The steady state is reached when the modes in the optical fiber have propagated over a certain distance, called the Equilibrium Length. After the Equilibrium Length, the EMD state is reached. After that, the relative power density between the modes remains constant.
In practice, the Equilibrium Length varies from a few meters to more than a kilometer. After the Equilibrium Length, the numerical aperture at the output of the optical fiber is independent of the numerical aperture of the optical source.