电磁场中的角动量是怎样调集进去的──费曼圆盘佯谬与角动量守恒的初等论证

本文以费曼所提出的圆盘佯谬为例，首先计算出磁场消失过程中圆盘所获得的机械角动量，再分析在建立稳态电磁场过程中升力矩的作用，由动量矩定理引入电磁角动量的概念，进而对佯谬中的角动量守恒给出定量的论证．     

费曼佯谬与电磁场角动量守恒

带电体在转动过程中，机械和电磁场联合系统角动量守恒，本文首先介绍费曼佯谬，然后从理论上提出电磁场角动量的概念，导出电磁场角动量守恒定律，并用带电体与电磁场联合系统角动量守恒的原理揭示了费曼转盘转动的机理。     

静止电磁场的角动量

并不是每个学生都会爽快地相信《费曼物理学》第二卷17.4[1]中的佯谬可以用初始就存在的静止电磁场角动量来解释.这里p是动量密度,它正比于坡印廷矢量[2],这一角动量在电流切断后变为0。为保证电磁角动量与机械角动量构成的总角动量守恒,塑料圆盘将开始旋转. 角动量概念是与绕轴运动相联系的.圆偏振波具有角动量似乎易于理解,因为电场与磁场均绕波传播的方向旋转,静止场具有角动量则难于理解. 下面我们来考虑一个可以绕轴自由旋转的力学系,它可借其上所带的电荷同时激发电场和磁场.它与费曼盘不是雷同的模型,但具有某些相同特性而且优点在于…     

费曼圆盘佯谬

该文讨论了一个表现违反角动 量守恒的佯谬问题，指出传给带电圆盘的 角动量是由于电磁感应的结果，本文通过 找出圆盘角动量的来源解决了这个佯谬．     

Feynman圆盘佯谬与角动量守恒

一、Feynman圆盘佯谬 在《Feynman物理学讲义》第二卷中提出了这样一个佯谬[1],如图1所示,考虑一个无摩擦自由转动的塑料圆盘,圆盘的中部有一个通以稳定电流的细长螺线管,在圆盘的边缘镶上一些带同号等量电荷的金属小球。现在切断电流,这样的操作不致于给圆盘绕轴旋转有什么力矩,因此,似乎圆盘也就不会绕轴旋转。可是根据电磁感应定律,切断电流,磁场消失,在螺线管周围产生涡旋电场,此电场作用于圆盘边缘带电金属小球上的力将使圆盘绕轴旋转。这里就发生了费曼圆盘旋转还是不旋转的作谬问题,费曼在这个佯谬的最后饶有风趣地说:“谁解答了这…     

暗态多极赝局域等离子模式的太赫兹涡旋光激发

理论分析和实验验证了太赫兹涡旋光与带有周期性亚波长金属褶皱圆盘中暗态多极赝局域等离子模式的相互作用.研究结果表明,携带不同轨道角动量和自旋角动量的太赫兹涡旋光可以决定最终激发出的太赫兹暗态多极等离子模式,此结果和光频段的理论分析一致.利用太赫兹近场扫描方法对涡旋光的自旋和轨道角动量与暗态多极等离子模式的对应关系进行了实验论证,实验结果与理论仿真符合较好.研究成果将对太赫兹物理、等离子体以及成像领域研究起到一定的促进作用.     

部分相干光的轨道角动量及其谱的分析研究

针对光束轨道角动量的研究主要集中在相干光束的研究，而对于部分空间相干光束的轨道角动量研究较少，依据部分相干光的Wigner分布函数推导出部分相干光的轨道角动量表达式，分析了部分相干光的轨道角动量谱特性。采用Mercer展开法得到了轨道角动量谱，计算了给定部分相干光束的轨道角动量谱，讨论了部分相干性对轨道角动量谱的影响。研究结果表明：部分相干光和相干光具有相同的轨道角动量表达式，部分相干光的轨道角动量谱随着相干性的变差而愈发弥散，携带轨道角动量的部分相干光束的轨道角动量谱比不携带轨道角动量的部分相干光束的轨道角动量谱更容易受相干度的影响。     

角动量的物理图象

根据角动量的定义，结合图形，分析和讨论角动量计算中各项以及各量的深刻意义，建立角动量的物理图象．明确对点的角动量和对轴的角动量的关系．     

复杂像散椭圆光束的轨道角动量的实验研究

提出一种直接测量光束的轨道角动量的方法，其原理是把具有轨道角动量的光束照射到一个金属靶上，使其在光束的角动量作用下发生转动. 通过测量靶转动的角度来计算光束的角动量值. 对几种不同参数的光束的轨道角动量进行了测量，获得了轨道角动量与光束参数之间的关系，实验结果与理论分析较好地符合. 关键词： 复杂像散椭圆光束 轨道角动量 测量     

