What is the reason behind most of the EDFAs (Erbium Doped Fiber Amplifier) using only 980nm and 1480nm as their pumping wavelengths and not any other wavelengths?

The pump wavelength used is either 980nm or 1480 nm due to the availability of these laser sources.  In the course of the explanation let see the energy level diagrams for the (Erbium) Er³⁺ ion, the absorption band of Er+, and the pump efficiency.

(a) Energy levels of erbium ions and (b) gain and attenuation spectra.

Excited State Absorption (ESA)

Ground-state absorption (GSA)

There are several states to which the erbium ions can be pumped using sources of different wavelengths, such as those operating at 1480, 980, and 800 nm. However, in practical optical systems, the pump wavelength must provide a high power to achieve a high gain per pump.

The commonly available laser diodes can operate at 800, 980, and 1480 nm, but the pump efficiency can go more than 1 dB/mW with low attenuation depending on the pump frequency.

The only pump wavelength laser sources that can give a high pumping efficiency with lower attenuations are those operating at 980 and 1480 nm.