Ferroelectric liquid crystals for fast switchable
circular Dammann grating [Invited]
Qi Guo (郭 琦)
1,2,
*, Tian Liu (刘 恬)
1,2
, Xiaoqian Wang (王骁乾)
3,
**,
Zhigang Zheng (郑致刚)
3
, Aleksey Kudreyko
4
, Huijie Zhao (赵慧洁)
1,2
,
V. Chigrinov
5,6,7
, and Hoi-Sing Kwok (郭海成)
6
1
School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191, China
2
Beihang University Qingdao Research Institute, Qingdao 266101, China
3
Physics Department, East China University of Science and Technology, Shanghai 200237, China
4
Department of Medical Physics and Informatics, Bashkir State Medical University, Ufa 450008, Russia
5
School of Physics and Optoelectronic Engineering , Foshan University, Foshan 528000, China
6
State Key Laboratory on Advanced Displays and Optoelectronics Technologies,
The Hong Kong University of Science and Technology, Hong Kong 999077, China
7
Department of Theoretical Physics, Moscow Region State University, Mytishi 141014, Russia
*Corresponding author: qguo@buaa.edu.cn; **corresponding author: xqwang@ecust.edu.cn
Received May 19, 2020; accepted June 3, 2020; posted online June 30, 2020
Diffractive optical elements attract a considerable amount of attention, mainly due to their potential applica-
tions in imaging coding, optical sensing, etc. Application of ferroelectric liquid crystals (FLCs) with photo-
alignment technology in diffractive optical elements results in a high efficiency and a fast response time. In this
study we demonstrate a circular Dammann grating (CDG) with a diffraction efficiency of 84.5%. The achieved
response time of 64 μs is approximately two orders of magnitude faster than the existing response time of nematic
liquid crystal devices. By applying a low electric field (V = 6 V) to the FLC CDG, it is switched between the
eight-order diffractive state and the transmissive diffraction-free state.
Keywords: ferroelectric liquid crystals; photo-alignment; fast switching; diffractive optical elements.
doi: 10.3788/COL202018.080002.
Diffractive optical elements with attractive characteris-
tics, i.e., excellent performance and compact size, are be-
coming increasingly important to a wide range of optical
system technologies
[1–7]
. Thus, an effective method of
design and fabrication of fast-switchable and highly effi-
cient diffractive optical elements is in high demand.
Circular Dammann gratings (CDGs), which generate a
concentric and uniform energy distribution, have many
applications in image coding
[8,9]
, beam shaping
[10]
, vortex
manipulation
[11,12]
, and precise measurements
[13,14]
. Much
effort has been expended to enhance the efficiency and
the uniformity of CDGs by profile optimization
[15–17]
. How-
ever, realization of tunable CDGs has been accomplished
only in recent years. Electro-optical properties of nematic
liquid crystals with a patterned alignment and sensitivity
to the electric field make it possible to fabricate tunable
CDGs, albeit with a relatively slow response time
[18–20]
.
In terms of response time, ferroelectric liquid crystals
(FLCs) are two orders of magnitude faster than the
existing nematic liquid crystals
[21,22]
, which makes FLCs
the promising candidate for a new generation of diffractive
optical elements. However, the intrinsic helix or ferro-
electric domains in FLC can cause scattering, and conse-
quently the efficiency drops. In order to eliminate the
formation of ferroelectric domains, the alignment anchor-
ing needs to be precisely adjusted, and uniform orientation
of the helical axis can be achieved
[23]
. On the other hand,
the operating conditions of the electrically suppressed
helix mode provide a fast response of helix-free switch-
ing
[24]
. Fabrication of FLC CDGs with a fast switching,
low power consumption, and uniform energy distribution
expands possible photonics applications.
In this Letter a prototype of FLC CDGs is demon-
strated. A two-step photo-alignment technique was uti-
lized to generate the patterned orientation of FLCs to
fabricate CDGs that perform as optical ring generators
for unifor m energy distribution. The uniformity and
the efficiency of the diffractive patterns are evaluated.
In addition, the advantage of a fast electro-optical re-
sponse is exhibited.
A circular Dammann grating generates a set of concen-
tric rings with a unifor m energy distribution in the far
field, which are radially patterned. The order is defined
by the number of the diffractive rings. Radially patterned
modulation function tðrÞ of CDG with the period Λ can be
expanded in a linear combination of sine functions:
tðrÞ¼
X
∞
n¼1
C
n
sin
2πnr
Λ
; (1)
where r is the radial coordinate. The Fourier spectrum of
Eq. (
1) is given by
TðqÞ¼
1
π
p
X
∞
n¼1
C
n
n∕Λ
ðn∕Λ þ qÞ
3∕2
δ
1∕2
ðq − n∕ΛÞ; (2)
COL 18(8), 080002(2020) CHINESE OPTICS LETTERS August 2020
1671-7694/2020/080002(4) 080002-1 © 2020 Chinese Optics Letters
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