Multiply subtractive Kramers-Kronig relations for arbitrary-order harmonic generation susceptibilities

Kramers-Kronig (K-K) analysis of harmonic generation optical data is usually greatly limited by the technical inability to measure data over a wide spectral range. Data inversion for real and imaginary part of chi(n) (nomega; omega,..., omega) can be more efficiently performed if the knowledge of one of the two parts of the susceptibility in a finite spectral range is supplemented with a single measurement of the other part for a given frequency. Then it is possible to perform data inversion using only measured data and subtractive K-K relations. In this paper multiply subtractive K-K relations are, for the first time, presented for the nonlinear harmonic generation susceptibilities. The applicability of the singly subtractive K-K relations are shown using data for third-order harmonic generation susceptibility of polysilane. (C) 2003 Elsevier Science B.V. All rights reserved.