Tunable spin splitting of Laguerre–Gaussian
beams in graphene metamaterials
WENGUO ZHU,
1,2,4
MENGJIANG JIANG,
3,2
HEYUAN GUAN,
1,5
JIANHUI YU,
2
HUIHUI LU,
2
JUN ZHANG,
3
AND ZHE CHEN
3
1
Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Jinan University, Guangzhou 510632, China
2
Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
3
Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, Jinan University,
Guangzhou 510632, China
4
e-mail: zhuwg88@163.com
5
e-mail: ttguanheyuan@jnu.edu.cn
Received 25 July 2017; revised 19 September 2017; accepted 7 October 2017; posted 9 October 2017 (Doc. ID 302961);
published 8 November 2017
Optical spin splitting has attracted significant attention owing to its potential applications in quantum infor-
mation and precision metrology. How ever, it is typically small and cannot be controlled efficiently. Here, we
enhance the spin splitting by transmitting higher-order Laguerre–Gaussian (LG) beams through graphene
metamaterial slabs. The interaction between LG beams and metamaterial results in an orbital-angular-
momentum- (OAM) dependent spin splitting. The upper bound of the OAM-dependent spin splitting is found,
which varies with the incident OAM and beam waist. Moreover, the spin splitting can be flexibly tuned by
modulating the Fermi energy of the graphene sheets. This tunable spin splitting has potential applications in
the development of spin-based applications and the manipulation of mid-infrared waves.
© 2017 Chinese
Laser Press
OCIS codes: (260.5430) Polarization; (050.4865) Optical vortices; (160.3918) Metamaterials; (310.6628) Subwavelength structures,
nanostructures.
https://doi.org/10.1364/PRJ.5.000684
1. INTRODUCTION
Graphene, an atomically thin layer of carbon atoms arranged in
a honeycomb lattice, has attracted significant interest owing
to its superior electronic and optical properties [1–3]. The
conductivity of graphene is very sensitive to external fields, such
that its optoelectronic properties can be precisely tuned [4].
Owing to its unique properties, graphene has been suggested
as an alternative to conventional metal-based structures to
confine light [5], guide surface plasmon polaritons [6], and
manipulate wavefronts [7,8]. The subwavelength metamaterial
structures made of graphene sheets show advantages over those
made of thin metal layers at frequency and amplitude tunable
properties [9]. Recently, the graphene metamaterial has been
experimentally realized in the mid-infrared range [10]. The
metamaterial experiences an optical topological transition from
elliptic to hyperbolic dispersion at a wavelength of 4.5 μm[10].
Spin splitting refers to the spatial separation of two opposite
spin components of bounded light beams reflected from or
transmitted through an interface between two different media
[11–14]. The spin splitting phenomenon was first observed
experimentally by Hosten and Kwiat in 2008 [11]. In their
experiment, a weak measurement was used since the spin
splitting of the transmitted beam through an air–glass interface
was very small—only a fraction of a wavelength [11,12]. Lately,
much larger spin splitting was found by reflected Gaussian
beams near Brewster incidence [13]. Götte and coworkers have
achieved a spin splitting of ten wavelengths near Brewster in-
cidence by properly choosing the incident polarization state
[14]. In 2015, a spin splitting equal nearly to the incident beam
waist w
0
was demonstrated when a one-dimensional Gaussian
beam with w
0
10.2 μm was reflected from an air–glass inter-
face [15]. For a two-dimensional Gaussian beam, however, the
spin splitting could only reach 0.4w
0
. It was demonstrated that
the spin splitting can also be enhanced by metal thin films [16]
and metamaterials [17,18]. Recently, the upper bounds of the
spin splitting of Gaussian incident beams were found, which
were equal to the incident beam waists w
0
[19].
Although less investigated, the beam shifts of higher-order
Laguerre–Gaussian (LG) beams are very interesting [20–22].
When reflected by an interface between two different media,
the complex vortex structures of LG beams will interact with
the angular Goos–Hänchen (GH) and Imbert–Fedorov shifts,
684
Vol. 5, No. 6 / December 2017 / Photonics Research
Research Article
2327-9125/17/060684-05 Journal © 2017 Chinese Laser Press