Multiply subtractive generalized Kramers-Kronig relations: Application on third-harmonic generation susceptibility on polysilane

We present multiply subtractive Kramers-Kronig (MSKK) relations for the moments of arbitrary order harmonic generation susceptibility. Using experimental data on third-harmonic wave from polysilane, we show that singly subtractive Kramers-Kronig (SSKK) relations provide better accuracy of data inversion than the conventional Kramers-Kronig (KK) relations. The fundamental reason is that SSKK and MSKK relations have strictly faster asymptotic decreasing integrands than the conventional KK relations. Therefore SSKK and MSKK relations can provide a reliable optical data inversion procedure based on the use of measured data only. (C) 2003 American Institute of Physics.