Page 160 - Photonics Essentials an introduction with experiments

Lasers

154 Photonic Devices

state. If level E 3 is a few k B T above level E 1 , it will be nearly empty by
Boltzmann statistics. The cycle starts when a high-energy photon
with energy hf = E 2 – E 1 excites an electron from the ground state to
the excited state (step 1). The photon is a particle, so all its energy
must be absorbed, making a direct transition to E 3 or E 4 impossible.
After excitation, the electron can be scattered into state E 4 during a
collision (step 2). Electrons are more likely to end up in state E 4 than
state E 3 or state E 1 because the energy difference is smaller, and
therefore easier to make up by phonon emission. After step 2, there
are electrons in state E 4 but not in state E 3 . Thus, a population inver-
sion between these two levels now exists. The recombination that fol-
lows is an example of optical gain, since emission between these levels
far exceeds absorption, which is practically zero (step 3). This transi-
tion can be a lasing transition if suitable feedback is provided. Final-
ly, electrons that reach level E 3 are recycled to level E 1 , leaving state
E 3 empty again (step 4). In this example, the number of photons ab-
sorbed is still equal to the number of photons emitted. However, there
is now one set of levels that does most of the absorption, and another
set that generates most of the emission. Optical amplification occurs
if the emission rate exceeds the absorption rate, and this is the case
for emission between states 4 and 3.
A semiconductor laser is a good example of a four-level system, and
this can be understood quickly from a simple band structure diagram
such as that in Fig. 7.6. Optical stimulation of lasing is relatively easy
to demonstrate in a direct gap material, and it proceeds following the
cycle outlined above. However, the cycle for obtaining gain by electri-
cal excitation is quite different. In this case, the behavior of the p-n
junction is used to create a population inversion.
The pumping cycle in Fig. 7.6 is different from the cycle in Fig. 7.5.
Initially, level E 3 is fully occupied by electrons. Optical excitation pro-
ceeds by the absorption of a photon (step 1) In order to conserve ener-
gy and momentum, the electron that is excited to the conduction band
must originate deep in the valence band as shown. Then nearly simul-
taneously, the excited electron in the conduction band relaxes to state
E 4 and the electron in state E 3 relaxes to state E 1 , leaving a hole be-
hind (step 2). Relaxation takes place by emission of phonons, and is
completed in 10 –12 sec. Now there is an electron in state E 4 and a hole
in state E 3 , creating a population inversion. This situation can persist
for about 10 –9 sec. That is three orders of magnitude longer than the
relaxation process. Finally, recombination occurs across the gap (step
3). This transition can be used to make a laser if suitable feedback is
provided.
In a semiconductor material, both spontaneous and stimulated
emission proceed by this “four-step” process. No matter what the en-
ergy of the optical excitation above the band gap, the energy of the

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