Controlling the Polarization and Vortex Charge of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi></mml:math> Photons via Nonlinear Compton Scattering

High-energy vortex γ photons have significant applications in many fields. However, their generation and angular momentum manipulation are still great challenges. Here, we first investigated the generation of vortex γ photons with controllable spin and orbital angular momenta via nonlinear Compton scattering of two-color counter-rotating circularly polarized (CP) laser fields. The radiation probabilities of vortex photons are calculated using the semiclassical approach that resolves angular momenta of emitted photons. We find that the angular momenta transferred to emitted photons are determined by the dominating photon absorption channel, leading to a structured spectrum with alternations in helicity and twist directions. By tuning the relative intensity ratio of the two-color CP laser fields, the polarization and vortex charge of the emitted γ photons can be controlled, enabling the generation of CP vortex γ photons with a user-defined polarization and topological charge, which may have multiple applications in nuclear physics, astrophysics, particle physics, etc.