Multiply subtractive Kramers-Krönig relations for arbitrary-order harmonic generation susceptibilities
نویسندگان
چکیده
Kramers-Krönig (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 χ(nω;ω, ..., ω) 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.
منابع مشابه
Verification of generalized Kramers-Krönig relations and sum rules on experimental data of third harmonic generation susceptibility on polymers
We present the first analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Krönig (KK) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental data of third harmonic generation susceptibility on different polymers, the polysilane (frequency
متن کاملResponse Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations
Abstract We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. ...
متن کاملEvidence of dispersion relations for the nonlinear response of the Lorenz 63 system
Abstract Along the lines of the nonlinear response theory developed by Ruelle, in a previous paper we have proved under rather general conditions that Kramers-Kronig dispersion relations and sum rules apply for a class of susceptibilities describing at any order of perturbation the response of Axiom A non equilibrium steady state systems to weak monochromatic forcings. We present here the first...
متن کاملGeneral Properties of Optical Harmonic Generation from a Simple Oscillator Model
The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transitions in molecules and crystals, in order to derive general properties of harmonic generation to all orders. In particular, we obtain Kramers-Krönig relations and sum rules referred to all momenta of the susceptibility, and Miller’s ...
متن کامل