RESUMEN
The properties of nonlinear inverse Thomson scattering (NITS) are investigated in the collision between a circularly polarized tightly focused intense laser pulse and a relativistic off-axis electron with numerical simulations. Due to the asymmetric effect of the laser field on the off-axis electrons, the electron trajectory is torqued to the off-axis direction, and the symmetry of the spatial radiation is also destroyed, which causes the concentrations of the radiation in the off-axis direction. With the increase of laser intensity, the torsion effect is more obvious, the radiation collimation improves, the direction turns to sideways. With the increase of electron's initial energy, the direction turns back to backwards and the degree of off-axis effect decreases. In both cases, the power exponentially enhances, the pulse width shortens, the spectrum broadens and super-continuity appears. With the laser intensity, the duration of sideways X-ray pulse from the low-energy (2.61MeV) electron is only 0.2 as, and the normalized intensity reaches 109. While using ultra-high-energy (100MeV) electrons, the duration of backwards γ-ray pulse reaches 1.22 zs, and the normalized intensity reaches 1017. These results help the understanding of nonlinear Thomson scattering and provide important numerical references for the research of NITS as high-quality X-ray and γ-ray sources.