Linear Polarisability [tex] \alpha_{ij} [/tex] is the amplitude of the electric field induced in the molecule in the i direction given a unit amplitude field in the j direction, hence(adsbygoogle = window.adsbygoogle || []).push({});

[tex] E_i^{induced} = \alpha_{ij} E_j^{incident} [/tex]

(observing summation convention)

Extending this physical interpretation, [tex] \beta_{ijk} [/tex] (X_{2}) is the amplitude of the electric field induced in the i direction given an unit incident field in the j direction applied after unit incident field in the k direction has already been applied, so

[tex] E_i^{induced} = \beta_{ijk} E_j^{incident2} E_k^{indicent1} [/tex]

But there is a third-order term (and fourth-order and fifth-order, etc.) so what do the indices represent in these cases?

Also, there is only one applied (indicent) field so what does it mean to say "the incident field in the j direction" compared to "the incident field in the k direction"?

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# Linear Polarisability interesting problem

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