In this thesis, the surface wave propagation along a periodically perforated conducting ground plane with dielectric coating has been studied for frequencies low enough for the ground plane to be approximated accurately by two bonded wire arrays. The field components have been obtained by using the z-directed electric and magnetic Hertz potentials which greatly simplify the application of the boundary conditions at the interfaces. The application of the appropriate boundary conditions on both sides of the plane of the wire mesh has resulted in a doubly infinite system of equations which, when truncated, can be solved for the wire currents and the propagation characteristics of the surface wave supported by the perforated ground plane. The plane is then modeled by a tensor impedance matrix relating the tangential components of the electric field to the components of the current density in the plane of the mesh. It has been shown that the surface wave propagation constant and the impedance matrix do not significantly depend on the direction of propagation for electrically small wire spacings. For such cases, it is shown that the components of the electric field can be directly related to the second order derivatives of the components of the current density flowing along the perforated ground plane.
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