Page 159 - Photonics Essentials an introduction with experiments

Lasers

Lasers 153

When is negative, you get gain rather than loss, and instead of us-
ing to describe this condition, we should define a gain coefficient k,
where
Gain coefficient = k = –
nhf
k = (N 2 – N 1 )P 21 (7.10)
c

7.4 Obtaining Population Inversion
So far we have considered light emission from a system of electrons
having two energy levels, E 1 and E 2 . Looking at Fig. 7.3 again, you
can see that there is one way for electrons to get pumped into the up-
per level: by stimulated absorption. We know that this rate is equal to
the stimulated emission rate. However, there is a second way for elec-
trons to be de-excited from the upper level: by spontaneous emission.
In addition, we know that this rate is much bigger than the stimulat-
ed absorption rate. The result is that there is no way you can obtain a
population inversion in a two-level system.
Of course, you might be able to get an inversion if electrons were
somehow fed into the upper level by another source: a third level. This
turns out to be the road to the solution. In general, lasing is easiest to
obtain in a four-level arrangement, this is diagrammed schematically
in Fig. 7.5.
At the beginning of the cycle, all the electrons are in the ground

Excited State
E
2
2
E 4

Lasing transition
1 3

E
3
4
E
1
Ground State
Figure 7.5. Population inversion can be obtained in a four-level system, in this case, be-
tween level 4 and level 3. The excitation and recombination cycle is given in sequence
by the numbers in the figure. There are four steps to the complete cycle.

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