The reflexion of internal/inertial waves from bumpy surfaces

1971 ◽  
Vol 46 (2) ◽  
pp. 273-291 ◽  
Author(s):  
P. G. Baines
Keyword(s):  
Plane Wave ◽  
Energy Flux ◽  
Incident Wave ◽  
Wave Number ◽  
Inertial Waves ◽  
Incident Wavelength ◽  
Reflected Wave ◽  
Incident Plane ◽  
The Difference ◽  
Reflecting Surface

When internal and/or inertial waves reflect from a smooth surface which is not plane, there is in general some energy flux which is ‘back-reflected’ in the opposite direction to that of the incident energy flux (in addition to that ‘transmitted’ in the direction of the reflected rays), provided only that the incident wavelength is sufficiently large in comparison with the length scales of the reflecting surface. The reflected wave motion due to an incident plane wave is governed by a Fredholm integral equation whose kernel depends on the form of the reflecting surface. Some specific examples are discussed, and the special case of the ‘linearized boundary’ is considered in detail. For an incoming plane wave incident on a sinusoidally varying surface of sufficiently small amplitude, in addition to the main reflected wave two new waves are generated whose wave-numbers are the sum and difference respectively of those of the surface perturbations and the incident wave. If the incident wave-number is the smaller, the difference wave is back-reflected.

The reflexion of internal/inertial waves from bumpy surfaces. Part 2. Split reflexion and diffraction

1971 ◽  
Vol 49 (1) ◽  
pp. 113-131 ◽  
Author(s):  
P. G. Baines
Keyword(s):  
Wave Field ◽  
Logarithmic Singularity ◽  
Fluid Velocity ◽  
Wave Theory ◽  
Dispersive Wave ◽  
Inertial Waves ◽  
Incident Wavelength ◽  
Wave Fields ◽  
Reflected Wave ◽  
Square Root Singularity

This paper considers the linear inviscid reflexion of internal/inertial waves from smooth bumpy surfaces where a characteristic (or ray) is tangent to the surface at some point. There are two principal cases. When a characteristic associated with the incident wave is tangent to the surface we have diffraction; when the tangential characteristic is associated with a reflected wave we have split reflexion, a phenomenon which has no counterpart in classical non-dispersive wave theory. In both these cases the problem of determining the wave field may be reduced to a set of coupled integral equations with two unknown functions. These equations are solved for the simplest topography for each case, and the properties of the wave fields for more general topographies are discussed. For both split reflexion and diffraction, the fluid velocity has an inverse-square-root singularity on the tangential characteristic, and the energy density has a corresponding logarithmic singularity. The diffracted wave field penetrates into the shadow region a distance which is of the order of the incident wavelength. Possibilities for instability and mixing are discussed.

scholarly journals Free space transmission lines in receiving antenna operation

2019 ◽  
Author(s):  
Reuven Ianconescu ◽  
Vladimir Vulfin
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Incident Wave ◽  
Transmission Lines ◽  
Incident Plane Wave ◽  
Software Simulation ◽  
Incident Plane ◽  
Receiving Antenna ◽  
Scattering Matrices ◽  
Simulation Results

This work derives exact expressions for the voltage and current induced into a two conductors non isolated transmission lines by an incident plane wave. The methodology is to use the transmission line radiating properties to derive scattering matrices and make use of reciprocity to derive the response to the incident wave. The analysis is in the frequency domain and it considers transmission lines of any small electric cross section, incident by a plane wave from any incident direction and any polarisation. The analytic results are validated by successful comparison with ANSYS commercial software simulation results, and compatible with other published results.

PLANE WAVE SPECTRA IN GRATING THEORY: V. SCATTERING BY A SEMI-INFINITE GRATING OF ISOTROPIC SCATTERERS

1966 ◽  
Vol 44 (11) ◽  
pp. 2839-2874 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Recent Analysis ◽  
Scattering Function ◽  
Cross Sectional ◽  
Half Wavelength ◽  
Incident Plane ◽  
Order Of Magnitude ◽  
Plane Solution ◽  
The Difference

