# The Backside Beam

Summary: Thinsats broadcast as much interference power from the backside as they emit as signal beam from the frontside. Fortunately, curvature plus array focus smears out the power and attenuates it by 100 dB compared to the main signal lobe.

Thinsats are a curved aluminum surface cut by slot antennas. Normally, a slot antenna has backside mirror or absorber least half a wavelength from the backside to prevent beam formation in that direction. Thinsats can't duplicate that, they are 30 to 50 μm thick and half a 60GHz wavelength is 2400 μm. The backside slots will be open, and they will broadcast as much power as the frontside, in a beam that is a mirror image of the frontside beam - if the thinsat is flat. This wastes power, which can be tolerated, but could create interference, which cannot be tolerated.

There are two mitigations. First, single thinsats do not produce much power, but arrays of thousands do. That does not change how much power is blown out the backside, but the array will not constructively add power in the backside emission the way it does for the front side.

Secondly, because of thinsat curvature, the phasing of the slots to produce a plane wave and narrow beam on the front side will produce a "doubly curved" and widely spread beam on the backside, again reducing interference. The diffraction spreading angle for the primary beam is \phi_\lambda = 1.24 \lambda / A where \lambda is the wavelength and A is the diameter of the emitter. If the thinsat is curved with a "bowl depth" of d across diameter A , then the curvature of the thinsat bowl is \phi_c = 8 d / A , and the curvature of the backside beam is double that, \phi_c = 16 d / A . The solid angle of the front side spread is \sigma_\lambda = ( \pi / 4 ) ( \phi_\lambda )^2 = 1.21 ( \lambda / A )^2 . The solid angle of the backside (for d >> \lambda ) is \sigma_c = ( \pi / 4 ) (16 d / A )^2 = 64 \pi ( d / A )^2 The power is smeared out over those solid angles, so the ratio of frontside to backside power density is 160 ( d / \lambda )^2 . The front side power is further concentrated into the main lobe by the coherent constructive interference of N thinsats. If \lambda is 5 mm, d is 10 mm, and N is 7842, then the main lobe to average backside power density ratio is 160 N ( d / \lambda )^2 = 5e6, 67dB .

The receive angle of an array working coherently will be approximately (1.24 \lambda / A ) / \sqrt { N } . If A = 150 mm and \lambda = 5 mm and N = 7942 , then the receive angle is 450 μradians, while the total arc of thinsats visible is about 2 radians, a selectivity of 36 dB. Total selectivity will be around 100dB, meaning that about 30 billion other arrays around the orbital arc may be spewing interference and any given pair of arrays can still talk to each other. That is far more arrays than will fit into one orbit, even into a toroidal orbit arrangement a thousand kilometers north to south, and the potential night sky pollution after meteoritic bombardment and random tumbling would be intolerable. We can assume that the backside beam interference will be quite tolerable under realistic conditions.