涡旋电子电磁场中非傍轴效应的动力学增强
Dynamical enhancement of nonparaxial effects in the electromagnetic field of a vortex electron
摘要：
电子的量子态影响其电磁场。如果电子波包的空间分布不是高斯分布，则粒子可能获得额外的固有多极矩，这会改变其场，特别是在小距离处。本文利用广义（非傍轴）拉盖尔-高斯光束，以保留电四极项的多极展开形式，得到了具有轨道角动量$\ell$的涡旋电子的场。四极贡献超出了傍轴近似，是线性增强的高度扭曲的包与$|\ell| \gg 1$，并可以是重要的扭曲光束与散装物质和人工结构的相互作用。此外，该项导致电子的静止坐标系中的磁场的方位角不对称性，这是由于包随时间的扩展而出现的。因此，与物理直觉有些相反的是，扩散可能会增强非傍轴现象。对于可用的电子束，这种不对称性原则上可以可靠地检测到，这将是涡旋电子的非傍轴效应的实验证据。
英文摘要：
A quantum state of an electron influences its electromagnetic field. If a spatial profile of the electron wave packet is not Gaussian, the particle may acquire additional intrinsic multipole moments, which alter its field, especially at small distances. Here the fields of a vortex electron with orbital angular momentum $\ell$ are obtained in a form of a multipole expansion with an electric quadrupole term kept by using the generalized (non-paraxial) Laguerre-Gaussian beams. The quadrupole contribution arises beyond a paraxial approximation, is linearly enhanced for highly twisted packets with $|\ell| \gg 1$, and can be important for the interactions of twisted beams with bulk matter and artificial structures. Moreover, this term results in an azimuthal asymmetry of the magnetic field in a rest frame of the electron, which appears thanks to the spreading of the packet with time. Thus, somewhat contrary to physical intuition, the spreading may enhance non-paraxial phenomena. For the available electron beams, this asymmetry can in principle be reliably detected, which would be experimental evidence of a non-paraxial effect with the vortex electrons.
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