As you might have guessed, I have thought about this topic
sending info via laser to random stars and hoping for it to be detected is impractical... however sending a beacon to invite others to 'listen' to your star more carefully is not. We look at the spectrum of other stars, and it would be possible with current tech to skew such spectrum measurments in a way that might attract interest.
All you have to do is beam a frequency that is unnatural for a star to other stars, and hope that other astronomers will be looking at your star and will notice that your star shows an anomaly...Marking your star for further study...
