Why does the beam of light fade with the distance from source?

Question

I was experimenting with lasers on planets in Universe sandbox 2 and this made me think wether it is really possible to blow planets with lasers (obviously not). But I have seen that the intensity of laser decreases with the distance. The reasons for this could be due to photons deflected by the particles of dust (and that's the reason why we can see the beam of light in smoke) but this is not a very good and heavy reason.
So my question is why does the beam of light fade away as it travels. And if I shine a laser from space on the moon will it really reach the moon.
Thank you in advance for your efforts.

Answer 1

Even in vacuum a laser beam's intensity will get weaker and weaker the more distance it travels. This is due to diffraction, meaning the wave will diverge and "take more space", thus the energy flux per unit area (intensity) will decrease. The total amount of energy is conserved, but the area it is distributed on gets larger and larger. You can see this yourself with a toy laser - the spot size gets bigger when you shine it on a more distant object, so the intensity at each point is weaker.

The angle of divergence of a TEM$00$ mode of a laser, the mode which diverges the slowest, is determined by the minimal spot size and the wavelength:

$$\theta=\frac{\lambda}{\pi w_0}$$ (where $w_0$ is the beam's waist radius)

Meaning if you want a beam to diverge really slowly and get to the moon with the smallest size (so the intensity will be larger), you should increase the beam diameter at the waist (the place where the beam is the smallest).