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.
© 2015 Optical Society of America
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
E
0
rexpiδ
1
jRiexpiδ
2
jLi, where r; θ are the polar
coordinates, E
0
is the background field, δ
1
l
R
θ θ
0
∕2
and δ
2
l
L
θ − θ
0
∕2 are phase distributions, l
R
and l
L
denote
the topological charges of spiral phases of the two sub-beams,
θ
0
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
0146-9592/15/194444-04$15/0$15.00 © 2015 Optical Society of America
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