Page 196 - High Power Laser Handbook

164 So l i d - S t at e La s e r s Intr oduction to h igh-Power Solid-State Lasers 165

Many SSL materials have long upper-state lifetimes, typically on the
order of τ ∼ 1 ms. This allows them to act as “optical capacitors,” storing
pump energy during a long pump cycle that can be released quickly in
the form of a short pulse. Even for continuous wave (CW) pumping, a
long upper-state lifetime is advantageous because it reduces the amount
of pump power needed to reach inversion. Heuristically, the inversion
density that can be accumulated by a pump power densityR (where
R is the number of photons per unit time per unit volume) is ∆N = τR.
One of the most useful figures of merit (FOMs) for SSL materials
is the product στ. Because στ = g /R, this FOM indicates how much
0
laser gain is obtained for a given pump rate. A material with high στ
will lase very easily—that is, it requires less pump power density R to
reach a certain gain g . Figure 7.1 shows values of σ and τ for some
0
common SSL families of materials.
For high-pulse energy lasers, the energy storage capability of a
material is of paramount interest. Obviously, high τ allows a material
to store more energy for a given pump rate, which is unambiguously
helpful for pulsed lasers. However, a high σ can be a disadvantage
for energy storage. Depending on the geometry of the gain material,
amplified spontaneous emission (ASE) can prematurely depopulate
the upper laser level, clamping the obtainable inversion density and
small-signal gain. Hence, ASE can severely limit the ability of a mate-
rial to store energy for pulsed operation. This is also an issue for
large-aperture CW lasers, in which high-transverse laser gain can
lead to parasitic lasing or loss of efficiency. Still, even for high-energy

100

Ti:sapphire Nd:Host Nd:YAG
10 Tunable

Sigma (x E-19 cm 2 ) 1 3-Level

0.1
Nd:glass

Yb:YAG
0.01
0.001 0.01 0.1 1 10
Lifetime (ms)
Figure 7.1 στ figure of merit for major solid-state laser (SSL) materials.