研究自由传播的扇形柱状矢量涡旋光束的光子自旋霍尔效应

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“Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams” 这篇研究论文深入探讨了自由传播的扇形圆柱矢量涡旋光束在近轴情况下的光子自旋霍尔效应（SHE）。光子自旋霍尔效应是一种量子力学现象，其中光束的自旋角动量导致其在空间中的偏振依赖性分离，这种现象在光子学领域具有重要的理论和应用价值。作者团队，包括YIZHANG、PENGLI、SHENGLIU和JIANLIN ZHAO，来自中国西北工业大学的空间应用物理与化学国家重点实验室和光学信息技术陕西重点实验室。文章于2015年7月10日提交，8月23日完成修订，并于同一天接受发表，最终于9月24日发布。研究中，他们提出了一种基于角谱衍射理论的新型模型来描述这种自由传播的光子SHE。该模型能够精确揭示自旋依赖的分裂与极化方位阶、螺旋相位的拓扑荷以及传播距离之间的紧密关系。这些参数是决定光束行为的关键因素。进一步的研究表明，扇形圆柱矢量涡旋光束的自旋依赖性分裂呈现出不对称性。这意味着光束的自旋状态会影响其在空间中的传播路径，这一特性在光束操控、量子信息处理、光通信和光学微操纵等领域具有潜在的应用前景。通过实验验证，研究人员能够观察到光束在传播过程中由于自旋霍尔效应引起的显著偏移，这证实了理论模型的准确性。这种现象的深入理解和控制将有助于开发新的光子器件和光学技术，例如，可能用于创建更高效的数据传输系统或改进的光学传感器。这项工作对理解并利用光子自旋霍尔效应提供了新的见解，不仅深化了我们对光束动力学的理解，也为未来的光子学研究和技术创新奠定了基础。

Unveiling the photonic spin Hall effect of

freely propagating fan-shaped cylindrical

vector vortex beams

YI ZHANG,PENG LI,SHENG LIU, AND JIANLIN ZHAO*

Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Shaanxi Key Laboratory of Optical

Information Technology, School of Science, Northwestern Polytechnical University, Xi’an 710072, China

*Corresponding author: jlzhao@nwpu.edu.cn

Received 10 July 2015; revised 23 August 2015; accepted 24 August 2015; posted 24 August 2015 (Doc. ID 245772); published 24 September 2015

An intriguing photonic spin Hall effect (SHE) for a freely

propagating fan-shaped cylindrical vector (CV) vortex beam

in a paraxial situation is theoretically and experimentally

studied. A developed model to describe this kind of photonic

SHE is proposed based on angular spectrum diffraction

theory. With this model, the close dependences of spin-

dependent splitting on the azimuthal order of polarization,

the topological charge of the spiral phase, and the propaga-

tion distance are accurately revealed. Furthermore, it is dem-

onstrated that the asymmetric spin-dependent splitting of a

fan-shaped CV beam can be consciously managed, even with

a constant azimuthal order of polarization. Such a control-

lable photonic SHE is experimentally verified by measuring

the Stokes parameters.

OCIS codes: (050.1970) Diffractive optics; (260.5430) Polarization;

(080.4865) Optical vortices; (270.0270) Quantum optics.

http://dx.doi.org/10.1364/OL.40.004444

The photonic spin Hall effect (SHE), which can be regarded as

the photonic analog of the spin Hall effect occurring in solid-

state systems [1], refers to the separation of right-handed (RH)

and left-handed (LH) circular polarization components

perpendicular to the incide nt plane due to spin–orbit interac-

tion [2,3]. Photonic SHE was first pioneered by Onoda [3] and

experimentally demonstrated by Hosten and Kwiat [4].

Recently, the photonic SHE has attracted intense research in-

terest, and a considerable amount of works have been reported

[5–9] because of its potential applications in metrology and

spintronics [10]. Up to now, the photonic SHE could tradition-

ally be classified into two categories. The first one is also known

as the Imbert–Fedorov shift [11], which occurs when a

bounded light beam is reflected or refracted at the interface

between two media [5–9,12]. The second one occurs when

a polarized beam is observed from a tilted reference frame with

respect to the propagation direction [13,14]. Such a shift occurs

without light–matter interaction and is thus called the geomet-

ric spin Hall effect.

The photonic SHE is generally interpreted in terms of geo-

metric phases [15] and angular momentum dynamics [16]. It is

well known that the geometric phase is strongly related to the

variations of polarization. As a class of beams possessing spa-

tially variant polarization, the cylindrical vector (CV) beams

are, naturally, an ideal candidate for producing photonic SHE.

Most recently, Ling et al. proposed a novel kind of spin-depen-

dent splitting phenomenon based on sym metry broken CV

beams [17–19], which is also called intrinsic photonic SHE.

This enhanced phenomenon exhibits the advantages of being

switchable and independent of beam–surface interaction and is

explained from the perspective of azimuthal phase gradient.

According to the perspective of the azimuthal energy flow of

vortex beams [20,21], the rotation of the peak intensity of the

vortex beams obstructed by a knife edge is independent of the

topological charge. Thus, it is hard to accurately describe

the dependence of the photonic SHE on the azimuthal order

of the vector beam.

In this Letter, we develop a theoretical model for explicitly

explaining the photonic SHE of fan-shaped CV vortex beams

(CV beams with spiral phase) based on angular spectrum

diffraction theory [22]. This model reveals the dependences

of the photonic SHE on the azimuthal order of polarization,

topological charge of the spiral phase, and the propagation

distance. Such a controllable photonic SHE is experimentally

verified by measuring the Stokes parameters. Furthermore, we

realize the conscious management of CV vortex beams with

constant azimuthal order of polarization.

In order to develop a more general model, we investigate the

photonic SHE of CV vortex beams. Generally, a CV vortex

beam can be considered as the superposition of two orthogo-

nally circularly polarized sub-beams with different spiral phases

[23,24]. Supposing a CV vortex beam propagating in the z di-

rection, the incident field can be expressed as E

r;θ

rexpiδ

jRiexpiδ

jLi, where r; θ are the polar

coordinates, E

is the background field, δ

 l

θ  θ

∕2

and δ

 l

θ − θ

∕2 are phase distributions, l

and l

denote

the topological charges of spiral phases of the two sub-beams,

represents the arbitrary phase retardation, and jRi and jLi

denote the RH and LH circularly polarized unit vectors,

4444

Vol. 40, No. 19 / Oc tober 1 2015 / Optics Letters

Letter

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研究自由传播的扇形柱状矢量涡旋光束的光子自旋霍尔效应

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