Possibility of an extremely directional antenna
Your requirements will never be met. 

A dish antenna is the best for providing focus and if you looked at voyager II, it used a 3.7 metre dish at about 3 GHz. This would give a 3dB half-beam-width of about 0.91 degrees.

I'm using the example of Voyager II because they would not ship something to the planets that had not been thought about (o-rings excluded from this statement).

At 1 GHz this half beam angle increases to 2.74 degrees

At 1 GHz and a 1m dish this increases to 10.2 degrees

See this calculator to check. To help you get further ideas about this follow these rules: -


If you double the frequency, the gain of an antenna will quadruple.
If you double the frequency, the beam-width of an antenna will halve.
If you double the antenna diameter (keeping the frequency the same),
the gain of the antenna will quadruple.
If you double the antenna diameter (keeping the frequency the same),
the beam-width of an antenna will halve.