Polarizabilities series-convergent properties

The (monochromatic) electric fields are characterized by Cartesian directions indicated by the Greek letters and by circular optical frequencies, ( i, ( 2, and 0)3. The induced dipole moment oscillates at (0 = 2i cOi. and are such that the p 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. Eq. (2) is not the unique phenomenological expression defining the (hyper)polarizabilities. Another often-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. 

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