Page 266 - Tunable Lasers Handbook

226 Norman P. Barnes

3d
electrons

4s bonding
1 s-2p
electronic : core electrons

FIGURE 1 Transition metal electronic configuration.

Crystal field effects contribute strongly to the energy levels of the 3d elec-
trons of a transition metal atom embedded in a laser material. The results of
turning on the various interactions that contribute to the energy levels of 2d
electrons, in order of their magnitude, are shown schematically in Fig. 2 [6].
Protons in the nucleus and filled subshells form a spherically symmetric central
potential for the 3d electrons. A net positive charge exists on the central potential
because the nucleus has more protons than there are electrons in the surrounding
cloud at this point. This net positive charge binds the 3d electrons to the transi-
tion metal atom. In many cases, next in importance is the mutual repulsion of the
individual electrons. To avoid each other and thus minimize mutual repulsion
effects, the 3d electrons tend to fill subshells in such a way that the spins of the
electrons are opposed. Thus the spins of the electrons couple together; making
the total spin quantum number, S, approximately a good quantum number. After
the mutual repulsion effects, the crystal field effects become important. Crystal
field effects tend to split the energy levels remaining after the spin coupling.
Levels are split into those that have orbitals which are directed toward the near-
est neighbors in the lattice and those that have orbitals directed between the
nearest neighbors.
Although this simple picture is useful to describe the situation, the calcula-
tion of the energy levels involve many more contributions than the effect of the
nearest neighbors. In some laser materials, the relative size of the mutual repul-
sion and the crystal field effects are roughly similar or the crystal field effects