Page 153 - Photonics Essentials an introduction with experiments

Lasers

Lasers 147

consists of a pair of mirrors so that light exiting the laser amplifier is
returned back to the amplifier medium. The other mechanism is the
principle of stimulated emission, which says that the probability for
photon emission is proportional to the number of photons already
present. In this section, we will develop a relationship between the
amount of stimulated emission and the amount of spontaneous emis-
sion.
A popularly recognized feature of a laser is the emission of a well-
collimated beam of monochromatic light. This characteristic is deter-
mined entirely by the properties of the feedback element, just as in
the case of the phase-shift oscillator circuit. The principle of stimulat-
ed emission says that an emission of a photon that accompanies the
transition of an electron to a lower energy state depends on the num-
ber of similar photons already present within a space determined by
the wavelength of the electron. These photons encourage the electron
to make the transition, with the probability increasing linearly with
the density of photons. This process of stimulated emission is the re-
verse of the property of stimulated absorption, in which the probabili-
ty that an electron makes a transition to a higher energy state de-
pends on the number of photons present that have the energy
corresponding to the energy difference between the initial and final
states.
There is a third process, called spontaneous emission. In this case,
an electron can make a transition to a lower energy state by emitting
a photon in order to conserve energy. This process can occur in the ab-
sence of other photons. Notice that there is no reverse process for ab-
sorption; that is, an electron cannot make a transition from the va-
lence band to the conduction band without absorbing a photon. To
understand better how a laser works, we need to develop some ideas
concerning the absorption and emission of light.
In Figure 7.3, we diagram in a very schematic way the three possi-
ble transitions that can take place in the absorption or emission of
light. We choose a simple two-level system having N 2 states in the up-
per energy level occupied by electrons and N 1 states in the lower ener-
gy level occupied by electrons. In equilibrium, N 2 < N 1 and the ratio
between the two occupation numbers is given by Boltzmann statistics

N 2 –( E/k B T)
= e
N 1
The probability that an electron can make a transition from the lower
energy state to the upper energy state by stimulated absorption (Fig.
7.3b) is equal to B 12 . Because stimulated absorption is the reverse of
stimulated emission, the probability for stimulated emission to occur

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