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

spaced levels.

Amplification Window :
EDFA can be used to amplify signal in two bands of wavelengths in the third transmission window. The wavelength range 1525 nm to 1565 nm is known as the C-band or the conventional band and trhe second band from 1568 nm to 1610 nm is known as the L- band or the long band. The name long band is given because the doped section used for this band is longer.

4. Rate Equations :
 

Let $ N_u, N_m$and $ N_g$denote the population of the three states. If $ W_p$is the pumping rate, $ W_s$is the rate of absorption of photons from the signal and $ \tau_{ij}$is the lifetime of spontaneous emission from the state $ i$to the state $ j$, we can write the following rate equations :

$\displaystyle \frac{dN_g}{dt}$

$\displaystyle =$

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

(1)

$\displaystyle \frac{dN_m}{dt}$

$\displaystyle =$

$\displaystyle \frac{N_u}{\tau_{um}} - W_s(N_m-N_g)$

(2)

$\displaystyle \frac{dN_u}{dt}$

$\displaystyle =$

$\displaystyle -\frac{N_u}{\tau_{um}} + W_p(N_g-N_u)$

(3)

Population inversion implies that $ N_m>N_g$. For steady state conditions, the time derivatives vanish. Since the lifetime of the state $ u$is much smaller than the lifetime of the state $ m$, the population of the excited state is essentially given by the Boltzmann distribution

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