Verification of generalized Kramers-Krönig relations and sum rules on experimental data of third harmonic generation susceptibility on polymers

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

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 th...

General 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 ...

Response 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. ...

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics

Evidence 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...