Page 161 - Photonics Essentials an introduction with experiments

Lasers

Lasers 155

Conduction Band

E 2 2
E
4

ENERGY Excitation 1 3 Emission

E
2 3
E 1

Valence Band

MOMENTUM
Figure 7.6. A direct band gap semiconductor is a good example of a four-level medium
for laser action. There is a significant difference in the pumping scheme, because level
E 3 is initially fully occupied by electrons. However, as soon as a photon is absorbed,
electrons leave this level to fill the hole in the valence band that is created by the exci-
tation.

photons emitted during recombination is always close to the band gap
energy. Optical gain only occurs in this range of energies, which we
can denote by a distribution function, g(f), called the optical gain
spectrum. This is always the situation because the lifetime for optical
recombination is orders of magnitude longer than the time for phonon
emission. Typical values for the energy width of the gain spectrum lie
in the range of 0.01 to 0.02 eV. In order to take account of this feature,
we will modify the equation for the gain coefficient:

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