[strainer]

The cross section of the beam can be any shape, the important thing is the signal source is an area not a point. The value of the inverse square (of distance from source) is dominates power density when the signal source is effectively a point - this becomes the situation for a laser or anything at long enough distance, but at distances where it is effectively a beam, the strength of power density does not dissipate by that value. The geometry of the beam concentrates the power density at its focal point, which can be far behind the source or in front of it. For an ideal beam focused to infinity (parallel rays) its power would never dissipate with distance - as all of the power goes in the same direction. We don't need to form an ideal beam to say its doesn't follow the inverse square rule, any focusing of rays breaks the rule (at scales where it is reasonable to treat it as a beam and not just rays emanating from a point)

I hope that helps picture the situation. My original comment that a beam can have a different exponent was incorrect except in some approximate sense. The inverse square value will still apply, but from the beams real or imaginary focal point (if it is a point) But it the case of a transmitter beaming a signal at another, that focal length can be far beyond the reciever, so the 'rule' can be completely confounded.