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KramersKronig Relations and Sum Rules in Nonlinear Optical Spectroscopy

Volume 58, Number 5 (May 2004) Page 499-509

Peiponen, Kai-Erik; Lucarini, Valerio; Saarinen, Jarkko J.; Vartiainen, Erik


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.