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By Proebsting T.A.

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Is a unit vector in the radial direction and 77 = ( p , / ~ , )=' 377 ~ ~ ohms is the impedance of free space. The transverse part of A is AT = l,Ae t 1,A,. 6) @(8, $) 1 = Tale(E x H*) It is customary to call that part of the radiation pattern associated with E, the 8polarizedpattern, or the vertically polarizedpattern, and to call that part of the radiation pattern associated with E# the $-polarized pattern, or the horizontally polarized pattern. 98), it can be seen that these two patterns are given by the functions Often one is interested only in the relative power densities being radiated in different directions (8, $), in which case the factor i[k2q/(4nr)2]can be suppressed.

103g). 103f then lead to from which with O and cD, called the electric and magnetic scalar potential functions, respectively. 10) and the solutions for F and @, are obviously similar. If the electric and magnetic sources are confined to reside in surfaces, then lineal current densities K amperes per meter and K, magnetic amperes per meter replace J and J,. In like manner, the areal charge densities p, coulombs per square meter and p,, magnetic coulombs per square meter replace p and p,. The potential functions are then given by Suppose one desires to find the values that these surface sources should have in order to give a specified electromagnetic field external to S but a null field within S.

A. Stratton and L. J. -Chu, "Diffraction Theory of Electromagnetic Waves," Phys. , 56 (1939), 99-107. Also, see the excellent treatment in S. Silver, Microwave Antenna Theory and Design, MIT Rad. Lab. Series, Vol. , 1939), pp. 80-9. The present development is a reproduction, with permission, of what appears in R. S. , 1966), pp. 272-80 and 534-8, and differs from Silver's treatment principally in the nonuse of fictitious magnetic currents and charges. 7 The Stratton-Chu Solut~on and letting A If A = = G and B F while B == = V x G, one obtains V x F, then When the difference in these results is integrated over the volume V, one obtains If 1, is chosen to be the inward-drawn unit normal vector from any boundary surface Siinto the volume V, use of the divergence theorem gives This result is the vector Green's theorem.

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