Manipulation of $\gamma$ ray polarization in Compton scattering

High-brilliance high-polarization $\gamma$ rays based on Compton scattering are of great significance in broad areas, such as nuclear, high-energy, astro-physics, etc. However, the transfer mechanism of spin angular momentum in the transition from linear, through weakly into strongly nonlinear processes is still unclear, which severely limits the simultaneous control of brilliance and polarization of high-energy $\gamma$ rays. In this work, we investigate the manipulation mechanism of high-quality polarized $\gamma$ rays in Compton scattering of the ultrarelativistic electron beam colliding with an intense laser pulse. We find that the contradiction lies in the simultaneous achievement of high-brilliance and high-polarization of $\gamma$ rays by increasing laser intensity, since the polarization is predominately contributed by the electron spin via multi-photon absorption channels. For instances, the spin-polarized electrons in high-intensity laser pulse can radiate high-brilliance high-polarization $\gamma$ rays, while, for the spin-nonpolarized electrons, to achieve the similar high-quality $\gamma$ beams with the same laser, the electrons must hold higher energies due to the spin contribution mainly from the laser via the single-photon absorption channel. Moreover, we confirm that the signature of $\gamma$ ray polarization can be applied for observing the nonlinear effects (multi-photon absorption) of Compton scattering with moderate-intensity laser facilities.