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We show how the semiclassical formulas for radiation emission of Baier,Katkov and Strakhovenko for arbitrary initial and final spins of the electronand arbitrary polarization of the emitted photon can be rewritten in a formwhich numerically converges quickly. We directly compare the method in the caseof a background plane wave with the result obtained by using the Volkov statesolution of the Dirac equation, and confirm that we obtain the same result. Wethen investigate the interaction of a circularly polarized short laser pulsescattering with GeV electrons and see that the finite duration of the pulseleads to a lower transfer of circular polarization than that predicted by theknown formulas in the monochromatic case. We also see how the transfer ofcircular polarization from the laser beam to the gamma ray beam is graduallydeteriorated as the laser intensity increases, entering the nonlinear regime.However, this is shown to be recovered if the scattered photon beam iscollimated to only allow for passage of photons emitted with angles smallerthan $1/\gamma$ with respect to the initial electron direction, where $\gamma$is the approximately constant Lorentz factor of the electron. The obtainedformulas also allow us to answer questions regarding radiative polarization ofthe emitting particles. In this respect we briefly discuss an application ofthe present approach to the case of a bent crystal and high-energy positrons.

Numerical approach to the semiclassical method of radiation emission for arbitrary electron spin and photon polarization