Generation of arbitrary vector vortex beams
on hybrid-order Poincaré sphere
Zhenxing Liu, Yuanyuan Liu, Yougang Ke, Yachao Liu, Weixing Shu, Hailu Luo,* and Shuangchun Wen
Laboratory for Spin Photonics, School of Physics and Electronics, Hunan University, Changsha 410082, China
*Corresponding author: hailuluo@hnu.edu.cn
Received September 13, 2016; revised November 8, 2016; accepted November 8, 2016;
posted November 11, 2016 (Doc. ID 275720); published December 16, 2016
We propose theoretically and verify experimentally a method of combining a q-plate and a spiral phase plate to
generate arbitrary vector vortex beams on a hybrid-order Poincaré sphere. We demonstrate that a vector vortex
beam can be decomposed into a vector beam and a vortex, whereby the generation can be realized by sequentially
using a q-plate and a spiral phase plate. The generated vector beam, vortex, and vector vortex beam are verified and
show good agreement with the prediction. Another advantage that should be pointed out is that the spiral phase
plate and q-plate are both fabricated on silica substrates, suggesting the potential possibility to integrate the two
structures on a single plate. Based on a compact method of transmissive-type transformation, our scheme may
have potential applications in future integrated optical devices. © 2016 Chinese Laser Press
OCIS codes: (260.5430) Polarization; (050.4865) Optical vortices; (350.1370) Berry's phase.
https://doi.org/10.1364/PRJ.5.000015
1. INTRODUCTION
In recent years, the vector beam [1], known as possessing a
spatially inhomogeneous polarization state, and the vortex
beam with spiral wavefronts [2] have been widely studied in
various aspects because of these respective intriguing proper-
ties and widespread applications, such as high-resolution im-
aging [1], vectorial structure and propagation model analysis
[3,4], bottle-hollow beam generation [5], and optical micros-
copy [6,7] for the vector beam; and data transmission [8],
optical tweezers [9], and optical trapping [10] for the vortex
beam. Most previous works focused on the complex manipu-
lation of cross-sectional polarization, especially on the vector
beam, which has intrinsic polarization symmetry.
Unlike a conventional homogeneous polarization state
represented by the fundamental Poincaré sphere [11], a vector
beam can be geometrically mapped by a higher-order Poincaré
sphere (HOPS) [12,13]. On the other hand, although a vortex
beam has a distribution of homogeneous polarization, its op-
tical topological structure possesses orbital angular momen-
tum characterized by expimϕ, where m is the topological
charge and ϕ is the azimuthal angle. Additionally, various ap-
proaches to generate vector beams and optical vortices have
been proposed with impressive performance, such as conical
Brewster prism [14], interferometry [15,16], subwavelength
gratings [17–19], laser intracavity devices [20,21], twisted nem-
atic liquid crystals [22–24], and metallic nanostructures [25–27].
Most recently, because it has both vector polarization and
helical phase, the vector vortex beam has been proposed and
explored in a range of advanced optical schemes, such as vec-
torial optical vortex filtering [28], particle acceleration [29],
photon entanglement [30], beam focusing [31], and the pho-
tonic spin Hall effect [32,33]. Compared with a single vector
beam and a single vortex beam, a vector vortex beam provides
more degrees of freedom in beam manipulation [31,34,35].
Encouraged by these advantages, a great variety of impressive
generation has also been demonstrated, including a spatial
light modulator [36], a liquid-crystal-based polarization con-
verter [37], a laser resonator configuration [20], and modified
interference of different modes [38,39]. However, the gener-
ated polarization states in previous works are usually referred
to as two special cases, azimuthal and radial polarization.
Additionally, these methods usually face challenges of low
damage threshold, lower conversion efficiency, and enormous
size. Therefore, to generate arbitrary vector vortex beams, a
flexible generation method of high efficiency and compact
structure should be taken into account.
In our work, to generate an arbitrary vector vortex beam on
the hybrid-order Poincaré sphere (HyOPS) [40], a flexible and
simple approach using the combination of an inhomogeneous
birefringent q-plate and a spiral phase plate is proposed. We
use a q-plate to convert a homogeneous polarized light beam
into a vector beam. Then, after passing through a spiral phase
plate, the vector beam is converted into a vortex-carrying vec-
tor beam, that is, a vector vortex beam. Here, although a spiral
phase plate is not a new product to be proposed to generate
vortex-carrying beams, it actually plays a new and crucial role
in the conversion from vector beam to vectorial vortex beam.
Moreover, the spiral phase plate and q-plate could be inte-
grated with the existing optical elements which enables the
generation of compact devices with multifunction.
2. THEORY
We now use a HyOPS to describe the state of a vector vortex
beam. Figure 1 depicts a HyOPS with l 0 and m 2. The
north and south poles represent two orthogonal bases, jN
l
i
and jS
m
i. Here, l and m are the topological charges. Since the
orthogonal circular polarization eigenstates are a Laguerre–
Gauss beam and a fundamental-mode Gauss beam, the HyOPS
can map the polarization and phase of arbitrary vector vortex
beams on its surface, leading to a more general representation
Liu et al. Vol. 5, No. 1 / February 2017 / Photon. Res. 15
2327-9125/17/010015-07 © 2017 Chinese Laser Press