The generations of the even-order harmonics from H₂⁺ and one of its isotope T₂⁺ have been theoretically investigated beyond the Born-Oppenheimer approximation. Normally, the high-order harmonic generation (HHG) only contains odd-order harmonics for the orbital symmetry along the direction of laser polarization. Here, we showed that due to asymmetric harmonic emission (asymmetric half-wave profile), the even-order harmonics can be generated in the rising and the falling part of the laser field. In detail, in the lower initial vibrational state, the even-order harmonics main come from the falling part of the laser field; while as the initial vibrational state increases, the identified even-order harmonics in the falling part of the laser field are decreased; while some other even-order harmonics coming from the rising part of the laser field can be produced. The interesting phenomena have been proved through studying the spatial distributions and the time profiles of the HHG.

H ₂ ⁺及其同位素之一T ₂ ⁺产生的偶数阶谐波在理论上已经进行了超出Born-Oppenheimer近似的研究。通常，对于沿着激光偏振方向的轨道对称性，高次谐波生成（HHG）仅包含奇数次谐波。在这里，我们表明由于不对称谐波发射（不对称半波轮廓），可以在激光场的上升和下降部分产生偶次谐波。详细地讲，在较低的初始振动状态下，偶次谐波主要来自激光场的下降部分。随着初始振动状态的增加，在激光场下降部分中识别出的偶次谐波减小；同时会产生来自激光场上升部分的其他偶次谐波。