Module 15 : ERBIUM DOPED FIBER AMPLIFIERS (EDFA)
Lecture : ERBIUM DOPED FIBER AMPLIFIERS (EDFA)
 

$\displaystyle N_u = N_me^{-(E_u-E_m)/kT}\equiv \beta N_m$

(4)

where $ \beta = e^{-(E_u-E_m)/kT}$. From Eqn. (1), we have, for steady state conditions

$\displaystyle \frac{N_m}{\tau_{mg}} + W_s(N_m-N_g) -W_p(N_g-N_u) = 0$

which can be simplified using Eqn. (4) to give the inversion level as

$\displaystyle n = \frac{N_m}{N_m-N_g} = \frac{(W_p+W_s)\tau}{W_p\tau(1-\beta) -1}$
The inversion level is thus related to both the pump and signal powers and also to the pump wavelength through the Boltzmann factor.
The factor $ \beta$explains why 980 nm pumping is more effective in achieving population inversion than 1480 nm pumping. It was seen that because of small lifetime of the level $ u$, the ions thermalize to the level $ m$. The energy difference between these two levels is substantial ( $ \sim 0.4$ eV) as a result of which $ \beta\simeq 0$. In case of 1480 nm pumping the thermalization occurs to the lowest energy sub-level within the group $ m$. The value of $ \beta$for this case is about 0.4.

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