The theory of the electro-optic effect and second harmonic generation
is developed in the context of the linear Stark effect. This leads to
an emphasis both on the optical bandwidth of the charge-transfer trans
itions responsible for the hyperpolarisability, and on the relationshi
p between the transition energies and optical frequency of an electro-
optic device. A simple treatment of vibronic coupling illustrates the
connection between the bond-length alternation in conjugated polyenes
and the sign and magnitude of the non-linearity. A brief survey is mad
e of current chemical strategies for optimising the non-linearity.