Filling factor

The efficiency of absorption of pumping energy in the fiber is an important parameter of a double-clad fiber laser. In many cases this efficiency can be approximated with^[4]

${\displaystyle 1-\exp \left(-F{\frac {\pi r^{2}}{S}}\alpha L\right),}$

where

${\displaystyle ~S~}$ is the cross-sectional area of the cladding

${\displaystyle ~r~}$ is the radius of the core (which is taken to be circular)

${\displaystyle ~\alpha ~}$ is the absorption coefficient of pump light in the core

${\displaystyle ~L~}$ is the length of the double-clad fiber, and

${\displaystyle ~F~}$ is a dimensionless adjusting parameter, which is sometimes called the "filling factor"; ${\displaystyle ~0<F<1~}$.

The filling factor may depend on the initial distribution of the pump light, the shape of the cladding, and the position of the core within it.