Analytical gain equation for erbium-doped fiber amplifiers including mode field profiles and dopant distribution

An analytical description of the gain of an erbium-doped fiber amplifier is proposed that takes into account the transverse extension of mode fields and dopant distribution. A single closed-form expression is derived that describes the relation between gain, input powers, and fiber length. The free parameters in this equation are given in their analytical form. A numerical evaluation of the equation is performed for a 980 nm pumped amplifier fiber with different doping radii. A comparison with a calculation using the full numerical integration of differential equations shows that the description is correct for conventional fiber geometries.>