RESEARCH ARTICLE | DECEMBER 15 2021
Broadband digital coding metasurface holography

Special Collection: Metasurfaces for Photonic Devices
Qiang Xiao ; Qian Ma  ; Liang Wei Wu; Yue Gou; Jia Wei Wang; Wei Han Li; Rui Zhe Jiang; Xiang Wan;
Tie Jun Cui 
J. Appl. Phys. 130, 235103 (2021)
https://doi.org/10.1063/5.0064675
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Broadband digital coding metasurface
holography
Cite as: J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
Submitted: 26 July 2021 · Accepted: 31 October 2021 ·
Published Online: 15 December 2021
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Qian Ma,1,2,3,a) Liang Wei Wu,1,2,3 Yue Gou,1,2,3 Jia Wei Wang,1,2,3 Wei Han Li,1,2,3
Qiang Xiao,1,2,3
1,2,3
Rui Zhe Jiang,
Xiang Wan,1,2,3 and Tie Jun Cui1,2,3,a)
AFFILIATIONS
1
Institute of Electromagnetic Space, Southeast University, Nanjing 210096, China
2
State Key Laboratory of Millimeter Wave, Southeast University, Nanjing 210096, China
3
Center of Intelligent Metamaterials, Pazhou Laboratory, Guangzhou 510330, China
Note: This paper is part of the Special Topic on Metasurfaces for Photonic Devices.
a)
Authors to whom correspondence should be addressed: qianma@seu.edu.cn and tjcui@seu.edu.cn
ABSTRACT
15 April 2025 02:04:53
Digital coding metasurfaces composed of subwavelength meta-atoms can flexibly control electromagnetic waves to achieve holography,
which has great potential in millimeter-wave imaging systems and data storage. In this paper, we propose a 3-bit reflective digital coding
metasurface. The incident linearly polarized waves can be transformed into cross-polarized components with distinct phase responses by
adjusting the rotational and open angles of the coding elements. The 3-bit phase performance can be retained over a wide bandwidth from
12 to 18 GHz by simultaneously changing the rotational and open angles. Based on the proposed broadband metasurface, broadband holography is successfully demonstrated with the optimization of a modified Gerchberg–Saxton algorithm. As a proof of concept, five schemes
with different holograms integrating the letters “S,” “E,” “U,” “X,” and “Z” are simulated from 12 to 18 GHz. Good simulation results validate the performance of the proposed broadband holography, showing a relative bandwidth of 40%. Two prototypes superposing the holograms of letters “U” and “X” are fabricated and measured in a near-field microwave anechoic chamber. The experimental results
corroborate well with simulated results, further supporting the demonstration. We believe that the proposed broadband holography based
on the digital coding metasurface paves a way to wideband applications for microwave imaging, information processing, and holographic
data storage.
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0064675
I. INTRODUCTION
As two-dimensional (2D) planar metamaterial, metasurface
has distinguished abilities to manipulate electromagnetic (EM)
waves by periodically or aperiodically arranging the artificial subwavelength elements in a thin profile. Generalized Snell’s laws1 introducing abrupt phase changes are innovatively put forward, which
accelerates the development of metasurfaces, resulting in the properties of EM wave (amplitude, phase, and polarization) to be flexibly
manipulated, hence accomplishing exciting physical phenomena,
such as perfect lens,2 invisibility cloak3–5 and so on. In 2014, the
concept of digital coding metasurfaces was proposed as a new
method to manipulate the EM waves by using the digital state
manner instead of effective medium paraments from the information perspective,6,43,44 which simplifies the design process and
simultaneously abandons manipulation dimensions. Most
J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
Published under an exclusive license by AIP Publishing
importantly, the digitalization of elements bridges the physical
world and the digital world by enabling physical metasurface to
interact with digital information,7–9 which is analogous to digital
signal processing. Thus, some basic information operations or theories of digital coding metasurfaces have been gradually developed,
from convolution,10 addition,11,12 differentiation, and integration13
operation to information entropy,14–16 speeding up the research of
multi-functional metasurfaces such as beam steering,17,18
polarization-modulation,19,20 and orbital angular momentum
(OAM) generator.21,22 By introducing active components
(positive-intrinsic- negative diodes, varactors, and photodiodes)
controlled by field-programmable gate arrays (FPGA), the digital
programmable metasurfaces are further studied to dynamically
manipulate EM waves by encoding the corresponding sequences in
real-time, and different EM functions are realized, such as
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II. PRINCIPLES OF BROADBAND HOLOGRAPHY
The principle of broadband holography based on the digital
coding metasurface is schematically demonstrated in Fig. 1. The
most important core to realize broadband holography is to carefully
design a broadband metasurface with good performance, which
keeps constant around 45° phase difference of 3-bit digital coding
elements. The proposed broadband metasurface can be achieved by
combining digital coding elements. For 3-bit digital coding case,
the coding elements are encoded as “0,” “1,” “2,” “3,” “4,” “5,” “6,”
and “7,” which have the adjacent phase difference of around 45°
from 12 to 18 GHz with high reflective amplitude. Note that the
incident x-polarized waves are changed to y-polarized waves
through the wave-manipulation of the metasurface. Then, by integrating the optimized hologram of the letter “U” in the metasurface, the image of the letter “U” can be reconstructed and clearly
observed from 12 to 18 GHz when an x-polarized electromagnetic
(EM) wave normally illuminates the proposed metasurface, hence
realizing broadband holography.
