利用圆形弧相控阵通过扭曲光子实现信号复用
Multiplexing signals with twisted photons by a circular arc phased array
AI总结：
本文提出利用圆形弧相控阵接收扭曲光子实现信号复用，理论分析了通道数与圆弧角度的关系，并给出病态问题缓解方法及条件数估计。
摘要：
本文发展了利用均匀圆形阵列（UCA）产生的扭曲光子进行电磁信号复用的理论，适用于接收天线为位于圆弧上的单元阵列的情形。辐射单元具有特定的电流分布，通常不是点源。所产生电磁波的极化被充分考虑。引入了$N$阶离散扭曲光子的概念，并建立了这些模式模$N$正交性。同时考虑了近轴和平面离散扭曲光子。获得了接收信号的显式表达式。研究表明，在最简单的情形下，接收阵列天线所在圆弧减小$K$倍会导致独立信息通道数量减少$K$倍。在更复杂的方法中，通过位于中心角为$2π/K$的圆弧上的$N$个单元阵列天线接收信号，可以恢复所有$N\gg1$个独立信息通道。然而，随着$K$的增加，该问题迅速变得病态。本文描述了缓解此问题的方法，并给出了相应条件数的估计。还研究了波束控制的情形，即UCA产生的辐射集中在接收圆弧阵列天线附近。在此情况下证明了信息通道的正交性，并求得了相应的变换矩阵及其条件数。
英文摘要：
The theory of multiplexing electromagnetic signals by means of twisted photons generated by a uniform circular array (UCA) is developed in the case when the receiving antenna represents an array of elements located on a circular arc. The radiating elements are characterized by certain current distributions and are not points, in general. The polarization of created electromagnetic waves is fully taken into account. The notion of discrete twisted photons of the order $N$ is introduced and orthogonality of these modes modulo $N$ is established. Both paraxial and planar discrete twisted photons are considered. The explicit expressions for the signals received are obtained. It is shown that, in the simplest scenario, a $K$ times decrease of the circular arc where the receiving array antenna is placed results in a $K$ times decrease of the number of independent information channels. In the more sophisticated approach, one can restore all $N\gg1$ independent information channels in receiving the signal by an array antenna with $N$ elements located on a circular arc with the central angle $2π/K$. However, this problem becomes rapidly ill-conditioned as one increases $K$. The method mitigating this issue is described. The estimates for the corresponding condition numbers are found. The scenario with beam steering, where the radiation produced by the UCA is concentrated near the receiving circular arc array antenna, is also investigated. The orthogonality of the information channels is proved in this case and the corresponding transformation matrix and its condition number are found.
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