Page 283 - Tunable Lasers Handbook

6 Transition Metal Solid-state Lasers 243
V

U
I I

FIGURE 8 Configuration coordinate energy-level diagram.

discrete energy levels and a zero point energy. Differences between discrete
energy levels associated with a quantum mechanical parabola are hv, where 17 is
Planck’s constant and v,. is a frequency. Parabolas associated with different mani-
folds can have different curvatnres with different frequencies. To describe the
different curvatures, ari angle 8 is introduced and defined by

where the subscripts 1’ and II denote the upper and lower parabolas, respectively.
In terms of the discrete energy difference. the zero point energy associated wifn
the v parabola is hv1,/2.
Parabolas for manifolds with different energies may be offset from each
other. Manifolds having different energies have different electronic charge con-
figurations. For these different electronic charge configurations, the equilibrium
position of the nearest neighbors can be different. For example, an electronic
charge distribution that has the electrons appear between the active atom and its
nearest neighbors may result in a stronger repulsion and consequently a longer
distance between them. A difference in the equilibrium position can affect the
energy of the manifold. In general, the active atom and its surrounding neighbors
will prefer to reside in a configurational coordinate position. which minimizes