Numerical aperture (NA) is a measure of the ability of an optical fiber to collect or confine the incident light ray inside it. It is defined as the sine of half of the angle of the fibers light acceptance cone. In other words, it characterizes the range of angles over which the system can accept or emit light. The NA of a fiber is defined as the sine of the largest angle an incident ray can have for total internal reflectance in the core. The numerical aperture of an optical system is defined as the product of the refractive index of the beam from which the light input is received and the sine of the maximum ray angle against the axis, for which light can be transmitted through the system based on purely geometric considerations.

The numerical aperture of an optical fiber is related to its acceptance angle, which is the maximum angle through which light enters the fiber. The higher the numerical aperture of an optical fiber, the more efficiently it can collect light and transmit it through the fiber. However, the relation between the numerical aperture and the beam divergence angle of an output beam emerging from a fiber end is generally not trivial.

In summary, the numerical aperture of an optical fiber is a measure of its light-collecting ability and is related to the maximum angle of an incident beam required for efficient launching.