Causal vs. Noncausal Description of Nonlinear Wave Mixing; Resolving the Damping-Sign Controversy

TL;DR

This paper compares causal and noncausal descriptions of nonlinear wave mixing, clarifying the controversy over the sign of radiative damping by analyzing their different analytical properties.

Contribution

It provides a unified framework for understanding causal and noncausal models of nonlinear wave mixing and resolves the damping-sign controversy.

Findings

Different analytical properties of response functions and scattering amplitudes.

Clarification of the damping-sign controversy in nonlinear wave mixing.

Unified theoretical framework for causal and noncausal descriptions.

Abstract

Frequency-domain nonlinear wave mixing processes may be described either using response functions whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symetrically with no specific time ordering. Closed Green's function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers Heisenberg) formula is put in a broader context.