瑞利和泰勒平面波多极级数近似的空间相位延迟效应比较
Comparison of the spatial-phase retardation effects between Rayleigh and Taylor plane-wave multipole series approximations
摘要：
随着实验学家探索由当前一代光源提供的强场辐射的新机会，新的理论工具在处理由于激光强度增加和波长更短而发挥作用的具有挑战性的非线性动力学方面变得不可避免。虽然许多理论研究采用电偶极子近似的方便的原因，在强场制度的有效性，这种近似是值得怀疑的。我们已经做了详细的比较的延迟项，$e^{i\mathbf{k} \cdot \mathbf{r}}$在泰勒和瑞利级数多极近似与径向矢量和传播方向之间的角度任意选择为$45^{\circ}$的扩展。本文证明了瑞利平面波展开式比泰勒展开式具有更大的适用范围。我们还注意到，泰勒近似的球面贝塞尔函数再现的下限，定期球面贝塞尔函数，但严重偏离的渐近区域。我们的结论是，使用瑞利平面波展开提供了最准确的贡献，任何给定的顺序的多极展开。利用短波长强激光脉冲与处于基态的氢原子相互作用，用这些近似方法预测的偶极和非偶极光电子能谱的差异表明了泰勒展开式中缺少的高阶项的重要性。
英文摘要：
As experimentalists explore new opportunities in strong field radiation offered by current generation light sources, new theoretical tools become inevitable in dealing with the challenging non-linear dynamics that come into play as a result of the increasing laser intensities and the shorter wavelengths. While many theoretical studies employ the electric dipole approximation for convenience reasons, in the strong-field regime the validity of this approximation is questionable. We have made a detailed comparison of the expansion of the retardation term, $e^{i\mathbf{k} \cdot \mathbf{r}}$ in both Taylor and Rayleigh series multipole approximations with the angle between the radial vector and the direction of propagation chosen arbitrarily to be $45^{\circ}$. It is verified in this paper that the Rayleigh plane-wave expansion provides a larger validity range in comparison to the widely used Taylor expansion. We also take note that the Taylor approximated spherical Bessel functions reproduce the lower limits of the regular spherical Bessel functions but deviates strongly in the asymptotic region. We conclude that the use of the Rayleigh plane-wave expansion provides the most accurate contribution of any given order of the multipole expansion. The discrepancy in the dipole and non-dipole photoelectron energy spectra as predicted by these approximations using short-wavelength intense laser pulses interacting with hydrogen atom in its ground state show the importance of the higher-order terms absent in the Taylor expansion.
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