High Frequency Diffraction Research Articles

High-Frequency Diffraction of a Dipole Field by a Strongly Elongated Spheroid

High-Frequency Diffraction of a Dipole Field by a Strongly Elongated Spheroid

Transition Zone in High-Frequency Diffraction on Impedance Contour with Jumping Curvature. Kirchhoff’s Method and Boundary Layer Method

Transition Zone in High-Frequency Diffraction on Impedance Contour with Jumping Curvature. Kirchhoff’s Method and Boundary Layer Method

High-frequency diffraction contribution by planar metallic–DNG metamaterial junctions

AbstractThe plane wave diffraction by a planar junction consisting of a thick metallic sheet and a lossy double-negative metamaterial slab is studied by using the Uniform Asymptotic Physical Optics approach. This approach assumes the radiation integral as a starting point and uses the physical optics surface currents as sources to be integrated. The integral is manipulated by taking advantage of useful approximations and evaluations, and re-formulated in order to apply an asymptotic procedure able to generate a closed-form approximate solution in the framework of the Uniform Geometrical Theory of Diffraction. Accordingly, advantages and drawbacks result from the application of the proposed solution. The jumps of the geometrical optics field are compensated. Implementation and handling of the computer code are facilitated by the evaluation of well-known functions and parameters. No differential/integral equations or special functions must be computed.

High-Frequency Diffraction by a Contour with a Jump of Curvature: the Limit Ray

High-frequency diffraction by a contour with a jump of curvature is addressed. The outgoing wavefield on the limit ray is studied in the framework of ray theory.

High-Frequency Diffraction of a Point Source Field by a Strongly Elongated Elliptic Cylinder

The problem of diffraction of a high-frequency point source acoustic field by an infinite elliptic cylinder with a strongly elongated cross-section is studied. At every direction of propagation, the solution is shown to be similar to those of a linear source field diffraction by a cylinder with correspondingly enlarged major semiaxis.

Diffraction of a Gaussian Beam by a Strongly Elongated Spheroid

A high-frequency diffraction problem is considered for a Gaussian beam incident parallel to the axis of a strongly elongated spheroid. The parabolic equation method in spheroidal coordinates is used to construct the leading order term of the field asymptotics in the boundary layer near the surface in the form of an integral containing Whittaker functions. The field amplitudes on the surface of a perfectly hard spheroid are computed. High-frequency diffraction effects are discussed.

On Two Alternative Uniformly Asymptotic Procedures for Analyzing the High-Frequency Diffraction of a Complex Source Beam by a Straight Wedge

When spectral wave integrals, representing the radiation and diffraction of electromagnetic waves, are characterized by a first-order saddle point and poles in the integrand, they can usually be evaluated, in essentially closed form, at high frequencies by the leading terms of any of the two well-known alternative uniformly asymptotic procedures, namely, the Pauli–Clemmow method (PCM) and the Van der Waerden method (VWM), respectively. The PCM has the advantage that its leading terms directly yield a solution in the simple ray format of the uniform geometrical theory of diffraction (UTD). On the other hand, it is commonly noted that it is not the leading term of the PCM but that of the VWM which remains valid for the case of complex waves. Nevertheless, it is shown here that the PCM can surprisingly work even for some special complex wave cases, only if certain conditions are met. Indeed, it is demonstrated here that the PCM meets these conditions for the special case of the diffraction of a complex source beam (CSB) by a wedge. Also, the PCM directly yields a UTD like solution for this case. The latter result is significant as it provides a strong justification for obtaining a simple UTD type solution for the more general problem of the diffraction of a CSB incident from an arbitrary direction on a wedge with arbitrary curvature, directly via analytic continuation of the corresponding UTD result available for a curved wedge illuminated by a point source in real space. It is also shown that the VWM solution can be trivially cast in the UTD format, by expressing it as a sum of the PCM solution plus a UTD slopelike correction term; a similar result was obtained previously using a higher order term from a generalization of the PCM procedure given elsewhere.

A hybrid method combining the surface integral equation method and ray tracing for the numerical simulation of high frequency diffraction involved in ultrasonic NDT

Ultrasonic Non-Destructive Testing (US NDT) has become widely used in various fields of applications to probe media. Exploiting the surface measurements of the ultrasonic incident waves echoes after their propagation through the medium, it allows to detect potential defects (cracks and inhomogeneities) and characterize the medium. The understanding and interpretation of those experimental measurements is performed with the help of numerical modeling and simulations. However, classical numerical methods can become computationally very expensive for the simulation of wave propagation in the high frequency regime. On the other hand, asymptotic techniques are better suited to model high frequency scattering over large distances but nevertheless do not allow accurate simulation of complex diffraction phenomena. Thus, neither numerical nor asymptotic methods can individually solve high frequency diffraction problems in large media, as those involved in UNDT controls, both quickly and accurately, but their advantages and limitations are complementary. Here we propose a hybrid strategy coupling the surface integral equation method and the ray tracing method to simulate high frequency diffraction under speed and accuracy constraints. This strategy is general and applicable to simulate diffraction phenomena in acoustic or elastodynamic media. We provide its implementation and investigate its performances for the 2D acoustic diffraction problem. The main features of this hybrid method are described and results of 2D computational experiments discussed.

