Page 305 - High Power Laser Handbook

274 So l i d - S t at e La s e r s Heat-Capacity Lasers 275

8 10 −20 3500
Crystalline Nd: YAG
7 10 −20 Coolant temperature: 28°C
3000
6 10 −20 <σ> = 3.4 × 10 −20 cm 2 2500
Absorption cross section (cm 2 ) 4 10 −20 2000 Intensity (arbitrary units)
−20
5 10

1500
−20
3 10
2 10

500
−20
1 10 −20 1000
0 0
785 790 795 800 805 810 815 820 825
Wavelength (nm)
Figure 11.8 The 808-nm absorption band of Nd:YAG. Superimposed in red is the
time-integrated laser diode pump spectrum.

where sl() is the absorption cross section, N is the neodymium con-
0
a
centration in the ground state, and the integral is done over the pump
band (typically 800–820 nm). Implicit in Eq. (11.1) is the assumption
that both surfaces of the slab see the same pump intensity.
The instantaneous pump spectral intensity i (,l t) may be further
p
written as
l
i (, t) = ft)exp[ 4 ln( − l t ()) /∆ l 2 t ( )] (11.2)
2
−
(
l
2
p p c
where ft() describes the overall pump profile; where
p
l t() = c A −  1 e Bt (erfc Bt  )  (11.3)
is the center wavelength, with A and B fit coefficients; and where
∆l() = t . + 27 t 235 nm is the spectral full-width, half-maximum
/
(FWHM) with time in ms.
Because there will be considerable heat buildup in the lasing
medium, we need to take into account the lower laser level’s thermal
population, as well as the thermal depopulation of the upper level.
The energy level diagram of interest is shown in Fig. 11.9. Because
we are dealing with a four-level laser system, the decay out of level
3 into level 2 (and likewise for level 1 into level 0) is extremely rapid
on the time scales of interest; levels 3 and 2 (and levels 1 and 0) are