Micro-patterned liquid crystal Pancharatnam–Berry
axilens
Jiarui Ren (任嘉瑞)
1,†
, Weichang Wang (王炜畅)
1,†
, Weiqiang Yang (杨魏强)
1,†
,
Conglong Yuan (袁丛龙)
1
, Kang Zhou (周 康)
1
, Xiao Li (李 萧)
1
,
Alwin Mingwai Tam (谈铭威)
1,2,4
, Cuiling Meng (蒙翠玲)
2
, Jiatong Sun (孙嘉曈)
3
,
Vladimir G. Chigrinov
2
, Hoising Kwok (郭海成)
2
, Xiaoqian Wang (王骁乾)
1,
*,
Zhigang Zheng (郑致刚)
1
, and Dong Shen (沈 冬)
1
1
Physics Department, East China University of Science and Technology, Shanghai 200237, China
2
ECE Department, Hong Kong University of Science and Technology, Hong Kong 999077, China
3
College of Information Science and Technology, Donghua University, Shanghai 201620, China
4
E-mail: amwtam@ust.hk
*Corresponding author: xqwang@ecust.edu.cn
Received February 7, 2018; accepted April 3, 2018; posted online May 25, 2018
A liquid crystal Pancharatnam–Berry (PB) axilens is proposed and fabricated via a digital micro-mirror-
device-based photo-patterning system. The polarization-dependent device behaves as an axilens for a left-
handed circularly polarized incident beam, for which an optical ring is focused with a long focal depth in
the transverse direction at the output, and an anti-axilens for a right-handed circularly polarized incident beam,
for which an optical ring gradually expands at the output. The modification of the size and the sharpness of the
diffracted ring beam is demonstrated by encoding a positive (negative) PB lens term into the director expression
of a PB (anti-)axicon.
OCIS codes: 230.3720, 160.3710, 050.1965, 230.3120, 260.5430.
doi: 10.3788/COL201816.062301.
Ring beams, sometimes also called annular beams or
hollow beams, have been well studied due to their peculiar
optical features for versatile applications. There are several
possible ways of generating ring beams, e.g., using
Laguerre–Gaussian (LG) modes with specific radial (p)
and azimuthal (l) indices
[1,2]
, making use of a spiral-phase
embedded optical element
[3–7]
, a light source passing
through an axicon-based optical system
[4,8–11]
, etc. Among
these methods, an axicon that usually possesses long focal
depth and high lateral resolution is effective to produce the
ring-shaped beam; thus, it is one of the most prospective
candidates for various applications, for instance, laser
machining
[9]
, laser surgery, and biomedical optics
[8,12,13]
. In-
deed, an axicon can be used to generate a non-diffracting
Bessel beam with the self-reconstruction property;
hence, it has an advantage in the application of optical
tweezers that can simultaneously trap spatially separated
particles
[14]
.
Conical-shaped axicons are conventionally made of op-
tically isotropic materials, such as glass or fused silica
[11,15]
.
Hitherto, researchers have proposed some methods of
fabricating liquid crystal (LC) axicons via a computer-
generated hologram
[16,17]
, patterned electrodes
[18,19]
, and
photoaligning LCs to induce the Pancharatnam–Berry
(PB) phase
[20]
. Distinct from the conventional LC ampli-
tude or phase diffractive optical elements (DOEs)
[21–29]
,
highly efficient PB-phase optical elements (PBOEs)
[30,31]
with continuous space-variant optical axis distributions
possess unique and interesting properties, among which
the investigation on the superposition of multiple distinct
PB phases is of great significance. Moreover, a single
PBOE with the integrated PB phases provides the oppor-
tunity to facilitate the achievement of a compact and ef-
ficient optical system or device, thus leading to the low
manufacture cost and low power consumption
[32–34]
.
In this Letter, we propose a novel polarization sensitive
LC Pancharatnam-Berry phase axilens (PBAL). The
optical properties of the LC PBAL containing a null/
positive/negative PB lens phase are individually investi-
gated under left-handed circularly polarized (LCP) light
and right-handed circularly polarized (RCP) light. In ad-
dition, the electro-optical (EO) behaviors of the proposed
LC PBAL are studied. Due to the flexibility of the param-
eters’ choosing, a PB lens with an arbitrary focal length
and a PB (anti-)axicon with an arbitrary pitch length
can be encoded into the micro-patterned LC PBAL to fac-
ilely modulate the outgoing beam.
Normally, an LC PBOE is a half-wave plate that has its
optical axis in the plane of the substrate with the azimu-
thal angle (α) spatially varying with respect to a fixed lab
axis in a continuous manner
[34]
. The optical axis distribu-
tion of our proposed LC PBAL meets the condition
α ¼ πr∕Λ þm·πr
2
∕2λf ; (1)
where r ¼
x
2
þ y
2
p
denotes the radius from the center
of the device, Λ ¼ 100 μm is the pitch length of the PB
(anti-)axicon, λ ¼ 632.8 nm is the designed wavelength,
and f ¼ 10 cm is the focal length of the PB lens. We
set the integer number m ¼ 1; 0; −1 in order to investigate
COL 16(6), 062301(2018) CHINESE OPTICS LETTERS June 10, 2018
1671-7694/2018/062301(5) 062301-1 © 2018 Chinese Optics Letters