Can Collimated Extraterrestrial Signals be Intercepted
The Optical Search for Extraterrestrial Intelligence (OSETI) attempts to detect collimated, narrowband pulses of electromagnetic radiation. These pulses may either consist of signals intentionally directed at the Earth, or signals between two star systems with a vector that unintentionally intersects the Solar System, allowing Earth to intercept the communication. But should we expect to be able to intercept these unintentional signals? And what constraints can we place upon the frequency of intelligent civilisations if we do? 
We carry out Monte Carlo Realisation simulations of interstellar communications between civilisations in the Galactic Habitable Zone (GHZ) using collimated beams. We measure the frequency with which beams between two stars are intercepted by a third. The interception rate increases linearly with the fraction of communicating civilisations, and as the cube of the beam opening angle, which is somewhat stronger than theoretical expectations, which we argue is due to the geometry of the GHZ. We find that for an annular GHZ containing 10,000 civilisations, intersections are unlikely unless the beams are relatively uncollimated. 
These results indicate that optical SETI is more likely to find signals deliberately directed at the Earth than accidentally intercepting collimated communications. Equally, civilisations wishing to establish a network of communicating species may use weakly collimated beams to build up the network through interception, if they are willing to pay a cost penalty that is lower than that meted by fully isotropic beacons. Future SETI searches should consider the possibility that communicating civilisations will attempt to strike a balance between optimising costs and encouraging contact between civilisations, and look for weakly collimated pulses as well as narrow-beam pulses directed deliberately at the Earth.