New approach to Fully Nonlinear Adiabatic TWM Theory

TL;DR

This paper introduces a novel elliptic function-based formulation of fully nonlinear adiabatic three-wave mixing (TWM), unifying linear and nonlinear cases and linking the adiabatic basis to geodesic lines on the generalized Bloch sphere.

Contribution

It presents a new elegant elliptic function formulation of FNA-TWM, unifies linear and nonlinear cases, and connects the adiabatic basis to geometric geodesics.

Findings

Unified description of linear and nonlinear TWM processes.

Elliptic function formulation simplifies the analysis of FNA-TWM.

Geometric interpretation of adiabatic basis as geodesic lines.

Abstract

I'm presenting a new elegant formulation of the theory of fully nonlinear adiabatic TWM (FNA-TWM) in terms of elliptic function here. Note that the linear case of SFG and DFG in the undepleted pump approximation described by the FVH representation has been exploited several years ago. For the sake of completeness, I present the pseudo-FVH representation to describe OPA. Moreover, I'm trying to display an overview of TWM processes and show that both the linear cases, the linear adiabatic SFG(DFG) and the linear OPA, are only the special cases of my theory. Finally I also point out that the geometric image of the so-called adiabatic basis acts as the geodesic line of the generalized Bloch sphere.