That’s highly unlikely basically because of the inverse square law. Even tightly focused beams dissipate quite effectively over light-hours, let alone light years. We’d be lucky to catch a single photon from our past selves over any significant distance.

For reference, look up how weak the signal is even just coming back from the moon when people try to hit the retroreflectors with lasers. Or how crazy weak the signals are when they reach Voyager.