COL 11(9), 091602(2013) CHINESE OPTICS LETTERS September 10, 2013
Design of an optical device with three functions
based on coordinate transformation
Tinghua Li (
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1
, Ming Huang (
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1∗
, Jingjing Yang (
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1
,
Yun Feng (
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)
2
, and Yan Liang (
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1
1
Wireless Innovation Laboratory, School of Information Science and Engineering,
Yunnan University, Kunming 650091, China
2
Radio Monitoring Center of Yunnan, Kunming 650228, China
∗
Corresponding author: huangming@ynu.edu.cn
Received April 19, 2013; accepted July 9, 2013; posted online August 28, 2013
Based on two-step coordinate transformation along the radial direction, an optical device with three
functions is proposed. The proposed device functions as a transparent device, a vision-enabling internal
cloak, and a movement-allowing external cloak. The general expressions of material parameters for the
optical device are determined, and each function of the device is confirmed using full-wave simulation.
The effect of material loss on device performance is also investigated. Future applications for the proposed
device include antenna protection and military stealth.
OCIS codes: 160.1190, 160.3918, 260.2710.
doi: 10.3788/COL201311.091602.
Transformation optics
[1,2]
(TO) is rooted in the ancient
subject of electromagnetics and an emerging field that
has inspired a review of the foundations of classical elec-
tromagnetic theory. TO helps create new paradigms
for the arbitrary control of electromagnetic waves us-
ing metamaterials. Based on the form invariance of
Maxwell’s equations under coordinate transfo rmations,
TO opens up many possibilities for explor ing extraordi-
nary optical phenomena and designing novel functional
devices
[3−6]
. The invisibility cloa k, perhaps one of the
most intriguing TO applications discovered thus far, has
attracted considerable attention in recent years
[7−15]
.
Two main kinds o f TO-based invisibility cloaks are ava il-
able: internal c loaks
[7−11]
and external cloaks
[12,13]
. The
internal cloak c an render whatever it covers undetectable
by steering waves around an enclosed domain. The ob-
ject concea le d by an internal cloak is “blind” because no
external electromagnetic waves can encroach on the hid-
den area and vice-versa. The external c loak removes the
bottleneck of the internal cloak and leaves the hidden ob-
ject out in the open so that it can see its surroundings.
This cloak employs an anti-object to optically cancel the
scattered field from the hidden object. However, a strict
one-to-one correspondence between the po sitions of the
anti-object and the hidden object is required in an ex-
ternal cloak. Thus, once the position of the anti-object
is fixed, the hidden object cannot move free ly. After the
first experimental demonstration of a TO-based meta-
material internal cloak in 2006
[7]
, intensive studies on
TO-based devices with novel functions, such as field rota-
tors, pe rfect lenses, illusion devices, transpare nt devices,
and electromagnetic cavities, have been conducted
[16−20]
.
The scope of TO r esearch has gradually expanded fro m
optics to acoustics
[21]
, ela stodynamics
[22]
, plas monics
[23]
,
and even thermodynamics
[24]
. In earlier investigations,
all theoretical analyses, numerical simulations, and pa-
rameter designs focused mainly on single-function de-
vices. Recently, however, bifunctional device s have been
designed under the theoretical framework of TO
[25−27]
.
In this letter, a proposal based on two-step coordinate
transformation is presented to design an optical device
with three distinct functions. Firstly, the device can serve
as a trans parent device to protect a ntennas or other ra-
dio equipment without affecting their performance. Sec-
ondly, the device functions as a traditional internal cloak
that hides objects fro m view. Thirdly, the device ex-
hibits the beneficial characteristics of a traditional ex-
ternal c loak and allows the hidden object to move freely
within the device. Full-wave simulation by the finite-
element method is performed to verify the performance
of the proposed device. The proposed strategy has po-
tential applications in antenna pr otection, and the device
obtained effectively compensates for the insufficiencies of
traditional internal and external cloaks. The results of
this work could result in a wider range o f applications
beyond that of normal invisibility c loaks.
TO fully uses the form-invariance of Maxwell’s equa-
tions under a spatial coordinate transformation to estab-
lish the equivalence between metric transformatio ns and
changes in material parameters. According to this theory,
the general relationship of material parameters between
original and transformed spaces under a cy lindr ic al coor-
dinate system can be written as
[8,28]
ε
r
/ε
0
= µ
r
/µ
0
= f(r)/rf
′
(r), (1a)
ε
φ
/ε
0
= µ
φ
/µ
0
= rf
′
(r)/f(r), (1b)
ε
z
/ε
0
= µ
z
/µ
0
= f
′
(r)f (r)/r, (1c)
where ε
r
, ε
φ
, ε
z
and µ
r
, µ
φ
, µ
z
are the permittivity
and permeability of the transformed space, respectively.
Here, ε
0
and µ
0
respectively denote the permittivity and
permeability o f the original space. The original space is
assumed to be fr e e space. The transformation equation
between the transformed space and the original space is
f(r), and f
′
(r) represents the derivative of f(r) in rela-
tion to radius r of the transformed space. For simplicity
1671-7694/2013/091602(5) 091602-1
c
2013 Chinese Optics Letters