Macroscopic quantum electrodynamics approach to nonlinear optics and application to polaritonic quantum-vacuum detection
Frieder Lindel, Robert Bennett, Stefan Yoshi Buhmann
Abstract
We provide an in-depth discussion of a theoretical framework recently introduced [Lindel et al., Phys. Rev. A 102, 041701(R) (2020)] which is capable of predicting the electromagnetic field emerging from a nonlinear crystal through which a coherent laser pulse is shone. This framework is based on macroscopic quantum electrodynamics and includes dispersion and absorption effects inside the crystal and allows for arbitrary optical environments through the classical Green's tensor. We introduce a diagrammatic approach with which the nonlinear processes contributing to the electric field operator up to certain orders in the perturbation series can be represented in a convenient way. Applying this framework to the setup of electro-optic sampling experiments of the polaritonic quantum vacuum, we derive analytical results for the electro-optic sampling between distinct spatiotemporal regions. Also, we discuss different approximations and the parameter ranges in which they apply including angled or diverging beams, thermal fluctuations, as well as (linear) absorption effects upon the polaritonic quantum vacuum. Finally, we compare these theoretical results to experimental data.