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t cavity , and the effect of the pumping rate on the magnitude and the persistence
of the oscillation.

FIGURE 4.7
The dynamics of a laser in the relaxation oscillations regime. Top panel: Plot of the higher
excited level atoms population as a function of the normalized time. Middle panel: Plot of
the number of photons as a function of the normalized time. Bottom panel: Phase diagram
of the photons number vs. the higher excited level atoms population.

Example 4.14
Using the rate equations developed in Example 4.13, simulate the Q-switch-
ing of a laser.

Solution: First, an explanation of the statement of the problem. In Example
4.13, we showed how, following an initial transient period whereby one
observes relaxation oscillations, a laser, in the presence of steady pumping,
reaches steady-state operation after a while. This is referred to as continuous
wave (cw) operation of the laser. In this example, we shall explore the other
mode of laser operation, the so-called pulsed mode. In this regime, the exper-
imentalist, through a temporary modification in the absorption properties of
the laser resonator, prevents the laser from oscillating, thus leading the
higher excited state of the atom to keep building up its population to a very
high level before it is allowed to emit any photons. Then, at the desired

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