Integral relations satisfied by the scattering function for a semi-infinite grating of isotropically scattering elements are obtained by specializing the results of earlier work. It is shown that the scattering function for the grating may be expressed simply in terms of a function f of one complex variable which satisfies a nonlinear integral equation analogous in form to Chandrasekhar's integral equation. The function f is proportional to the scattering function for the first element of the grating; it also satisfies a more simple functional equation for which a solution has been given elsewhere. The relationship between the present work and the recent analysis of Hills and Karp is examined; except for one minor point, general agreement is found. The difference between the scattering functions for an element in the semi-infinite grating and the corresponding element in the infinite grating is investigated, and its order of magnitude as a function of position in the structure is estimated. An explicit solution (which may be identified with the Sommerfeld half-plane solution) is obtained in the limit as the spacing between elements tends to zero. The scattered far field is examined, special attention being given to the limiting forms in circumstances which correspond to the Rayleigh wavelengths of the infinite grating. It is demonstrated that the form of f depends radically upon whether or not the grating constant is a multiple of a half-wavelength of the incident plane wave; in each case, the behavior of f near its singularities is determined. Some required properties of the scattering function for an element in the infinite grating are obtained. In particular, it is shown that if the grating constant is less than a half wavelength, then this function has poles at certain complex angles of incidence which depend both on the cross-sectional dimensions of a cylinder and on the grating constant. These poles might correspond to resonances in the grating.

An approximate treatment of high-frequency scattering

1957 ◽  
Vol 53 (3) ◽  
pp. 691-701 ◽  
Author(s):  
D. S. Jones ◽  
G. B. Whitham
Keyword(s):  
Approximate Method ◽  
Energy Flux ◽  
Incident Wave ◽  
High Frequency ◽  
Harmonic Wave ◽  
Incident Beam ◽  
Scattered Wave ◽  
The Body ◽  
Scattering Coefficient ◽  
Wave Number

In some recent work Kodis* considers the scattering of a plane harmonic wave by a circular cylinder and uses variational methods to deduce an asymptotic formula for the scattering coefficient in the case of high-frequency waves. The scattering coefficient, σ, is denned as the total energy flux outward from the cylinder in the scattered wave divided by the energy flux in the beam of the incident wave which falls on the cylinder. In the limit, of geometrical optics, the scattered wave is made up of a wave reflected from the forward half of the cylinder with energy flux equal to that in the incident beam, and a wave behind the cylinder cancelling the incident wave there to form the shadow. Thus σ → 2 as ka → ∞, k being the wave number of the incident wave and a the radius of the cylinder. The next term in the asymptotic expansion for σ is proportional to . It has been determined already from the exact series expression for the field by White (6), Wu and Rubinow (7) and Kear (3). But Kodis gives an approximate method which also supplies this result and, since the coefficient is in good agreement with the values obtained from the exact solution, concludes that his approximate procedure could also be used for more general obstacles. In the present paper, we propose an alternative approximate method which is related to the one given by Kodis but is very much simpler. Also we go on to obtain the correction terms for general obstacles in detail. Various writers (see, for example, Keller (4) and van de Hulst(8)) have suggested previously that the correction is still proportional to , where a is some length defined by the body shape. However, the determination of a and of the numerical coefficient has been limited to two-dimensional obstacles.

Electromagnetic modelling of 3D periodic structure containing magnetized or polarized ellipsoids

2006 ◽  
Vol 14 (3) ◽  
Author(s):  
M. Koledintseva
Keyword(s):  
Plane Wave ◽  
Incident Wave ◽  
Surrounding Medium ◽  
Boundary Plane ◽  
Angle Of Incidence ◽  
Incident Plane Wave ◽  
Regular Array ◽  
Incident Plane ◽  
Electromagnetic Modelling ◽  
Infinite Array

AbstractCoupling matrix and coupling coefficient concepts are applied to the interaction of an incident plane wave with a regular array of small magnetized or polarized ellipsoids, placed in a homogeneous surrounding medium. In general case, the angle of incidence and polarization of the plane wave upon an array of ellipsoids can be arbitrary. In this model, it is assumed that all the ellipsoids are the same, and the direction of their magnetization is also the same. The direction of magnetization is arbitrary with respect to the direction of the propagation of the incident wave and to the boundary plane between the first medium, where the incident wave comes from, and the array material under study. Any magnetized or polarized ellipsoid is represented as a system of three orthogonal elementary magnetic radiators (EMR) and/or three orthogonal elementary electric radiators (EER). Mutual interactions of individual radiators in the array through the incident plane wave and corresponding scattered electromagnetic fields are taken into account. The electrodynamic characteristics — reflection from the surface of the semi-infinite array (in particular, containing uniaxial hexagonal ferrite resonators), transmission through the array, and absorption are analyzed.

