Oscillating dipole, second-order

In a molecule acted on simultaneously by two electric fields E(coj) and E(o), oscillating at frequencies cu and cuj, a second-order dipole moment... 

The (monochromatic) electric fields are characterized by Cartesian directions indicated by the Greek letters and by circular optical frequencies, coi, a>2, and The induced dipole moment oscillates at a> = EjO,. and are such that the jS and y values associated with different NLO processes converge towards the same static value. The 0 superscript indicates that the properties are evaluated at zero electric fields. Eqn (2) is not the unique phenomenological expression defining the (hyper)polarizabilities. Another widely-applied expression is the analogous power series expansion where the 1/2 and 1/6 factors in front of the second- and third-order terms are absent. The static and dynamic linear responses, o(0 0) and a(—correspond to the so-called static and dynamic polarizabilities, respectively. At second order in the fields, the responses are named first hyperpolarizabilities whereas second hyperpolarizabilities correspond to the third-order responses. Different phenomena can be distinguished as a function of the combination of optical frequencies. So, (0 0,0), a>,a>)... 

It is because (11.5.11) involves transition energies and densities for all excited states b that the calculation of second-order quantities such as the polarizability is difficult, since usually the available excited states and their number is very limited. We note in passing, however, a connection with quantities encountered in spectroscopy the intensity of a spectral line for the (electric-dipole-induced) transition a b, under the influence of isotropic radiation, is usually characterized by a dimensionless quantity, the oscillator strength , and this is defined by... 

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