Answer to the Question 06/02
ISOTROPIC RADIATORThe question was:
Is it possible to build and antenna that will radiate coherent electromagnetic radiation with intensity independent of direction?
(12/02) It was definitely a difficult problem, and it seems that no solutions can be expected. Therefore, we publish the known solution of the problem. This problem was originally considered and solved by H. Matzner, M. Milgrom and S. Shtrikman in their article Magnetoelectric symmetry and electromagnetic radiation which was published in Ferroelectrics, 161, 213-219 (1994).
The solution:
A direct calculation of the vector potential, electric field and radiation intensity produced by the following current shows that it produces direction independent radiation intensity. The current density is:
J(x,y,z)=-D(x)D(y)D(z+1/8)x+D'(x)D(y)cos({pi}/4+2{pi}z)z
for -1/8 < z < 1/8, where all distances are measured in wavelengths, D denotes Dirac delta-function, and D' denotes its derivative. Such current distribution is produced by U-shaped antenna (depicted in the following figure) when h-> 0. For a detailed calculation see the paper mentioned above.
It should be noted that the polarization of the radiation emitted by such an antenna depends on the direction and changes from linear to elliptic to circular (right and left polarized) depending on the direction.
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