The Use of Complex Field Vectors in Diffraction Theory.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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A rigorous solution to the diffraction problem is obtained using two complex field vectors Q-bar mu H-bar i square root of mu epsilon E-bar and P-bar mu H-bar - i mu epsilon E-bar. The field equations which are uncoupled in terms of Q-bar and P-bar can be integrated directly to yield a pair of uncoupled vector integral equations involving the tangential components of Q-bar and P-bar on an arbitrary open surface. When the surface is planar, the vector equations are expressed in a more useable set of six component integral equations. The restrictions in the derivation of these latter equations are that the initial E-bar and H-bar satisfy Maxwells equations on the open surface, and that the resultant field is calculated at least several wavelengths from the initial field. The Rayleigh-Sommerfeld equation of scalar diffraction theory is obtained as a special case of the component set of equations. A discussion of the physical meaning of these component equations lends insight into the diffraction process. The complex field vector approach is seen to be a rigorous, yet simple and straightforward, method of solving the diffraction problem. Author
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