Lecture 8: Laser amplifiers

Gain and bandwidth
The wave is amplified with a gain coefficient () (per unit
length) and undergoes a phase shift () (per unit length).
() > 0 corresponds to amplification, () < 0 corresponds
to attenuation.
Recall that the probability density (s -1 ) that an unexcited
atom absorbs a single photon is
W i
( )
where the transition cross section at the frequency
2
c
( )
2 2
8n
gˆ(
)
Here we assume the probability density for stimulated
emission is the same as that for absorption. ( a () = e () =
())
sp
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