Abstract
In this paper, we study the solution of the 3-dimensional reduced wave equation above an infinite plane 2-dimensional surface wave supporting structure. The structure is simulated by a multiple impedance boundary condition that allows for the excitation of two different cylindrical surface wave modes. At first we investigate the problem of a simple source which is then generalized to multi-pole sources. For the cases considered, we are able to give an explicit solution that exhibits the character of the surface wave field. Furthermore, using a virtual structure notion, we are able to identify the power travelling within the impedance structure associated with a given external surface wave mode. Thus, a definition of the total surface wave power is applied in a manner that modal power flow separability is maintained. The far field pattern is observed to vanish in certain directions, in particular along the impedance plane. Furthermore, the far field power is calculated in terms of a non-elementary definite integral which is then estimated at high and low frequencies so that a partial verification of our calculations can be made by observing that power is conserved to these orders.
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