  The angular drift of a laser beam is of particular concern in applications
such as seeded free-electron lasers. A systematical study of the obliquely
incident laser and electron beam interaction in an undulator is presented in
this paper. Theoretical analysis and numerical simulations demonstrate that the
interaction would imprint energy and angular modulations on the electron beam
simultaneously. Compared with the normally incident pattern, the obliquely
incident laser-electron interaction leads to reductions in the bunching factors
of HGHG and EEHG. In the meanwhile, proactive applications of this
multi-dimensional modulation technique may bring vitality to the field of
laser-electron manipulation
