中文摘要：

原子在强激光电场中高次谐波辐射的理论与实验研究是当今科学前沿之一.利用量子力学理论和鞍点方法,细致地研究了高次谐波辐射光子的能量与激光相位的关系.对于时间宽度无限长激光,在一个激光周期内特定相位处产生的高阶辐射（X射线）有特定的能量.能量分布在71.80°处成峰,有高斯形函数的对称形状.给出了这种分布的参数化公式.对于不同宽度的飞秒激光,能量分布的成峰位置、最大值和带宽等参数会发生变化.计算表明,三个振荡周期（半高宽）的飞秒激光,当载波-包络相位为17.5°和105°时,可以分别得到纯净的阿秒单脉冲和双脉冲.在能量-相位图上,基本对称的单脉冲峰位为载波相位53.86°,宽度53.34°;高度基本相同的双脉冲峰位分别为-31.51°和143.81°,宽度分别72.19°和73.34°,相位间隔175.33°.这些研究结果,有助于研究超短X射线脉冲的产生、分离、测量和应用.

英文摘要：

The behavior of an atom in strong laser field and the dynamic process of high-order harmonic generation （HHG） are analyzed with the quantum theory and saddle-point method. Within a laser optical cycle of a long duration laser, the relations between the radiative energy and the laser phase of HHG show a Gaussian-like distribution which peaks at 71.80°. A parameterized formula is deduced to calculate the high harmonic emission duration and the bandwidth of the HHG energy-phase distribution. The peak position, maximum and the bandwidth of a selected energy-phase distribution pulse depend on the laser parameters. Calculations show that a pure single （double） energy-phase distribution pulse（s） can be generated by a 3-cycle laser with a carrier-envelope phase of 17.5°（105°） . A single symmetric energy-phase distribution pulse peaks at the carrier phase of 53.86° and spans 53.34°. The double energy-phase distribution pulses separated by 175.33° have the same height. They peak at - 31.51° and 143.81°, and span 72.19°and 73.34°, respectively. These results may be useful for researches of ultra-short X-ray generation, pulse separation, measurement and its application.