Arbitrarily polarized $γ$-photon source from nonlinear Compton scattering

We investigate the nonlinear Compton photon source for upcoming laser-particle experiments in the collision scenario of high-energy electron beams and relativistic laser pulses. The stronger laser field could not only improve the scattering probability but also induce broader photon beam divergence. To maximize the photon flux in a realistic narrow angular acceptance, we show that a balance must be met for the laser intensity to boost the scattering probability and simultaneously confine its beam divergence. For the currently experiment-concerned $10~\textrm{GeV}$ energy regime, the balanced laser intensity locates in the intermediate intensity regime of $ξ\sim O(1)$. In these regimes of laser intensity and electron energy, the accepted photons within a relatively narrow acceptance are highly polarized in the state closely relating to the polarization of the laser pulse, which actually implies a potential route to finely control the photon polarization via the laser polarization.