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## Wide-angle method for vortex electromagnetic wave generation using field transformation

Feng Jia-Lin, Shi Hong-Yu, Wang Yuan, Zhang An-Xue, Xu Zhuo
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• #### 摘要

场变换是一种与入射角度无关的新型电磁变换方法, 可对电磁波极化和阻抗进行调控. 本文提出了一种基于场变换理论的大角度入射涡旋电磁波产生方法. 基于该方法设计了一种用于涡旋电磁波生成的人工媒质, 并通过对其仿真验证了所提出的方法. 设计的人工媒质为多层环形结构, 可以透射生成2阶涡旋电磁波, 并且具有较好的入射角度稳定性, 在60°斜入射时仍能产生涡旋电磁波.

#### Abstract

The Field transformation (FT) is a novel theory for controlling the polarization and impedance of electromagnetic waves, which is independent on the angle of incidence. Thus, the FT method is superior for wide-angle devices design. In this paper, we propose a wide-angle method for generating vortex beam based on the FT theory. According to this method, an artificial media for vortex beam generation is designed and simulated, which demonstrates the proposed method. The designed artificial media is a multi-layered structure, which can generate vortex beam of order 2 with an incident angle stability up to 60°.

#### 施引文献

• 图 1  场变换示意图

Fig. 1.  Schematic diagram of the FT medium.

图 2  人工双折射材料: $xyz$轴绕y轴旋转45°变成${x'}y{z'}$, 入射波在$xy$平面内, $\theta$为入射角, ${k_0}$是入射波的波数

Fig. 2.  Artificial birefringence medium: The $xyz$ coordinate is twisted along the y -axis by 45° to the ${x'}y{z'}$ coordinate. The incident plane is x-y plane, $\theta$ is the incident angle, ${k_0}$ is the wave vector of the incident wave.

图 3  Pancharatnam-Berry(几何)相位, 入射波沿y方向照射到单元上, 单元绕y轴旋转$\alpha$, 带来$2\alpha$的相位变化

Fig. 3.  Pancharatnam-Berry phase: When the EM wave incident on the unit along y direction, and the unit rotates $\alpha$ around the y axis, the phase changed $2\alpha$.

图 4  单元模型

Fig. 4.  The model of unit cell.

图 5  (a) ${J_{xx}}$${J_{yy}}的幅度 ; (b) {J_{xx}}$${J_{yy}}$的相位

Fig. 5.  (a) The amplitude of ${J_{xx}}$ and ${J_{yy}}$; (b) the phase of ${J_{xx}}$ and ${J_{yy}}$.

图 6  ${J_{xy}}$${J_{yx}}$的幅度

Fig. 6.  The amplitude of ${J_{xy}}$ and ${J_{yx}}$.

图 7  (a)旋转所形成的介质圆环的主视图, 由100个圆环组成每个圆环的半径为4 mm; (b)介质圆环的侧视图

Fig. 7.  (a) Main view of dielectric rings, it’s consists of 100 rings with radius of 4 mm and thickness of dielectric rings is 30 mm; (b) side view of dielectric rings.

图 8  (a)垂直入射的透射波; (b)介质圆环周围空间的电场分布; (c)13 GHz时右旋圆极化波的幅度; (d)13 GHz时右旋圆极化波的相位

Fig. 8.  (a) The transmission wave while incident angle is 0°; (b) E-field distribution around dielectric rings; (c) amplitude of RCP wave at 13 GHz ; (d) phase of RCP wave at 13 GHz.

图 9  (a) 20°斜入射时的透射波; (b)介质圆环周围空间的电场分布; (c) 20°斜入射时13 GHz的右旋圆极化波的幅度; (c) 20°斜入射时在13 GHz的右旋圆极化波的相位

Fig. 9.  (a) The transmission wave while incident angle is 20°; (b) E-field distribution around dielectric rings; (c) amplitude of RCP wave at 20° oblique incidence; (d) phase of RCP wave at 20° oblique incidence.

图 10  (a) 40°斜入射时的透射波; (b)介质圆环周围空间的电场分布; (c) 40°斜入射时13 GHz的右旋圆极化波的幅度; (d) 40°斜入射时13 GHz的右旋圆极化波的相位

Fig. 10.  (a) The transmission wave while incident angle is 40°; (b) E-field distribution around dielectric rings; (c) amplitude of RCP wave at 40° oblique incidence; (d) phase of RCP wave at 40° oblique incidence.

图 11  (a) 50°斜入射时的透射波; (b)介质圆环周围空间的电场分布; (c) 50°斜入射时13 GHz的右旋圆极化波的幅度; (d) 50°斜入射时在13 GHz的右旋圆极化波的相位

Fig. 11.  (a) The transmission wave while incident angle is 50°; (b) E-field distribution around dielectric rings; (c) amplitude of RCP wave at 50° oblique incidence; (d) phase of RCP wave at 50° oblique incidence.

图 12  (a) 60°斜入射时的透射波; (b) 60°入射时介质圆环周围的电场分布; (c) 60°斜入射时13 GHz的右旋圆极化波的幅度; (d) 60°斜入射时13 GHz的右旋圆极化波的相位

Fig. 12.  (a) The transmission wave while incident angle is 60°; (b) E-field distribution around dielectric rings at 60° oblique incidence; (c) amplitude of RCP wave at 60° oblique incidence; (d) phase of RCP wave at 60° oblique incidence.