Polarization evolution of vector beams
generated by q-plates
WEIXING SHU,
1,4
XIAOHUI LING,
2,3
XIQUAN FU,
1
YACHAO LIU,
2
YOUGANG KE,
2
AND HAILU LUO
2,5
1
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
2
Laboratory for Spin Photonics, School of Physics and Electronics, Hunan University, Changsha 410082, China
3
College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang 421002, China
4
e-mail: wxshu@hnu.edu.cn.
5
e-mail: hailuluo@hnu.edu.cn.
Received 4 November 2016; accepted 1 January 2017; posted 6 January 2017 (Doc. ID 280016); published 9 February 2017
The polarization evolution of vector beams (VBs) generated by q-plates is investigated theoretically and exper-
imentally. An analytical model is developed for the VB created by a general quarter-wave q-plate based on vector
diffraction theory. It is found that the polarization distribution of VBs varies with position and the value q.In
particular, for the incidence of circular polarization, the exit vector vortex beam has polarization states that cover
the whole surface of the Poincaré sphere, thereby constituting a full Poincaré beam. For the incidence of linear
polarization, the VB is not cylindrical but specularly symmetric, and exhibits an azimuthal spin splitting. These
results are in sharp contrast with those derived by the commonly used model, i.e., regarding the incident light as a
plane wave. By implementing q-plates with dielectric metasurfaces, further experiments validate the theoretical
results.
© 2017 Chinese Laser Press
OCIS codes: (260.5430) Polarization; (160.3918) Metamaterials; (260.1960) Diffraction theory; (050.2555) Form birefringence;
(350.1370) Berry’s phase; (050.4865) Optical vortices.
https://doi.org/10.1364/PRJ.5.000064
1. INTRODUCTION
Vector beams (VBs) with inhomogeneous polarization have
lately attracted much attention [1]. Different from the common
homogeneously polarized beams, VBs have unique optical prop-
erties owing to their inherent symmetry. For example, a radially
polarized light beam, when tightly focused, can have a strong
longitudinal and nonpropagating electric field [2], resulting
in a sharper focus than a homogeneously polarized beam [3].
This result leads to significant enhancements in the interaction
between light and material [4] and in the microscope resolution
[5]. In addition, an azimuthally polarized beam can be highly
focused into a hollow dark spot [3,6]. Due to their distinguished
properties, VBs have found applications in a variety of realms
ranging from classical to quantum optics. In classical optics, VBs
have be used in optical trapping [7], optical microfabrication
[8], ultra-sensitive metrology [9], high-resolution imaging
[5,10], optical data storage [11], polarization encryption [12],
and optical communications [13]. In the quantum regime, VBs
have been applied to create hybrid entangled states exploiting
the polarization and the spatial degrees of freedom to realize
quantum communications [14,15].
Motivated by these applications, various methods for
generating VBs have been proposed [1], which may be divided
into two classes. One is the intracavity generation technique
involving the cohere nt summation of two orthogonally polar-
ized modes inside either the laser resonator [16,17] or optical
fibers that are also cylindrically symmetric resonators [18,19].
The other method is the extracavity generation that includes the
interferometric combination of orthogonally polarized beams
[20–27] and the direct conversion of uniformly polarized light
using polarization-sensitive optical elements. Such optical ele-
ments can be implemented by segmented birefringent crystals
[28,29], subwavelength diffractive gratings [30–32], and twisted
liquid crystals [33,34]. These devices are characterized by
singular optic axis distributions with topological charge q and
are usually called q-plates [33].
The VBs generated by the direct conversion method are
often analyzed by regarding the light beam as a plane wave in
the literature. Actually, this simplified model can conveniently
account for the vector polarization generated by the commonly
used half-wave q-plates [35–38
]. For these q-plates there occurs
a complete conversion between the two circular polarization
components of the incident light [33], and thus the polariza-
tion of the combined VB is the same as that obtained by replac-
ing the beam with a plane wave and does not change upon
propagation [39].
However, for a q-plate with an arbitrary phase retardation,
this plane wave model may not hold true. For a general
q-plate, an incomplete cross-polarization conversion may occur
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Vol. 5, No. 2 / April 1 2017 / Photonics Research
Research Article
2327-9125/17/020064-09 Journal © 2017 Chinese Laser Press