Two-dimensional transmission type volume holograms for incident plane waves of arbitrary amplitude distribution

1977 ◽  
Vol 9 (5) ◽  
pp. 437-444 ◽  
Author(s):  
L. Solymar ◽  
M. P. Jordan
Keyword(s):  
Plane Waves ◽  
Amplitude Distribution ◽  
Two Dimensional ◽  
Volume Holograms ◽  
Incident Plane ◽  
Arbitrary Amplitude

SYMMETRY AND COUPLING EFFICIENCY OF THE DEFECT MODES IN TWO-DIMENSIONAL PHONONIC CRYSTALS

2007 ◽  
Vol 21 (22) ◽  
pp. 1479-1488 ◽  
Author(s):  
Y. J. CAO ◽  
Y. Z. LI
Keyword(s):  
Phononic Crystal ◽  
Plane Waves ◽  
Coupling Efficiency ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Defect Modes ◽  
Transmission Coefficients ◽  
Resonant Modes ◽  
Incident Plane ◽  
Match Theory

We study theoretically the symmetric property and coupling efficiency of the defect modes in a two-dimensional phononic crystal by calculating band structures, field distributions and transmission coefficients of the defect modes. The results show that the point defect could act as a microcavity surrounded by the phononic crystal, and the confining ability of the phononic crystal to the resonant modes strongly depends on the thickness of the phononic crystal. By investigating the transmission spectra, we also find that the defect modes cannot be absolutely excited by the normally incident plane waves. The transmission coefficients are calculated by using the eigen-mode match theory method under the supercell technique, which is applied to the phononic crystals with the defects for the first time.

scholarly journals Localization of Scattering Objects Using Neural Networks

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 11
Author(s):  
Domonkos Haffner ◽  
Ferenc Izsák
Keyword(s):  
Neural Networks ◽  
Plane Waves ◽  
Measurement Data ◽  
Scattered Wave ◽  
Training Data ◽  
Data Set ◽  
Main Compound ◽  
Incident Plane ◽  
The Neural Networks ◽  
Simulation Package

The localization of multiple scattering objects is performed while using scattered waves. An up-to-date approach: neural networks are used to estimate the corresponding locations. In the scattering phenomenon under investigation, we assume known incident plane waves, fully reflecting balls with known diameters and measurement data of the scattered wave on one fixed segment. The training data are constructed while using the simulation package μ-diff in Matlab. The structure of the neural networks, which are widely used for similar purposes, is further developed. A complex locally connected layer is the main compound of the proposed setup. With this and an appropriate preprocessing of the training data set, the number of parameters can be kept at a relatively low level. As a result, using a relatively large training data set, the unknown locations of the objects can be estimated effectively.

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

Optimization of Phononic Crystals for the Simultaneous Attenuation of Out-of-Plane and In-Plane Waves

2011 ◽  
Author(s):  
Osama R. Bilal ◽  
Mahmoud I. Hussein
Keyword(s):  
Genetic Algorithm ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Phononic Crystals ◽  
Gap Size ◽  
Two Dimensional ◽  
Dispersion Characteristics ◽  
Out Of Plane ◽  
Optimization Methodology ◽  
Application Specific

The topological distribution of the material phases inside the unit cell composing a phononic crystal has a significant effect on its dispersion characteristics. This topology can be engineered to produce application-specific requirements. In this paper, a specialized genetic-algorithm-based topology optimization methodology for the design of two-dimensional phononic crystals is presented. Specifically the target is the opening and maximization of band gap size for (i) out-of-plane waves, (ii) in-plane waves and (iii) both out-of-plane and in-plane waves simultaneously. The methodology as well as the resulting designs are presented.

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.

THE ELECTRIC AND MAGNETIC FIELDS IN A STRATIFIED FLAT CONDUCTOR FOR INCIDENT PLANE WAVES

1965 ◽  
Vol 43 (5) ◽  
pp. 898-909 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Magnetic Fields ◽  
Plane Waves ◽  
Incident Plane ◽  
Electric And Magnetic Fields

The electric and magnetic fields in the upper layer of a stratified flat conductor in the field of plane waves are studied. Expressions for the amplitude and phase of the components of the electric and magnetic fields are obtained and evaluated for various frequencies, angles of incidence, layer thicknesses, depths, and conductivities. The conductivities σ = 10−11 to 10−16 e.m.u. and the frequencies ƒ = 10−3 to 104 cycles/second considered are of interest in geophysics.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

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