Polarization of photons scattered by electrons in any spectral distribution

On the basis of the quantum electrodynamics, we present a generic formalism of the polarization for beamed monochromatic photons scattered by electrons in any spectral distribution. The formulae reduce to the components of the Fano matrix when electrons are at rest. We mainly investigate the polarization in three scenarios, i.e., electrons at rest, isotropic electrons with a power-law spectrum, and thermal electrons. If the incident beam is polarized, the polarization is reduced significantly by isotropic electrons at large viewing angles; the degree of polarization caused by thermal electrons is about half of that caused by power-law electrons. If the incident bean is unpolarized, soft γ-rays can lead to about 15% polarization at viewing angles around π/4. For isotropic electrons, one remarkable feature is that the polarization as a function of the incident photon energy always peaks roughly at 1 MeV; this is valid for both the thermal and power-law cases. This feature can be used to distinguish the model of the inverse Compton scattering from that of the synchrotron radiation.