Arbitrarily shaped retro-reflector by
optics surface transformation
Fei Sun (孙 非)
1
, Yichao Liu (刘一超)
1,
*, Yibiao Yang (杨毅彪)
1
,
Zhihui Chen (陈智辉)
1
, and Sailing He (何赛灵)
2,
**
1
Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education and Shanxi Province,
College of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China
2
Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation,
National Engineering Research Center for Optical Instruments, Zhejiang University, Hangzhou 310058, China
*Corresponding author: liuyichao@tyut.edu.cn; **corresponding author: sailing@zju.edu.cn
Received May 19, 2020; accepted June 23, 2020; posted online August 27, 2020
A novel way to design arbitrarily shaped retro-reflectors by optics surface transformation is proposed. The entire
design process consists of filling an optic-null medium between the input and output surfaces of the retro-
reflector, on which the points have 180 deg reverse corresponding relations. The retro-reflector can be designed
to be very thin (a planar structure) with high efficiency. The effective working angles of our retro-reflector are
very large (from −80 deg to +80 deg), which can, in principle, be further extended. Layered metal plates and zero
refractive index materials are designed to realize the proposed retro-reflector for a TM polarized beam.
Keywords: retro-reflector; optics surface transformation.
doi: 10.3788/COL202018.102201.
A retro-reflector can reflect incoming light back to its
source with minimal scattering in other directions (the
reflected wave is always parallel to, but in the opposite
direction of, the incoming wave; see Fig.
1). If the angle
of the incoming wave changes, the direction of the re-
flected wave will change accordingly. Retro-reflectors
have been widely used in our daily life (warning indicators,
life-saving indicators, road signs, reflective vests, commu-
nication systems, etc.). A retro-reflec tor can be placed
on a moving platform without requiring the component
to be aligned, which makes them very convenient in opti-
cal measurements
[1]
, navigation
[2]
, optical free space com-
munication
[3]
, laser trackers
[4]
, sensing
[5]
, head-mounted
display
[6]
, etc.
Two classical methods, designed using geometrical op-
tics, to achieve a retro-reflection are corner -cube reflectors
(three mutually perpendicular flat mirrors)
[7]
and cat’s
eyes reflectors (two concentric hemispheres with different
radii)
[8]
. However, for these classical retro-reflectors, the
effective working angles are limited, and they are both
bulk devices (not easy to integrate practically). In recent
years, new ways to achieve a retro-reflection based on an
Eaton lens
[9]
and meta-surfaces have been introduced
[10]
.
An Eaton lens with transmuted singularity can achieve
a full-angle (360 deg) retro-reflection
[9]
. However, it re-
quires inhomogeneous media (refractive index is not con-
stant), and it is still a bulk device (not a compact planar
structure). Recently, a planar meta-surface retro-reflector
(two cascaded meta-surfaces) has been design ed and fab-
ricated
[10]
. The planar shape of the meta-surface retro-
reflector (very thin and lightweight) makes it very easy
to integrate with planar modulators. However, its effi-
ciency drops quickly, as the viewing angle changes from
0 deg (nearly 78%) to 50 deg (nearly 16%).
In this study, we design an arbitrary-shaped retro-
reflector with high efficiency and wide working angles
using a novel theory, optical surface transformation
(OST)
[11,12]
, which is a new branch of transformation optics
(TO)
[13–15]
and has been widely applied to various fields in
recent years. In TO, a coordinate transformation method
is used to design optical devices (transformation media),
transforming from the fields and materials in the reference
space to the fields and materials in the real space. Many
novel optical devices that cannot be designed by tradi-
tional methods have been designed by TO, such as
invisibility cloaks
[13]
, optical black holes
[16]
, and optical
wormholes
[17,18]
. In recent years, some novel methods based
on TO have been proposed to design retro-reflectors
[19,20]
.
However, these TO-based methods require complex math-
ematical calculations (coordinate transformations and
tensor calculations). The required materials designed by
TO are complicated (often inhomogeneous, anisotropic,
and magnetic). Once a geometrical parameter (shape or
size) changes, the devices must be redesigned, and the re-
quired materials change correspondingly. OST provides
a much simpler way to make designs, in which only the
geometrical shape of the device and how to fill the optic-
null medium (ONM) inside the device (choosing the
Fig. 1. Different types of reflection: (a) specular reflection,
(b) diffuse reflection, and (c) retro-reflection.
COL 18(10), 102201(2020) CHINESE OPTICS LETTERS October 2020
1671-7694/2020/102201(5) 102201-1 © 2020 Chinese Optics Letters