Verification of generalized Kramers-Kronig relations and sum rules on experimental data of third harmonic generation susceptibility on polymer

We present an analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Kronig (KK) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental data of the third-harmonic generation susceptibility for different polymers: polysilane (frequency range 0.4-2.5 eV), and polythiophene (frequency range 0.5-2.0 eV). We show that, without extending the data outside their range with the assumption of an a priori asymptotic behavior, independent truncated dispersion relations connect the real and imaginary parts of the moments of the third-harmonic generation susceptibility omega(2)alphachi((3))(3 omega, omega, omega, omega), 0 less than or equal to alpha less than or equal to3, in agreement with theory, while there is no convergence for alpha = 4. We report the analysis for omega(2alpha)[chi((3))(3 omega; omega, omega, omega)](2) and show that a larger number of independent KK relations connect the real and imaginary parts of the function under examination. We also compute the sum rules for the suitable moments of the real and imaginary parts, and observe that only considering higher powers of the susceptibility the correct vanishing sum rules are more precisely obeyed. Our results are in fundamental agreement with recent theoretical findings. Verification of KK relations and sum rules constitutes an unavoidable benchmarks for any investigation that addresses the nonlinear response of matter of radiation over a wide spectral range. (C) 2003 American Institute of Physics.