HIGH FREQUENCY APPROXIMATION FOR THE MODAL ACOUSTIC IMPEDANCE COEFFICIENTS OF A CIRCULAR PLATE LOCATED AT THE BOUNDARY OF THE THREE-WALL CORNER REGION

2013 ◽  
Vol 21 (04) ◽  
pp. 1350016 ◽  
Author(s):  
KRZYSZTOF SZEMELA
Keyword(s):  
Circular Plate ◽  
Computational Efficiency ◽  
Acoustic Impedance ◽  
High Frequency ◽  
Approximation Error ◽  
Asymptotic Formulas ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Corner Region ◽  
Integral Formulas

The high frequency asymptotic formulas for the acoustic impedance modal coefficients of a clamped circular plate located at the boundary of the three-wall corner region have been obtained. The method of contour integral analysis, the series for the Bessel and Neumann functions and the stationary phase method have been used. Some sample modal coefficients of the acoustic resistance and reactance together with the absolute approximation error have been illustrated as the functions of a parameter proportional to the vibration frequency. The computational efficiency of the presented asymptotic formulas has been compared with the computational efficiency of the integral formulas. The cases, in which the asymptotic formulas allow to reduce the calculation time in comparison with the integral formulas, have been determined. The presented formulas can be used to decrease the computation time of the acoustics power radiated by a clamped circular plate located at the boundary of the three-wall corner region. Moreover, the sound pressure calculations can be performed much faster by using these formulas when the acoustic attenuation is included.

scholarly journals Coherence Properties and Intensity Distribution of a Partially Coherent Lorentz–Gauss Beam Emerging from the Axicon

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Abdu A. Alkelly ◽  
Labiba F. Hassan
Keyword(s):  
Intensity Distribution ◽  
Focal Length ◽  
Beam Width ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Intensity Pattern ◽  
Gauss Beam ◽  
Partially Coherent ◽  
Integral Formulas ◽  
Diffractive Axicon

The propagation of a partially Lorentz–Gauss beam in a uniform-intensity diffractive axicon is studied according to the Huygens–Fresnel principle, the Hermite–Gaussian expansion of a Lorentz function, and using the stationary phase method. We have derived the intensity equation of a partially coherent Lorentz-Gauss beams propagating through uniform-intensity diffractive axicon, and we proved mathematically that it is the superposition of Bessel beams of various orders after emerging from axicon, using Hermite’s function series and the Bessel function integral formulas. The results show that the intensity distribution of the diffracted beam is the intensity pattern evolved from a Lorentz–Gauss shaped spot into a Gaussian-shaped spot at any position on the focal length of the axicon, and the intensity distribution of a partially Lorentz–Gauss beam generated by an axicon becomes uniform by increasing the beam width and more uniform and constant with the larger coherence width.

scholarly journals The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1339
Author(s):  
Sotiris Bourgiotis ◽  
Panayiotis Frangos ◽  
Seil Sautbekov ◽  
Mustakhim Pshikov
Keyword(s):  
Asymptotic Solution ◽  
High Frequency ◽  
Spectral Domain ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Radiation Problem ◽  
Sommerfeld Integrals ◽  
Special Cases ◽  
Em Field ◽  
The Given

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. Simulations for various frequencies, distances, altitudes, and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases leading to analytical field expressions close as well as far from the interface are examined.

scholarly journals The Radiation Problem from a Vertical Hertzian Dipole Antenna above Flat and Lossy Ground: Novel Formulation in the Spectral Domain with Closed-Form Analytical Solution in the High Frequency Regime

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
K. Ioannidi ◽  
Ch. Christakis ◽  
S. Sautbekov ◽  
P. Frangos ◽  
S. K. Atanov
Keyword(s):  
Closed Form ◽  
High Frequency ◽  
Numerical Results ◽  
Spectral Domain ◽  
Image Point ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Radiation Problem ◽  
Frequency Regime ◽  
Em Field

