In the lunar laser communication demonstration the transmitted laser power at the moon was ~0.5 watts, when it reached the surface of the earth that half watt of power was spread out over a spot kilometers in radius... so power density was measured in nano-watts per square meter...

If the laser was in the visible part of the spectrum, you MIGHT be able to see that with your eye, or certainly with a small telescope... but only if you were within the few kilometer diameter spot- the laser would have to be targeting you... the laser wavelength was in the short wave infrared, however, which is invisible to the human eye.

This is what makes lasercom so secure... unless you are in the small spot, you can't detect it... it doesn't matter how good you are at cracking encryption, unless you are actually in the beam, you have no hope of receiving it... this physical security makes it attractive for some applications.

The signal from the moon was pulsed rapidly, with the information content encoded in the timing of the pulses, and a data rate of 622Mbps was achieved using a signal format known as pulse position modulation.

A set of telescopes on the ground received nano-joules of signal per second, and those nanojoules were divided among 10's of millions of pulses...

The receiver telescope collected the signal light and coupled it into optical fiber which carried these faint pulses to photon counting detectors... super-conducting nano-wire detectors that are kept at sub 1 kelvin temperatures. They are highly sensitive and able to detect a single photon.

The detectors detect the weak signal pulses and turn them into electrical pulses, and the modem processes the signal to get the data encoded in the timing of the pulses.

More later... its late and I have to get some sleep.