The generations of the even-order harmonics from vibrating H2+ have been theoretically investigated and identified. The results showed that due to asymmetric harmonic emission (asymmetric half-wave profile) on the rising and the falling parts of the laser field, the even-order harmonics can be generated. In detail, for the case of the lower initial vibrational state, the even-order harmonics mainly come from the falling part of the laser field; while as the initial vibrational state increases, the identified even-order harmonics on the falling part of the laser field decreases; while some other even-order harmonics coming from the rising part of the laser field are gradually enhanced.
