https://doi.org/10.1007/PL00011069
Asymptotic behaviour and general properties of harmonic generation susceptibilities
Scuola Normale Superiore, P.za dei Cavalieri 7, 56100 Pisa, Italy
and Istituto Nazionale di Fisica della Materia, Corso Perrone 24, 16152 Genova, Italy
Received:
17
April
2000
Published online: 15 October 2000
We use the Kubo response function formalism to derive the asymptotic behaviour of the
harmonic generation susceptibilities to all orders n. The results show a stringent correspondence
with the ones previously obtained from the classical anharmonic oscillator model. They are
characterized by a 
dependence and a coefficient proportional to the trace of the (n+1)th derivative of the potential energy on the equilibrium density matrix. Using the above results we derive new Kramers-Krönig relations and sum rules for all orders of harmonics susceptibilities.
PACS: 42.65.-k – Nonlinear optics / 42.65.An – Optical susceptibility, hyperpolarizability / 42.65.Ky – Harmonic generation, frequency conversion / 78.20.-e – Optical properties of bulk materials and thin films
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