High-frequency diffraction by a narrow hyperboloid of revolution

High-frequency diffraction of a plane acoustic wave incident at a small angle to the axis of a narrow hyperboloid of revolution is considered. By the parabolic equation method in spheroidal coordinates, the leading term of field asymptotics in the near-surface boundary layer is constructed in the form of an integral involving Whittaker functions. Difficulties associated with its calculation are considered. Results obtained for the field at the surface of a perfectly rigid hyperboloid are presented. They reproduce the predicted high-frequency diffraction effects.

High-frequency wave diffraction by an impedance segment at oblique incidence

The plane problem of high-frequency acoustic wave diffraction by a segment with impedance boundary conditions is considered. The angle of incidence of waves is assumed to be small (oblique). The paper generalizes the method previously developed by the authors for an ideal segment (with Dirichlet or Neumann boundary conditions). An expression for the directional pattern of the scattered field is derived. The optical theorem is proved for the case of the parabolic equation. The surface wave amplitude is calculated, and the results are numerically verified by the integral equation method.

Line source diffraction by perfectly conducting successive steps

A rigorous investigation for the high frequency diffraction of the cylindrical waves by the perfectly conducting successive step discontinuities is considered by using the Fourier transform technique in conjunction with the mode-matching method. The corresponding boundary value problem is formulated into a modified scalar Wiener–Hopf equation of the third kind whose approximate solution, which is obtained by iterations of a pair of Fredholm integral equations of the second kind, contains five sets of infinite number of unknown constants satisfying five infinite systems of linear algebraic equations and two types of branch-cut integrals which can be evaluated approximately and numerically due to their types. The effects of the characteristic parameters of the problem such as width and height of the steps on the diffraction phenomenon are shown graphically.

High-frequency plane wave diffraction by an ideal strip at oblique incidence: Parabolic equation approach

The problem of diffraction of a high-frequency plane wave by a strip with ideal boundary conditions is considered for the case of oblique incidence. The study is based on the parabolic approximation, which is used to construct an expression for the directional pattern in terms of single quadratures. A similar result is obtained using the embedding formula. It is shown that the derived expression approximates the classical Michaeli result. A proof of the optical theorem for the parabolic problem is presented.

High-Frequency Diffraction by a Strip for Almost Grazing Incidence

We construct the far-field asymptotics in the problem of diffraction by a perfectly conducting strip at almost grazing incidence. The problem is considered as the limiting case of diffraction by an elliptic cylinder. The asymptotics of the total scattering cross-section describes the transition from one classical asymptotic expansion valid for the case of the grazing incidence to another one valid for the nongrazing incidence to the strip.

High-Frequency Diffraction by an Elliptic Cylinder With a Strongly Elongated Cross-Section

High-Frequency Diffraction by an Elliptic Cylinder With a Strongly Elongated Cross-Section

High-frequency diffraction by an elliptic cylinder: the far field

In this work, we derive the asymptotics of the far field in the directions of forward and backward sectors for near-axial scattering, on the basis of the asymptotic formulas for the induced currents on the surface of a perfectly conducting elliptic cylinder with strongly elongated cross-section.

Uniform Asymptotics for High-Frequency Diffraction by an Elliptic Cylinder

We construct the far field asymptotics in the problem of diffraction by a perfectly conducting cylinder with the cross-section approximated by a strongly elongated ellipse. The asymptotic representation appears uniform with respect to the rate of elongation. It allows for the variation of the RCS from the limiting case of the strip to the case of the circular cylinder to be traced.

High-frequency diffraction by an elliptic cylinder: the near field

The problem of diffraction by a perfectly conducting cylinder with the cross section being an ellipse with high aspect ratio is examined. The high-frequency asymptotics of the currents induced by a plane electromagnetic wave incident along or at a small angle to the major axis of the ellipse is constructed. The field in the boundary layer near the surface is represented as a sum of the forward and the backward waves, both considered in parabolic equation approximation. Comparison with numerical test shows that the leading order term of the asymptotics provides sufficiently accurate approximation for the induced currents on cylinders of one wavelength size and larger.

Erratum to: High-frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder

In this note we correct some typographical errors in the above paper.

High-frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder at grazing incidence

We shall derive new results for the electromagnetic scattered far wave field produced when a high frequency plane E-polarized wave is at grazing incident on an imperfectly conducting rectangular cylinder. The solution to the problem is obtained by using the geometrical theory of diffraction, multiple diffraction methods, the canonical solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with a novel analytic approach.

Strong Elongation Versus a Large Transverse Curvature in the Problems of High-Frequency Diffraction

The effects of the high transverse curvature and of the strong elongation on the high-frequency diffraction are studied on the examples of the perfectly conducting elliptic cylinders and spheroids with high aspect ratio.