Page 277 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Interacting Subsystems
of the propagating electromagnetic wave inside the laser cavity. A deriva-
tion is given in [7.20], we will explain the result
ω χ Qγ 2 D
0
˙
I = – ---- 1 ----------------------------------------- I (7.90)
–
2
Q γ + ( ω – ω) 2 D 0
0
In (7.90) we see that light intensity is lost through the quality factor of
the cavity. The factor Q ω⁄ is the energy stored divided by the energy
lost per second. So the first term gives a negative contribution to the time
derivative of the intensity. The second term contains a product of inver-
sion density and light intensity and is a nonlinear driving term for the
light field intensity. So we end up with a set of two coupled nonlinear
equations (7.89) and (7.90). They describe how the laser field intensity
and the inversion density evolve in time. In a small signal analysis around
˙
˙
the steady state I = 0 and D = 0 we see that the system exhibits relax-
ation oscillations which are typical for the switching on and off of such a
device. An external control parameter is the steady state inversion density
D . This density can be externally set by the current injection of carriers
0
into the device and eventually controls the laser intensity.

For the laser to work, the laser field has to be kept in the active region,
i.e., a cavity electromagnetic wave mode must be provided by specifying
special boundary conditions for the electromagnetic field. The simplest
way to do this is to place mirrors at the ends of the active region. This
ensures that a high density of photons of the selected cavity wave mode is
present where the active electronic system is situated. In terms of our
simple two level picture, Figure 7.10, this means that there is a strong
stimulated emission pumping almost all transition energies into the one
electromagnetic wave mode, i.e., the stimulated photons have the same
phase as the present electromagnetic wave and therefore this yields an
I
amplification of the light field intensity . This is what LASER stands
for: Light Amplification by Stimulated Emission of Radiation. The rest
of the recombination processes not coupling to the laser mode are losses
that decrease the inversion density without pumping the laser mode. The

274 Semiconductors for Micro and Nanosystem Technology