THE RADAR CROSS SECTION OF A SEMI-INFINITE BODY

1960 ◽  
Vol 38 (1) ◽  
pp. 48-56 ◽  
Author(s):  
H. Brysk
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Ad Hoc ◽  
Simultaneous Occurrence ◽  
Body Of Revolution ◽  
Infinite Body ◽  
Incident Plane ◽  
The Cross ◽  
The Difference ◽  
Definition Of

The concept of cross section as applied to a semi-infinite scattering body seems to require some clarification. The need for careful formulation of the problem arises because of the simultaneous occurrence of two characteristic lengths tending to infinity: the range from the radar to the target, and the size of the target. The infinite range assumption in the definition of the cross section allows the incident wave to be approximated as a plane wave in the case of a finite scatterer. For a semi-infinite body, it is customary to retain the plane-wave incidence, and introduce ad hoc arguments to dispose of the awkwardness due to the infinite extent of the scatterer. A return to the basic definition of a cross section, and examination of its motivation, lead here to an unequivocal formulation for the cross section of a semi-infinite body. Its consequences are pursued in the physical optics approximation. In particular, the nose-on backscattering from a body of revolution is exhibited, and results are computed for the paraboloid and the cone (which turn out to agree with the traditional ones). The broadside backscattering from a cylinder is also calculated, and the difference in this case between mono-static backscattering and the return in the backward direction from an incident plane wave is discussed.

scholarly journals Core-Shell Nano-Antenna Configurations for Array Formation with More Stability Having Conventional and Non-Conventional Directivity and Propagation Behavior

Nanomaterials ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 99
Author(s):  
Qaisar Hayat ◽  
Junping Geng ◽  
Xianling Liang ◽  
Ronghong Jin ◽  
Sami Ur Rehman ◽  
...  
Keyword(s):  
Plane Wave ◽  
Propagation Direction ◽  
Core Shell ◽  
Incident Plane Wave ◽  
Polarization Direction ◽  
Shell Nanoparticles ◽  
Incident Plane ◽  
Core Shell Nanoparticles ◽  
Coated Nanoparticle ◽  
2D Array

The enhancement of optical characteristics at optical frequencies deviates with the choice of the arrangement of core-shell nanoparticles and their environment. Likewise, the arrangements of core-shell nanoparticles in the air over a substrate or in liquid solution makes them unstable in the atmosphere. This article suggests designing a configuration of an active spherical coated nanoparticle antenna and its extended array in the presence of a passive dielectric, which is proposed to be extendable to construct larger arrays. The issue of instability in the core-shell nanoantenna array models is solved here by inserting the passive dielectric. In addition to this, the inclusion of a dielectric in the array model reports a different directivity behaviour than the conventional array models. We found at first that the combination model of the active coated nanoparticle and passive sphere at the resonant frequency can excite a stronger field with a rotated polarization direction and a propagation direction different from the incident plane-wave. Furthermore, the extended 2D array also rotates the polarization direction and propagation direction for the vertical incident plane-wave. The radiation beam operates strong multipoles in the 2D array plane at resonant frequency (behaving non-conventionally). Nevertheless, it forms a clear main beam in the incident direction when it deviates from the resonance frequency (behaving conventionally). The proposed array model may have possible applications in nano-amplifiers, nano-sensors and other integrated optics.

Array design

1968 ◽  
Vol 58 (3) ◽  
pp. 977-991
Author(s):  
Richard A. Haubrich
Keyword(s):  
High Resolution ◽  
Data Processing ◽  
Least Square ◽  
Wave Number ◽  
Array Design ◽  
Least Square Fit ◽  
The Difference ◽  
Set Of Points ◽  
Array Output

abstract Arrays of detectors placed at discrete points are often used in problems requiring high resolution in wave number for a limited number of detectors. The resolution performance of an array depends on the positions of detectors as well as the data processing of the array output. The performance can be expressed in terms of the “spectrum window”. Spectrum windows may be designed by a general least-square fit procedure. An alternate approach is to design the array to obtain the largest uniformly spaced coarray, the set of points which includes all the difference spacings of the array. Some designs obtained from the two methods are given and compared.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

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