I have read a book that demonstrate the origin of electrical susceptibility of high order in harmonic generation: (in Robert Boyd's book : "Nonlinear optics").(adsbygoogle = window.adsbygoogle || []).push({});

For example, he show clearly for the case of second harmonic generation, how [itex]\chi^{(2)}[/itex] depends on matrix element of electric dipole operator on the basis of eigenvector of electronic states.

[itex]\chi^{(2)}_{ijk}(\omega_{\sigma},\omega_q,\omega_p)=\frac{N}{\hbar^2} P_F\sum_{mn} \frac{\mu_{gn}^i\mu_{nm}^j\mu_{mg}^k}{(\omega_{ng}-\omega_{\sigma})(\omega_{mg}-\omega_p)}[/itex]

Where [itex] \mu_{nm}=\langle{\phi_n} |\hat{\mu} |{\phi_m}\rangle[/itex] and [itex]\phi_n[/itex], [itex]\phi_m[/itex] are electronic wavefunctions.

It assumes that the transitions mentionned in the [itex]\chi^{(2)}[/itex] expression are between eletronic level.

My question:

Is it possible to make second or third harmonic generation with transition taking place in vibrational level or rotationnal level of a molecules?

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# Nonlinear susceptibility in second harmonic generation

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