Suppose for just a sec that there is more than 1 communication-capable species in the same galaxy at the same time. How could they send messages to each other?
One way would be to use radio transceivers, and SETI is searching the radio spectrum to see if we can hear any signals. However, it would seem more likely that stars themselves would be used as the transmitter beacons. An advanced civilization could construct a Dyson sphere completely around the star, with shutters that could open to allow light to escape through the opening. By controlling the opening and closing of the shutters, you could allow light to alternately be blocked or to escape the opening, sending a clear flashing light signal to the other civilization.
However the civ doesn't need to build a dyson sphere in order to use the star as a transmitter. Any structure with a controllable shutter placed in orbit around the star will block a certain amount of light while it is between the star and the other civ. This could be detected by the receiving civ, using the same technique that is used to hunt for occluding planets. The bigger the structure, the more obvious the signal, but even a small-ish structure could give a detectable signal to the other civ across the other side of the galaxy. A big advantage for the transmitting civ is that large amounts of power are not needed, and signals can be sent to multiple different civs (assuming you know approximately where they are) by adding additional orbiting shutters. The shutters that are modulating the star light would be able to open and close with relatively little energy, powered probably by the solar rays from the star itself.
There is an outside chance that a search of the Kepler Dataset or new optical data could throw up some random comms chatter.
With some clever orbital mechanics, you could re-use the same shutter to communicate with more than one civ at the same time, assuming that you both had sufficient patience.
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