Page 156 - Photonics Essentials an introduction with experiments

Lasers

150 Photonic Devices

This ratio is normally much greater than unity; that is, the sponta-
neous emission rate far exceeds the stimulated emission rate. If we
consider photons with an energy of 1 eV ( = 1240 nm) then /k B T = 40
at room temperature. R, as a result, is a very big number. However, in
order to have laser action, the reverse must be true; that is, the stimu-
lated emission rate must be greater than the spontaneous emission
rate. To see how this can happen, read on through the next section.

7.3 Optical Gain
Optical gain and optical absorption are closely related. We will start
by recalling some ideas about optical absorption that we already have
discussed in Chapter 3. When light is incident on a semiconductor
surface, only two things can happen: reflection or transmission. Nor-
mally, both can occur at the same time. Absorption can take place if
the energy of the incident photons is greater than the band gap. Ab-
sorption does not occur all in one spot at the surface, but rather pro-
gressively as the photons propagate into the semiconductor. At any
point inside the semiconductor, the amount of light that gets absorbed
is proportional to the total intensity that is present. The constant of
proportionality is called the absorption coefficient. The simple model
shown in Fig. 7.4 gives an excellent description of this reality.
We can write down an equation that describes this situation:

I(x + x) – I(x) = I(x)
and
I(x) = – ·I(x)

∆x

I(x) I(x + ∆ x)

Figure 7.4. A simple schematic diagram of light passing through a section of material
in which absorption is taking place. Absorption causes the intensity of light to decrease
as a function of distance traveled. The change in the intensity between points x and x +
x is proportional to the intensity at point x.

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