The equilibrium mode [power] distribution of light travelling in an optical waveguide or fiber, is the distribution of light that is no longer changing with fibre length or with input modal excitation.
The term equilibrium length is sometimes used to describe a stationary mode distribution, which is the length of multi-mode optical fiber necessary to attain a static mode distribution from a specific excitation condition.
Equilibrium mode [power] distributions were reported in early multimode transmission systems at propagation distances as short as a few hundred metres.
However, as fibre manufacturing improved, the minute waveguide dimensional and structural changes that produce mode-mixing have been greatly reduced.
If a well-aligned laser is the optical source, the mode power distribution is highly concentrated in the lowest order modes, and remains essentially unchanged with distance due to the lack of mode-mixing.