Page 306 - High Power Laser Handbook

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

12519
12432 4 F 5/2 Level 3
12370

11512 4
11427 F 3/2 Level 2
Energy (cm −1 ) 2521 Laser emission

2468

2147 4 I 11/2 Level 1
2110
2029
2002

0 4 I 9/2 Level 0
(Individual lines not shown)
Figure 11.9 Energy-level diagram of Nd:YAG, showing the levels considered
in the model. Pumping is into the F 5/2 band.
4
in thermodynamic equilibrium. Consequently, if ∆E and ∆E are
32
10
the energy differences between levels 1, 0 and 3, 2 respectively, we
may write the populations of level 1 at temperature T as
NT() = Ne −∆ E / kT (11.4)
10
0
1
where ∆E = 0.26 eV, and k is Boltzmann’s constant. Likewise the
10
population of level 2 at temperature T is
Z ()
T
0
0
NT() = 32 NT() (11.5)
T
2 Z () 2 0
0
32
where T is the reference temperature and where
0
ZT()
Z () = 2 (11.6)
T
32 ZT() + ZT()
3
2
0
is the fraction of atoms in level 2. The population NT() refers to the
2
population of level 2 by the pump process at temperature T. It is dis-
tinguished from the purely thermal population NT(), which, because
2