Attenuation

A beam of radiant energy going through the air will have some of that energy absorbed, or removed from the beam by making the radiation no longer exist, and some of it scattered, or removed from the beam by making the radiation go in a different direction.

Numerically, the attenuation is represented by an attenuation length $R_{0}$, which is the distance at which the intensity of the light (or beam power, or pulse energy) has been reduced to approximately 37% of its original value. If you start off with an intensity $I_{0}$, or a power $P_{0}$, or an energy $E_{0}$, then the intensity $I$, power $P$, and energy $E$ after a given range $R$ will be

${\begin{matrix}I&=&I_{0}\,\exp[-R/R_{0}]\\P&=&P_{0}\,\exp[-R/R_{0}]\\E&=&E_{0}\,\exp[-R/R_{0}].\end{matrix}}$

This is called the Beer-Lambert law.

If you have more than one physical phenomenon contributing to attenuation (for example, absorption and scattering, or absorption off of oxygen and absorption off of nitrogen), the inverses of the attenuation lengths of each phenomena add together. In particular, if you have scattering with a characteristic scattering length $R_{s}$ and absorption with a characteristic absorption length $R_{a}$, then

${\frac {1}{R_{0}}}={\frac {1}{R_{a}}}+{\frac {1}{R_{s}}}.$

Absorption

The first thing to worry about with the air is that it can absorb light. It can absorb some colors of light better than others. Clear air with an Earth-like composition is very transparent to visible light, as well as to nearby invisible colors like near and short-wave infrared, or ultraviolet A, B, and C. But some wavelengths of mid-wave, long-wave, and far infrared are absorbed, and some get through depending on the exact wavelength. Also, any light with a shorter wavelength than ultraviolet-C gets rapidly absorbed by air, hence the name “vacuum ultraviolet” for frequencies higher than UV-C, as they can only propagate in vacuum. If your laser works at a frequency that is absorbed by the air, it will not be very useful in that environment.

The absorption length varies a lot depending on the wavelength of the beam, the weather, and the atmospheric conditions.

Scatter

Laser beam made visible by atmospheric scattering.

The next thing to worry about is scatter. Rather than simply making the light in your beam go away, scatter is what makes the light go in a different direction. Particulates or aerosols in the air are good at scattering light. This is why we can’t see through fog or clouds. But even perfectly clean air will scatter light to some extent. The electric field in the light will make the electrons in air molecules slosh back and forth at the light’s frequency. And these electrons then act like antennas to radiate light away in different directions (while simultaneously taking that energy away from the beam). This is called Rayleigh scattering, and it is more effective for higher frequency light than lower frequency light. This is why, for example, the sky looks blue - more high frequency blue light from the sun is being scattered into our eyes than lower frequency light of other colors.

Note that scatter makes it so you can see the laser beam. Even a 1 watt blue laser shows up clearly in clean air from its Rayleigh scattering. A very powerful visible light laser like you would use for a weapon will give an obvious trace through the air.