Realation between a class of two-dimensional and three dimensional diffraction problems
- 1 July 1960
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Antennas and Propagation
- Vol. 8 (4) , 407-414
- https://doi.org/10.1109/tap.1960.1144860
Abstract
By means of a certain transformation, a relationship is demonstrated between a class of two-dimensional and three-dimensional scalar or electromagnetic diffraction problems. The basic three-dimensional configuration consists of a perfectly reflecting half plane excited by a ring source centered about the edge and having a variation exp (\pm i\phi/2), where\phi, is the azimuthal variable; in addition, a perfectly reflecting rotationally, symmetric obstacle whose surface is defined byf(\rho, z) = 0(\rho, zare cylindrical coordinates) may be superposed about the edge (zaxis). This problem is shown to be simply related to the two-dimensional problem for the line source excited configurationf(y, z)= 0, whereyandzare Cartesian coordinates. Various special obstacle configurations are treated in detail. For the general case of arbitrary electromagnetic excitation, the above-mentioned transformation is used to construct the solution for the diffraction by a perfectly conducting half plane from the knowledge of appropriate scalar solutions, namely those which obey the same equations and boundary conditions, and have the same excitations, as the Cartesian components of the electromagnetic field.Keywords
This publication has 2 references indexed in Scilit:
- The excitation of a perfectly conducting half-plane by a dipole fieldIEEE Transactions on Antennas and Propagation, 1956
- THE DIFFRACTION OF A DIPOLE FIELD BY A PERFECTLY CONDUCTING HALF-PLANEThe Quarterly Journal of Mechanics and Applied Mathematics, 1953