> ... This search would have revealed optical laser light from the directions of Alpha Cen B if the laser had a power of at least 1.4–5.4 MW (depending on wavelength) and was positioned within the 1 arcsec field of view (projecting to 1.3 au), for a benchmark 10-m laser launcher
For comparison, with our measly human technology...
> The Vulcan 20-20 laser is so named because it will generate a main laser beam with an energy output of 20 Petawatts (PW) alongside eight high energy beams with an output of up to 20 Kilojoules (KJ). This is a 20-fold increase in power which is expected to make it the most powerful laser in the world.
> The entire message consisted of 1,679 binary digits, approximately 210 bytes, transmitted at a frequency of 2,380 MHz and modulated by shifting the frequency by 10 Hz, with a power of 450 kW.
> The broadcast was particularly powerful because it used Arecibo's megawatt transmitter attached to its 305 meter antenna. The latter concentrates the transmitter energy by beaming it into a very small patch of sky. The emission was equivalent to a 20 trillion watt omnidirectional broadcast, and would be detectable by a SETI experiment just about anywhere in the galaxy, assuming a receiving antenna similar in size to Arecibo's.
A perfectly parallel source wouldn't fall off with inverse square, but all real sources are not — and cannot be — perfectly parallel.
What you get from lasers is very high gain in the direction it is pointed in, but it's still subject to the inverse square law.
It's capable of being enough gain to be interesting, to be seen from a great distance.
If you engineer it so the gain is enough to outshine the rest of the parent galaxy in the direction it is pointed, then that's effectively good enough because the galaxy is also following inverse-square and you'll continue to outshine the parent galaxy even as you and it both get weaker, but it's still falling off inverse-square.
The energy density drops off as inverse square law, but the photons go forever. Radio is just photons (light) so it goes forever until it interacts with something it hits. The expanding universe will stretch it's wavelength slightly however.
Sure, but the amount of photons as a percentage of the background radiation drops as a function of the distance. It's not all that far away in cosmic distances when any signal from Earth is millions of times less powerful than the noise level.
A single photon is not a viable communication signal, certainly not at interstellar distances. In practice you need to send out some sort of modulated beam. Even very narrow beams have nonzero dispersion, so the further you get the lower the signal energy will be at an antenna of a given size. So to get more energy you'd need a bigger antenna, but that in turn means receiving more of the background noise as well. In practice there is a minimal signal strength level at which it is still practical to receive the signal.
Long story short: A photon will go on forever (unless it hits something), but a radio signal rapidly spreads out so much that no realistic receiver will be able to recover it from out of the cosmic background noise.
Regular EM Radio waves are not photons. Photons have special configuration which prevents leaks into surrounding space, while regular radio waves are just waves.