The present high-power laser systems have reached an output of 10 PW  and 1022 W/cm2 . One of the elementary processes tested at such laser facilities is electromagnetic radiation processes of a highly energetic electron, i.e., nonlinear Compton scattering (NCS)/radiation reaction (RR). This nonlinearity is the same as multi-photon absorption in nonlinear optics, an electron absorbs laser photons in a single QED process and it emits a single photon. The QED correction of radiation (the quantumness) provides a modification of the radiation spectrum from the classical model. Thus, the dependence of NCS for its nonlinearity and quantumness in the uncharted domain is a large interest in experiments.
We will discuss a theoretical model of polarization-dependent NCS to understand that regime, based on Ref. [3,4] with locally constant field approximation. The information of a polarization mode of an emitted photon provides a finer resolution of the collision process. We will see it by emission probability rates (decay rates). We will also discuss the conceptual design of its experiment at the ELI-NP laser facility .