title: Kramers-Kronig relations and sum rules in nonlinear optical spectroscopy.
abstract: The full potential of the Kramers-Kronig relations and sum rules for nonlinear susceptibilities has unfortunately drawn relatively little attention in nonlinear optical spectra analysis. In this feature article a simple treatment of an anharmonic oscillator model in description of the nonlinear susceptibility of media and holomorphic properties of the nonlinear susceptibility were utilized. Using such concepts, conventional Kramers-Kronig, multiply-subtractive Kramers-Kronig, and generalized Kramers-Kronig dispersion relations can be derived. We demonstrate how in practice the variety of different Kramers-Kronig relations mentioned above, as well as various sum rules, can be applied in nonlinear optical spectra analysis. As an example we treat the third-harmonic wave generation spectrum from a polymer.
authors.affiliation: Department of Physics, University of Joensuu, FIN-80100 Joensuu, Finland.
authors.forename: Kai-Erik
authors.initials: KE
authors.lastname: Peiponen
authors.forename: Valerio
authors.initials: V
authors.lastname: Lucarini
authors.forename: Jarkko J
authors.initials: JJ
authors.lastname: Saarinen
authors.forename: Erik
authors.initials: E
authors.lastname: Vartiainen