  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.