We consider the problem of radiation from a vertical short (Hertzian) dipole above flat lossy ground, which represents the well-known “Sommerfeld radiation problem” in the literature. The problem is formulated in a novel spectral domain approach, and by inverse three-dimensional Fourier transformation the expressions for the received electric and magnetic (EM) field in the physical space are derived as one-dimensional integrals over the radial component of wavevector, in cylindrical coordinates. This formulation appears to have inherent advantages over the classical formulation by Sommerfeld, performed in the spatial domain, since it avoids the use of the so-called Hertz potential and its subsequent differentiation for the calculation of the received EM field. Subsequent use of the stationary phase method in the high frequency regime yields closed-form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so-called “space wave” in the literature represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results are presented, in comparison with corresponding numerical results based on Norton’s solution of the problem.

scholarly journals Dispersive Estimates for Full Dispersion KP Equations

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Didier Pilod ◽  
Jean-Claude Saut ◽  
Sigmund Selberg ◽  
Achenef Tesfahun
Keyword(s):  
Stationary Phase ◽  
Initial Value Problem ◽  
Bessel Functions ◽  
Linear Part ◽  
Independent Interest ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Initial Value ◽  
Kp Equations ◽  
Well Posed

AbstractWe prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev–Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev–Petviashvili equations. The proof of these estimates combines the stationary phase method with sharp asymptotics on asymmetric Bessel functions, which may be of independent interest. As a consequence, we prove that the initial value problem associated to the Full Dispersion Kadomtsev–Petviashvili is locally well-posed in $$H^s(\mathbb R^2)$$ H s ( R 2 ) , for $$s>\frac{7}{4}$$ s > 7 4 , in the capillary-gravity setting.

Splitting in lateral shift induced by strong coupling in Kretschmann configuration involving molecular J-aggregates

2019 ◽  
Vol 33 (30) ◽  
pp. 1950370
Author(s):  
Kunwei Pang ◽  
Haihong Li ◽  
Gang Song ◽  
Pengfei Zhang
Keyword(s):  
Strong Coupling ◽  
Metal Film ◽  
Previous Experiment ◽  
Lateral Shift ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Incident Wavelength ◽  
Rabi Splitting ◽  
Kretschmann Configuration ◽  
J Aggregates

Molecular J-aggregates are widely used as emitters to achieve the quantum effects, such as the strong coupling phenomenon. We investigate the lateral shift splitting/Goos–Hänchen (GH) shift splitting induced by strong coupling in Kretschmann configuration involving molecular J-aggregates by using classical methods. The optical response of molecular J-aggregates is modeled by a single Lorentzian oscillator, and Fresnel equations and the stationary phase method are employed to solve our proposed structure. Our results show that the lateral shift versus the incident wavelength shows Rabi splitting-like line shape and the reflection spectrum exhibits the strong coupling phenomenon. Based on the results of the previous experiment work, we well explain the relation between Rabi splitting and the thickness of the metal film and provide a new method to choose the parameters of the structure for experiment.

scholarly journals Focusing properties of an axicon pair

1993 ◽  
Vol 71 (1-2) ◽  
pp. 70-78 ◽  
Author(s):  
Marc Couture ◽  
Michel Piché
Keyword(s):  
Stationary Phase ◽  
Numerical Method ◽  
Gaussian Beam ◽  
Fresnel Diffraction ◽  
Optical Systems ◽  
Phase Method ◽  
Stationary Phase Method ◽  
Diffraction Integral ◽  
Peak Intensity ◽  
Focusing Properties

The focusing properties of a so-called reflaxicon (a combination of a diverging and a converging axicon) are studied both theoretically and experimentally. Calculations of intensity distributions produced by this system are made by evaluating the Kirchhoff–Fresnel diffraction integral, first by means of an approximate technique, the stationary phase method, then by a more exact numerical method. The calculations are presented for various planes along the axis of the axicons. The effects of the presence of the supporting mount of the axicons and of some important misalignments of the system on the distributions is also investigated. Experimental results of actual intensity distributions produced by focusing a near-fundamental Gaussian beam by such a system are also presented and are seen to be in fair agreement with numerical calculations. Such calculations would be valuable in many applications for predicting important characteristics (e.g., peak intensity, length of the focal line, degree of asymmetry) of the intensity distributions formed by optical systems containing an axicon pair as the focusing component.

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