角动量的物理图象

根据角运量的定义，结合图形、分析和讨论角动量计算中各项以及各量的深刻意义，建立角动量的物理图象，明确对点的角动量和对轴的角动量的关系。     

电磁场角动量守恒定律的简明推导

对电磁场角动量守恒定律作了一种简明的推导。     

Angular momentum of low frequency electromagnetic fields

The total angular momentum of propagating electromagnetic fields in the SVE-approximation is proportional to the power and the inverse frequency P/ω. This relation holds also in the low frequency range, but is decreasing due to the frequency dependent power of the antennas and becomes zero for ω → 0. Nevertheless, it is possible to generate strong angular momentum at low frequency by non-propagating electromagnetic fields (quasi-static fields).     

Intrinsic angular momentum in HMO

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Contribution of Electromagnetic Field to Atomic Spin

We examine the contribution of electromagnetic field to the atomic spin, by adopting two different, both gauge invariant definitions of the electromagnetic angular momentum: \vec{J}_I ≡ ∫d³ x ε₀ \vec{r} X (\vec{E} X \vec{B}) and \vec{J}_II ≡ ∫d³ x ( ε₀ \vec{E} X \vec{A}^\bot + ε₀ E_i \vec{r} X \vec{\nabla }A^{\bot}_i ). Notably, at the classical level, \vec{J}_II gives an exactly null result while \vec{J}_I gives a finite value. This suggests that \vec{J}_II leads to a simpler and more reasonable picture of the atomic spin, therefore qualifies as a more appropriate definition of the electromagnetic angular momentum. Our observation gives important hint on the delicate issue of gluon contribution to the nucleon spin.     

Rotational Doppler Effect: A Review

Generally, the linear motion between the source of a wave and an observer leads to a linear Doppler effect. It is associated with the linear momentum of the wave. For electromagnetic beams having a circular polarization or an azimuthal phase distribution, the rotation between the source and the observer results in a less well-known rotational Doppler effect. It is associated with the angular momentum of the wave. This is particularly the case for vortex beams. Here, the various physical insights that are given to explain the origin of the rotational Doppler effect is reviewed. The focus is on different cases where such an effect gives information on the rotational nature of the probed systems, and also on cases where the rotational Doppler effect is useless. Still debated issues and possible applications are then presented.     

Lorentz-boosted evanescent waves

Polarization, spin, and helicity are important properties of electromagnetic waves. It is commonly believed that helicity is invariant under the Lorentz transformations. This is indeed so for plane waves and their localized superpositions. However, this is not the case for evanescent waves, which are well-defined only in a half-space, and are characterized by complex wave vectors. Here we describe transformations of evanescent electromagnetic waves and their polarization/spin/helicity properties under the Lorentz boosts along the three spatial directions.     

基于双层超表面的宽带、高效透射型轨道角动量发生器

提出一种宽带、高传输效率的双层超表面,其单元结构是在介质层两边对称刻蚀结构参数相同的十字型金属贴片且将两层超表面沿y方向错位半个周期长度形成.通过引入y方向的错位,双层超表面的透射带宽得到大幅度提升.同时,采用等效电路理论分析了该双层超表面的带宽展宽机理.在此基础上,进一步结合Pancharatnam-Berry相位原...     

Transmissive 2-bit anisotropic coding metasurface

Coding metasurfaces have attracted tremendous interests due to unique capabilities of manipulating electromagnetic wave. However, archiving transmissive coding metasurface is still challenging. Here we propose a transmissive anisotropic coding metasurface that enables the independent control of two orthogonal polarizations. The polarization beam splitter and the orbital angular momentum (OAM) generator have been studied as typical applications of the anisotropic 2-bit coding metasurface. The simulated far field patterns illustrate that the x and y polarized electromagnetic waves are deflected into two different directions, respectively. The anisotropic coding metasurface has been experimentally verified to realize an OAM beam with l = 2 of right-handed polarized wave, resulting from both contributions from linear-to-circular polarization conversion and the phase profile modulation. This work is beneficial to enrich the polarization manipulation field and develop transmissive coding metasurfaces.     

Ku/K波段双频涡旋电磁阵列天线设计

涡旋电磁波具有携带轨道角动量的特性,利用这一特性,采用涡旋电磁波作为信号的载体,可以实现同一时间、同一频段的多路信号传输,极大地提高系统容量和频带利用率。以同轴馈电的半圆型开槽微带天线为单元,设计出了一种能工作在Ku波段和K波段的涡旋电磁阵列天线。使用三维电磁场仿真软件建模并且优化参数,最终得到在中心频率分别为17.1 GHz和19.7 GHz时,阵列天线产生的电磁波携带有轨道角动量。结论表明：该阵列天线能够产生双频涡旋电磁波。