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

TL;DR

This paper introduces multiply subtractive Kramers-Kronig relations for harmonic generation susceptibility, demonstrating improved data inversion accuracy over conventional methods using experimental third-harmonic data from polysilane.

Contribution

The paper develops multiply subtractive Kramers-Kronig relations for arbitrary order harmonic susceptibilities, enhancing data inversion accuracy in nonlinear optical measurements.

Findings

SSKK relations outperform conventional K-K in data inversion accuracy

Faster asymptotic decay of integrands improves reliability

Experimental validation on polysilane third-harmonic data

Abstract

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 (K-K) relations. The fundamental reason is that SSKK and MSKK relations have strictly faster asymptotic decreasing integrands than the conventional K-K relations. Therefore SSKK and MSKK relations can provide a reliable optical data inversion procedure based on the use of measured data only.