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.