed. The first one is a generalization of the perfect conductor boundary condition and the second one corresponds to the confining boundary condition used in QCD for gluons. For the geometry of a brane intersecting the AdS boundary, the case of a scalar field is considered. The corresponding energy–momentum tensor, apart from the diagonal components, has nonzero off-diagonal component. As a consequence of the latter, in addition to the normal component, the Casimir force acquires a component parallel to the brane.

X-ray Fourier transform holography by amplitude-division-type Fresnel zone plate interferometer

2018 ◽  
Vol 25 (1) ◽  
pp. 241-247 ◽  
Author(s):  
Minas Balyan ◽  
Levon Haroutunyan
Keyword(s):  
Fourier Transform ◽  
Plane Wave ◽  
Fresnel Zone ◽  
Spherical Wave ◽  
Zone Plate ◽  
Fresnel Zone Plate ◽  
Focal Distance ◽  
X Ray ◽  
Wave Forms ◽  
The Fourier Transform

A two-block X-ray Fresnel zone plate system forms two-beams – a plane wave and a spherical wave – which interfere at the focal distance of the virtual source of the spherical wave. An object placed in the path of the plane wave forms an object wave and the spherical wave is the reference wave. The recorded intensity distribution is the Fourier transform hologram of the object. Analytical and numerical calculations show the possibilities of this scheme to record the hologram and reconstruct the object image. Examples of recording holograms of a one-dimensional cosine-like grating and a two-dimensional grid object as well as reconstruction of the images are considered.

scholarly journals Super-Weak Force and Neutrino Masses

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 107 ◽  
Author(s):  
Zoltán Trócsányi
Keyword(s):  
Abelian Group ◽  
Scalar Field ◽  
New Right ◽  
Neutrino Masses ◽  
Anomaly Cancellation ◽  
Weak Force ◽  
Left Handed ◽  
Free Extension ◽  
The Standard Model ◽  
Standard Model Gauge Group

We consider an anomaly free extension of the standard model gauge group G SM by an abelian group to G SM ⊗ U ( 1 ) Z . The condition of anomaly cancellation is known to fix the Z-charges of the particles, but two. We fix one remaining charge by allowing for all possible Yukawa interactions of the known left-handed neutrinos and new right-handed ones that obtain their masses through interaction with a new scalar field with spontaneously broken vacuum. We discuss some of the possible consequences of the model.

3-D Shape Measurement Based on Optic Interferometric Projection

2010 ◽  
Vol 139-141 ◽  
pp. 1981-1984
Author(s):  
Jiang Hong Gan ◽  
Li Ping Zhou ◽  
Liang Zhou Chen ◽  
Long Xu
Keyword(s):  
High Speed ◽  
Fringe Pattern ◽  
Phase Distribution ◽  
Spherical Wave ◽  
Three Dimensional ◽  
Experimental System ◽  
Shape Measurement ◽  
Small Object ◽  
Dimensional Shape ◽  
The Fourier Transform

This paper aimed to use a novel optic interferometric fringe projection to measure the three-dimensional shape of small object with high resolution. In this method, the projecting fringe pattern, which has a sinusoidal density distribution, good contrast and equal spacing, is generated by a spherical wave incident into a triangle-section prism. Project the fringe onto the subject under test, the image of the deformed fringe pattern modulated by object surface is captured by a high-speed CMOS camera and processed by the Fourier Transform technique to extract the phase distribution which is related to height information. An experimental system is set to conduct 3-D shape measurement and the result shows the validity of the proposed method. The projecting system is simple and compact, which helps to realize the integration and miniaturization of the system.

scholarly journals Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

2018 ◽  
Vol 173 ◽  
pp. 02007 ◽  
Author(s):  
Dmitriy Divakov ◽  
Mikhail Malykh ◽  
Leonid Sevastianov ◽  
Anton Sevastianov ◽  
Edik Ayryan
Keyword(s):  
Thin Film ◽  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Diffraction Problem ◽  
Polarized Light ◽  
Vector Model ◽  
Scalar Diffraction ◽  
Proposed Model ◽  
Vector Diffraction ◽  
Small Change

Maxwell equations describe the propagation with diffraction of waveguide modes through a thin-film waveguide lens. If the radius of the thin-film lens is large, then the thickness of the lens varies slowly in the yz plane. For this case we propose the model, which is based on the assumption of a small change in the electromagnetic field in a direction y. Under this assumption the vector diffraction problem is reduced to a number of scalar diffraction problems. The solutions demonstrate the vector nature of the electromagnetic field, which allows us to call the proposed model a quasi-vector model.

The classical scalar field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Scalar Field ◽  
Symmetry Breaking ◽  
Free Field ◽  
Scalar Fields ◽  
Global Symmetry ◽  
Lagrange Equations ◽  
Complex Scalar ◽  
Klein Gordon ◽  
Complex Scalar Field ◽  
The Fourier Transform

This chapter explains some of the properties of scalar fields, which are paradigmatic in relativistic field theory. It also shows how a complex scalar field can confer an effective mass to a ‘gauge’ field. The chapter first provides the Klein–Gordon equation derived from the Euler–Lagrange equations outlined in the previous chapter. It then illustrates the Fourier transform of a free field, before embarking on further discussions on complex fields, charge, and symmetry breaking. Finally, this chapter considers that the fact that global symmetry breaking leads to the appearance of a massless, and therefore long-range, scalar field is problematic because such a field is not observed experimentally. It thus takes a look at the BEH mechanism (named after its inventors, Robert Brout, François Englert, and Peter Higgs), which can make it ‘disappear’.

scholarly journals FERMION MASS HIERARCHY IN LIFSHITZ TYPE GAUGE THEORY

2010 ◽  
Vol 25 (19) ◽  
pp. 1613-1623 ◽  
Author(s):  
KUNIO KANETA ◽  
YOSHIHARU KAWAMURA
Keyword(s):  
Gauge Theory ◽  
Scalar Field ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Left Handed ◽  
Fermion Masses ◽  
The Standard Model ◽  
Flavor Mixing ◽  
The Hierarchical Structure ◽  
Associated Operators

We study the origin of fermion mass hierarchy and flavor mixing in a Lifshitz type extension of the standard model including an extra scalar field. We show that the hierarchical structure can originate from renormalizable interactions. In contrast to the ordinary Froggatt–Nielsen mechanism, the higher the dimension of associated operators, the heavier the fermion masses. Tiny masses for left-handed neutrinos are obtained without introducing right-handed neutrinos.

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