Solution of a matrix Wiener-Hopf equation connected with the plane wave diffraction by an impedance loaded parallel plate waveguide

Abstract

SUMMARYA matrix Wiener-Hopf equation connected with a new canonical di raction problem is solved explicitly. We consider the di raction of a plane electromagnetic wave by an impedance loaded parallel plate waveguide formed by a two-part impedance plane and a parallel perfectly conducting half-plane. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to a matrix Wiener-Hopf equation. The exact solution is obtained in terms of two inÿnite sets of unknown coe cients satisfying two inÿnite systems of linear algebraic equations. These systems are solved numerically and the in uence of the parameters such as the waveguide spacing and the surface impedances of the two-part plane on the di raction phenomenon is shown graphically.

A Hybrid Method for the Solution of Plane Wave Diffraction by an Impedance Loaded Parallel Plate Waveguide

“…This problem is a generalization of a previous work by the authors [1] who considered the same geometry in the case where the half plane is perfectly conducting. In [1] the related boundary value problem is formulated as a matrix WienerHopf equation which is uncoupled by the introduction of infinite sum of poles. The exact solution is then obtained in terms of the coefficients of the poles, where these coefficients are shown to satisfy infinite system of linear algebraic equations.…”

“…The surface impedances of the upper and lower faces of the half-plane are assumed to be Z 3 = η 3 Z 0 and Z 4 = η 4 Z 0 respectively (see Figure 1). This problem is a generalization of the one considered in [1] where the half plane is assumed to be perfectly conducting. The method of formulation adopted in this work involves an appropriate definition of the total field such that in the waveguide region the field component may be expressed in terms of normal modes and the Fourier transform technique can be applied elsewhere.…”

“…The method of formulation adopted in this work involves an appropriate definition of the total field such that in the waveguide region the field component may be expressed in terms of normal modes and the Fourier transform technique can be applied elsewhere. Notice that the problem considered in [1] can also be reduced to the solution of a scalar Modified Wiener-Hopf equation by using this hybrid method of Modal expansion and the Fourier transform technique. …”

“…The important difference of this kind of formulation from the one applied in [1], was the simultaneous use of Mode-Matching technique with the Fourier transform. The Mode-Matching technique allows us to express the field component defined in the waveguide region in terms of normal modes as…”

“…Numerical solution to this system is obtained for different values of the surface impedances and height of the waveguide. In the case where the impedance of the semi-infinite plane vanishes, the results are compared numerically with those obtained in [1] by solving a matrix Wiener-Hopf equation, and it is shown than both results coincide exactly…”