# Formula for transverse decrease in signal strength?

Alice is transmitting an electromagnetic beam to Bob.
Assume it is a well collimated beam, like a laser beam, or a maser beam.
As Bob's distance from Alice increases, his signal strength decreases according to the well known inverse square law.

Eve, the eavesdropper, is beside the beam, not in the beam.
As Eve's transverse distance from the beam increases, the strength of her signal decreases.
What is the formula for Eve's signal strength as a function of her transverse distance?

(see comment below for my speculations and subsidiary questions)

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 Does it decrease exponentially, like the tail of a Gaussian, or in an inverse power law, like the electromagnetic potential? Does the signal strength depend on whether the signal is coherent or not? What if the signal is charged, ie an electron beam in a vacuum? The signal strength might also depend on Eve's detector type? For instance, a detector based on the photoelectric effect will fall off exponentially, but one based on induction would fall off as a power law? – Jim Graber Nov 23 '12 at 13:55