MODULE 23_03
LASER SOURCES: OPERATION
These days the excitation flash is universally derived from pulsed lasers. Flash lamp
sources are virtually extinct. Population inversion must be transiently achieved in the
lasing level for stimulated emission to be
2
favored over spontaneous emission. Figure
3
23.1 shows the operating principle of a
typical 4-level laser.
Levels 3 and 4 are
initially empty and
level
3
becomes
populated before level 4, and it is therefore
relatively easy to obtain a population
inversion. In such a system it is typical that
4
approximately 5% of input energy is
converted to laser output.
1
A minimal laser consists of a pair of highly
FIG 23.1
reflecting mirrors, a lasing medium, and a pump source (Figure 23.2). The lasing
medium can be a solid crystal (Nd:YAG, Ti:sapphire, etc), a semiconductor, a liquid (a
dye solution), or a gas cell (HeNe, Ar+, etc). Of the two mirrors one is 100% reflective
over the laser emission band, and the other is ca 99.5% reflective. Thus only a small
fraction of the total energy stored in the cavity is allowed to leak out. Depending on
whether the laser is to be cw or pulsed, the pump source can be an electric discharge (gas
lasers), a cw lamp, a flash lamp, or another laser.
Pump source
Rear reflector
Lasing medium
FIG 23.2
Output coupler
Maintaining the optical cavity carefully aligned with the reflecting surfaces exactly
parallel ensures minimum losses and allows that sufficient lasing states will be formed to
bring the system over the "gain threshold." Then the laser will lase in a free-running
manner with a long pulse (  ss ) or a ragged profile (Figure 23.3). This is useless for
time resolved work and the pulsing mechanism needs to be controlled.
stored
energy
FIG. 23.3
GAIN THRESHOLD
Pump flash profile
time
To achieve controlled narrow pulses we use a Q-switch-- a device that keeps the cavity
closed (and in a high gain mode) until the gain is optimal, then it is opened and rapidly
closed again. This generates a short pulse. Modern Q-switches are electro-optic devices
(Pockels cells) that operate by briefly rotating the direction of polarization of the
oscillating pulse in the cavity. Such Q-switched solid state lasers can deliver pulses of
few ns duration with energies of 1 J or more (gigawatts). To achieve shorter pulses (as
short as a few fs) from solid-state lasers we need a method other than Q-switching-mode
locking.
Mode-locking
Mode-locked lasers can deliver pulses in the fs regime. A laser cavity will only amplify
those light ray trajectories that are precisely on the axis of the cavity. These will undergo
many reflections through the gain medium and thus be amplified. All rays of the axis
will be lost from the cavity. Only those on-axis rays that exhibit nodes at the mirror
surfaces will be reflected and become standing waves (recall the physics of the stretched
string and the particle in the box). All other frequencies will destructively interfere.
Thus the standing wave condition is n  2d , where d is the cavity length (mirror-tomirror distance).
Within a given gain vs. frequency profile (gain envelope) - which depends on emission
spectrum of laser medium - there are usually many radiation frequencies that can obey
the standing wave conditions. These are the longitudinal modes of the cavity. The
existence of many such modes provides the capability of tuning the output wavelength,
i.e., the cavity can be adjusted to select only a sub-set of the longitudinal modes.
In normal laser operation there is no particular phase relationship between different
modes. They oscillate randomly and the output is a superposition of the standing waves
without any particular temporal structure. However, a very different output results if
longitudinal modes can be forced into phase at some arbitrary origin. Figure 23.4 shows
the intensity-time profiles of three cosine functions that have different phase factors but
which are forced to all have their maxima at the same point, here the zero time. It can be
seen that this locking of the longitudinal modes into a phase relationship imparts
temporal structure on the output profile of the superposition. Now we see sharp peaks at
t = 0, +/-2, with subsidiary peaks between. Adding more waves into the superposition
suppresses the minor peaks and enhances the major ones, as shown in Figure 23.5 where
40 such waves are included.
9
s( x)
FIG.23.4
2
y ( x)
z ( x)
f ( x)
10
2
2
5
2
0
0
3
3
2
1
0
x
1
2
3
3
1
FIG.23.5
0.8
0.6
z ( k  x)
2
0.4
0.2
0
2
1.5
1
0.5
0
0.5
1
x
WAVE PACKET k=1 thro' 40
The result of the phase locking is the development of constructive interference at the
locking points which occur every 2d/c seconds inside gain envelope of the cavity. Thus
the output of a mode-locked laser cavity is a train of narrow pulses within the gain
k  x)
envelopep (of
the lasing medium (dye, gas, solid state). The pulses are separated in time by
2d/c seconds, the inverse of the inter-mode frequency spacing. The quantity 2d/c is
termed the cavity round trip time.
The width of the mode-locked pulses is governed by the bandwidth of the light that
oscillates in the cavity ( vosc ).
t  1/ vosc
x
and the wider the bandwidth, the shorter the pulse. Gas lasers such as the Ar+ ion have
very narrow bandwidths and mode-locked pulses of not less than 100 ps are obtainable.
About 20 ps pulses can be obtained from Nd:YAG lasers. The wide bandwidths of dyes
and Ti:sapphire media allow pulses in the sub-ps range to be generated.