Rami Arieli: "The Laser Adventure" Chapter 6, Helium-Neon Lasers, page 2
Red Wavelength out of He-Ne Laser
Most of the applications of He-Ne Laser use the red wavelength, because it is the strongest line and it is in the visible region of the spectrum.
As shown in figure 6.1, this red light is emitted when the Neon atom goes from the energy level labeled E5 to the energy level labeled E2, a much bigger energy difference than for the other transitions.

A problem with creating this red light is that a Neon atom in state E5 may also emit 3.3913 [mm] radiation. This emission decreases the population of the E5 level, without producing visible radiation.

The solution to this problem is to use a special coating on the laser mirrors which selectively reflect only the red light. This coating causes reflection back into the optical cavity of only the desired (red) wavelength, while all other wavelengths are transmitted out, and not forced to move back and force through the active medium.

In a similar way, other selective reflecting coating can be used on the mirrors to select other transitions. This procedure allows commercial production of He-Ne lasers at other wavelengths in the visible spectrum. For example, orange, yellow and green He-Ne lasers can be produced, but the laser efficiency is much lower than for the red.