
14
NONLINEAR OPTICS
In Chapter 6, we discussed the interaction of light with materials, using the Lorentz model
which treats the electron as a mass on a spring, as shown in Figure 6.4. The restoring force,
and the resulting acceleration in the x direction were linear as in Equation 6.26:
d
2
x
dt
2
=−E
r
e/m −κ
x
x/m,
where
e is the charge on the electron
m is its mass
The restoring force, −κ
x
x, is the result of a change in potential energy as the electron moves
away from the equilibrium position. The force is in fact the derivative of a potential function,
which to lowest order is parabolic. However, we know that if we stretch a spring too far, we
can observe