Adiabatic following model for two-photon transitions: Nonlinear mixing and pulse propagation

Two-photon resonantly enhanced parametric generation processes have generally been described using time-dependent perturbation theory. In this paper we show that a theory of two-photon coherent effects can be used to derive and explain these nonlinear mixing processes. Our technique makes use of the adiabatic following (AF) approximation to obtain solutions to a vector model describing the two-photon resonance. We show that the usual results for the nonlinear susceptibilities correspond to the r vector of Feynman, Vernon, and Hellwarth adiabatically following the gamma vector in the small-angle limit. Consequently, the theory allows a natural extension to large angles, and power-dependent nonlinear susceptibilities are obtained. We then use these AF results for the polarization to study the propagation of pulses nearly resonant with a two-photon transition, and we demonstrate that the pulse reshaping is due to the two related effects of a nonlinear pulse velocity and self-phase modulation.Peer reviewedElectrical and Computer Engineerin

Additional file 4 of Mapping age- and sex-specific HIV prevalence in adults in sub-Saharan Africa, 2000–2018

Additional file 4: Supplemental results.1. README. 2. Prevalence range across districts. 3. Prevalence range between sexes. 4. Prevalence range between ages. 5. Age-specific district ranges