Electron injection into a laser wakefield by the colliding of two circularly polarized laser pulses is analyzed by the Hamiltonian approach and particle-in-cell simulations. If the pump pulse driving the laser wakefield is right-circularly-polarized, electron injection is found only when the counter-propagating injection pulse is left-circularly-polarized and vice versa. This holds when the injection pulse is at low intensity and has a frequency near the pump pulse frequency ω0. For a moderately intense injection pulse, even if the two pulses have the same polarization, electron injection is found but with less efficiency. It is also found that the injection pulse with the frequency within [0.5ω0,3ω0] can still create electron injection efficiently provided it has the opposite polarization with the pump pulse.
