How can you make any object invisible to radar at a given frequency?

All you need to do is to place on a closed surface surrounding the object an electric surface current distribution Ke = nxH (Amp/Meter), and magnetic current distribution Km = -nxE (Volt/Meter) , where E and H are the time-varying electric and magnetic fields of the radar on the object surface, and n is the outward normal to the surface, x denotes vector cross product.  The resulting electromagnetic fields are the same as the original electromagnetic fields outside the object and E = 0, H = 0 inside the object. This is guaranteed by Love’s Equivalence Theorem. [1]. Therefore, the scattered fields have been eliminated!

The difficult problem remains: to generate the required electric and magnetic current distributions on the closed surface. The electric current sheet can be achieved by curved conducting wires driven by a current source. The magnetic current sheets are much more difficult to realize but can be approximated as a doublet of two electric surface currents fed by oppositely directed current sources. [2], [3], [4].  (Patent pending, 6/17/2010)

Example of a metal sphere of radius R illuminated by a plane wave
E = e^-jωz/c (0, 1, 0), H = -(1/Zo) e-^jωz/c (1,0,0), Zo=377 ohms,  ω = angular frequency, c = speed of light

This can be converted into spherical coordinates
Ke on the sphere = n x H = e^-jωz/c ((z/R), 0, (x/R)}
Km on the sphere = -n x E = e^-jωz/c ((0, (-z/R)), (y/R))

Where x = Rsin(θ)sin(φ), y = Rsin(θ)cos(φ), z = Rcos(θ)
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These equations simplify for the magnitude of the currents.  Οn the sphere, in the x-z plane, |Ke| are circles, ((1 – (y/R)2)0.5 and in the y-z plane,  |Km| are also circles ((1 – (x/R)2)0.5.
The phase factors are given by  e^-jωz/c

More ideas on how to realize these currents will be given in the next blog.
1.    A. E. H. Love, “The Integration of Equations of Propagation of Electric Waves,” Phil. Trans. Roy. Soc. London, Ser A, 197, 1901, pp. 1 – 45.
2.    S. A. Schelkunoff, “Some Equivalence Theorems of Electromagnetics and Their Application to Radiation Problems,” Bell System Technical Journal, Vol. 15, 1936, pp. 92 – 112
3.    S. Rengarajan, Y. Rahmat-Samii, “The Field Equivalence of the Non-Intuitive Null Fields, “ IEEE Trans. on Antennas and Propagation Magazine, Vol. 42, No. 4, August 2000
4.    S. A. Schelkunoff, “Antennas Theory and Practice,” John Wiley & Sons, NY, 1952,  pp. 44 -45.