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FIGURE 4.8
The temporal profile of the photon burst emitted in a Q-switched laser for different initial
values of the excited level atoms population. Top panel: N(0) = 50. Middle panel: N(0) =
100. Botton panel: N(0) = 300.

moment, the laser resonator is allowed back to a state where the optical losses
of the resonator are small, thus triggering the excited atoms to dump their
stored energy into a short burst of photons. It is this regime that we propose
to study in this example.
The laser dynamics are, of course, still described by the rate equations [i.e.,
Eqs. (4.58) and (4.59)]. What we need to modify from the previous problem are
the initial conditions for the system of coupled ODE. At the origin of time [i.e.,
t = 0 or the triggering time, N(0)], the initial value of the population of the
higher excited state of the atom is in this instance (because of the induced
build-up) much larger than that of the corresponding photon population n(0).
Figure 4.8 shows the ensuing dynamics for the photon population for different
values of N(0). We assumed in these simulations the following values for the
parameters in the laser1 function M-file (p=0; B=3; c=100; gamma=0.01).
In examining Figure 4.8, we observe that as N(0) increases, the pulse’s total
energy increases — as it should since more energy is stored in the excited
atoms. Furthermore, the duration of the produced pulse (i.e., the width of the
pulse temporal profile) narrows, and the delay in the position of its peak from
the trigger time gets to be smaller as the number of the initial higher excited
level atoms increases.

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