For fiber-coupling purposes an effective fiber NA_{e²} defined at the 1/e² level is more convenient than the nominal fiber NA defined by the refractive indices since normally Gaussian beams are defined by their 1/e² diameter, too.

Schäfter+Kirchhoff defines an effective fiber NA which corresponds to the divergence of the power distribution emitted by the fiber taken at the 1/e² level of the Gaussian angle distribution.

This NA value is designated the effective numerical aperture NA_{e²}.
For a typical singlemode fiber the value is NA_{e²} = 0.075.

For singlemode fibers and for polarization-maintaining fibers, the effective NAe2 slightly decrease with increasing wavelength l.

Beam profile of a singlemode fiber: definition of numerical aperture NA, NA

_{e²}, and mode field diameter MFD