Semi-infinite Parallel-plate Waveguide Research Articles

Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: The Case of H-Polarization

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail.

Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: Rigorous Wiener-Hopf Analysis

Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: Rigorous Wiener-Hopf Analysis

DIFFRACTION BY A TERMINATED SEMI-INFINITE PARALLEL PLATE WAVEGUIDE WITH TWO-LAYER MATERIAL LOADING AND IMPEDANCE BOUNDARIES

The plane wave diffraction by a terminated semi infinite parallel-plate waveguide with two-layer material loading and impedance boundaries is rigorously analyzed for E polarization using the Wiener-Hopf technique. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations, which are solved via the factorization and decomposition procedure. The scattered field is evaluated by taking the inverse Fourier transform and applying the saddle point method. The numerical examples of the radar cross section (RCS) are represented for various physical parameters and backscattering characteristics, of considered geometry for open ended cavity and discussed in detail.

Diffraction by a Terminated, Semi-Infinite Parallel-Plate Waveguide with Three-Layer Material Loading: The Case of H Polarization

Diffraction by a Terminated, Semi-Infinite Parallel-Plate Waveguide with Three-Layer Material Loading: The Case of H Polarization

Article

The diffraction of acoustic plane waves by a semi-infinite parallel platewaveguide satisfying Dirichlet (soft) and Neumann (hard) boundary conditionson its exterior and interior faces, respectively,is investigated rigorously by using the Fouriertransform technique in conjunction with the mode-matching method.This mixed method offormulation gives rise to ascalar Wiener-Hopf equation of the second kind, the solutionof which contains infinitely many constants satisfying an infinite system of linearalgebraic equations.A numerical solution of this system is obtained forvarious values of the thickness of the parallel plate waveguideand the incidence angle, through which the effect of these parameters on the diffraction phenomenon is studied.PACS No.: 43.20

Diffraction by a terminated semi-infinite parallel-plate waveguide with three-layer material loading

The plane wave diffraction by a terminated semi-infinite parallel-plate waveguide with three-layer material loading is rigorously analyzed for E polarization using the Wiener-Hopf technique. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations, which are solved via the factorization and decomposition procedure. The scattered field is evaluated by taking the inverse Fourier transform and applying the saddle point method. Representative numerical examples of the radar cross section (RCS) are given for various physical parameters and the backscattering characteristics are discussed in detail. Some comparisons with a high-frequency technique are also given to validate the present method.

Rays versus modes: pictorial display of energy flow in an open-ended waveguide

The problem of a plane wave impinging on a semi-infinite parallel-plate waveguide is investigated. It is demonstrated that, for waveguide separation large compared to the wavelength, the fields inside the waveguide obey a simple ray optics description. The beam behavior persists for more than 1000 \lambda into a 50 \lambda waveguide. For a small 3 \lambda waveguide, the beam picture begins to blur approximately 5 \lambda into the guide.

Internal reflections at the open end of a semi-infinite waveguide

The reflection coefficients of those waveguide modes, with propagation constants near cutoff, which are excited at the open end of a semi-infinite parallel-plate waveguide for frequencies from the microwave to the optical region are discussed in this paper. The reflection coefficients are obtained from a recently developed form of the factorization formula for the Wiener-Hopf kernel associated with this problem. This particular formula is suitable for numerical processing over the complete frequency spectrum. Results of representative calculations are presented graphically as functions of the ratio of waveguide size to wavelength.

Numerical results for diffraction by a parallel-plate waveguide

In designing waveguide phased arrays, it is often found useful to have the knowledge of the diffraction pattern and excitation coefficients of a semi-infinite parallel-plate waveguide illuminated by a plane wave. To the best of these authors' knowledge, numerical results for the above quantities have not appeared elsewhere in the literature. It is the purpose of this note to present some calculated results for the above quantities, with the guide dimension and the incident angle of the plane wave as parameters.

Evanescent-mode effects in the double-wedge problem

The diffraction of the principal mode at the open end of a semi-infinite parallel-plate waveguide terminated by an infinite plane flange (double-wedge) is studied in the interval 0.1 ≤ka ≤ 1.7, wherek is the wave number and 2a is the guide width. The evanescent-mode correction to the reflection amplitude and the amplitudes of the evanescent modes are computed by three different approximation methods. The agreement among these methods in the considered interval is good. The evanescent-mode correction to the reflection coefficient is small, but the correction to the phase is quite large, attaining values of the order of 10% forka ∼ 1.7. The domain of applicability of the various methods is discussed.

Solution of a diffraction problem - Solution of a diffraction problem. I The wide double wedge

The problem of radiation from a semi-infinite parallel-plate waveguide, terminated by an infinite plane flange (‘double wedge’) is investigated in the k -representation. The problem is reduced to an infinite system ( S ) of linear equations. Part I deals with the case of a ‘wide double wedge’ (the width of the waveguide much greater than the wavelength). This may be considered as a perturbation of the problem of diffraction by a single rectangular wedge, the rigorous solution of which is known (Reiche 1912). In the k -representation, this solution satisfies an integral equation, which is a limiting form of system ( S ). This leads to an approximate solution of the wide double-wedge problem, which appears to be a very good approximation, except in the neighbourhood of critical frequencies of the waveguide. The diffraction patterns and the reflexion coefficient are evaluated in this approximation. The accuracy and limits of applicability of classical diffraction theory are discussed. In the neighbourhood of critical frequencies, strong reflexion appears. This is a new limiting case of the problem, which is connected with the theory of quasi-stationary currents. Neumann’s iteration method is applied to system ( S ), in order to investigate the possibility that Kirchhoff’s approximation is the first step of an accurate solution by successive approximations. The convergence of Neumann’s series is discussed.