The structure of the proposed coding element is depicted in
Figs. 2(a) and 2(b), which are composed of three layers: metal
structure layer, metal-ground layer, and substrate layer. Two
C-shaped symmetrical rings connected with the metal bar of the
width w = 1.5 mm and the length of r = 4.25 mm are printed on the
substrate. The substrate F4B has a thickness of h = 3 mm with relative permittivity 2.6 and loss tangent 0.009. The period p of the
unit cell is optimized to 10 mm. The proposed coding elements can
exhibit broadband performance, similarly performing as the linear
polarization conversion resonator as reported in detail in Ref. 44.
When an x-polarized wave illuminates the coding element of a
rotation angle β = ± 45°, multiple resonate modes supported by the
metal bar and the corresponding C-shaped symmetrical rings are
excited, resulting in polarization conversion and realizing broadband performance. More importantly, the coding element
(β = ± 45°) and its mirror counterpart (β = ∓ 45°) will have the
15 April 2025 02:04:53
nonreciprocity,23,24 space–time-coding metasurfaces,25 and intelligent imaging.26 It is worth mentioning that the programmable
metasurfaces are widely explored and become a potential participant
in the sixth-generation communication system.27–29
Furthermore, metasurfaces can enable holography and become
a potential paradigm of imaging techniques by precisely reconstructing the amplitude and phase information of target objects,
emerging the advantage of low profile, small size, and high resolution compared with traditional holography.30 Recently, various
emerging forms of metasurface holography were proposed, such as
phase-only,31–33 complex amplitude,34,35 helicity-multiplexed,36
and vectorial,37,38 hence facilitating the development of metasurface
holography. Furthermore, OAM is introduced to achieve encrypted
holography with the advantages of numerous OAM orthogonal
modes.39,40 Loading active components in the metasurface, reprogrammable holography can be dynamically realized by updating the
metasurface holograms in real-time.41 However, there is little
research on broadband microwave metasurface holography, which
may further broaden the application boundary of imaging
technology.
Comparing with the earlier work,32 we further expand the
working bandwidth of holography. The imaging efficiencies of the
proposed holography are greater than about 50% from 12 to
18 GHz. In addition, inducing of digital coding metasurfaces
enables the optimization procedures of holograms to be more flexible, and the information of holograms can be easily edited or processed. 360° phase coverage can be achieved by setting different
C-shaped split rings open angles and eight coding elements are
selected as 3-bit digital states. To obtain high imaging efficiency, a
modified Gerchberg–Saxton (GS) algorithm is applied to generate
the final holograms.39,42 We present five proof-of-concept coding
metasurfaces with the holograms of letters “S,” “E,” “U,” “X,” and
“Z,” successfully verifying broadband holography with a relative
bandwidth of 40%.
ARTICLE
FIG. 1. Schematic diagram of broadband metasurface holography. The proposed metasurface is composed of eight digital coding elements: digital “0,” “1,” “2,” “3,” “4,”
“5,” “6,” and “7” with a phase increment of 45°. The letter “U” can be clearly observed from 12 to 18 GHz when x-polarized EM waves illuminate the proposed
metasurface.
J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
Published under an exclusive license by AIP Publishing
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same reflective amplitude with a stable phase difference of 180°. To
achieve the 3-bit phase characteristic of the coding element, four
kinds of coding elements with a phase difference of around 45° can
be obtained by tuning the open-angle α of C-shaped symmetrical
rings and mirroring these coding elements symmetrically to get the
remaining four coding elements.
The full-wave simulation of the unit cell is performed in the
commercial software, Computer Simulation Technology (CST)
Microwave Studio with the unit-cell boundary condition, in which
mutual coupling between adjacent elements can be taken into consideration. The entire 360° phase coverage can be achieved by
changing the combination of (α, β) under the illumination of an
x-polarized wave. It means that 180° phase coverage can be
extended to 360° phase coverage by a mirror operation of the rotational angle β in the above coding elements. To simplify the design
process, the eight digital coding elements with different combinations of (α, β) = (40°, 45°), (65°, 45°), (90°, 45°), (115°, 45°), (40°,
−45°), (65°, −45°), (90°, −45°), and (115°, −45°), in which the adjacent phase difference is around 45° from 12 to 18 GHz, are carefully selected to realize the entire 3-bit phase coverage and hence
mimic the digital states: “0,” “1,” “2,” “3,” “4,” “5,” “6,” and “7,” as
shown in Fig. 2(d). The reflected amplitude of the cross-polarized
J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
Published under an exclusive license by AIP Publishing
15 April 2025 02:04:53
FIG. 2. The geometry structure of broadband coding element and the corresponding reflective performance. (a) and (b) The designed coding element. (c) and (d) The
simulated reflective amplitude and phase response of 3-bit coding elements from 10 to 18 GHz.
state is greater than −3 dB in Fig. 2(c). The eight digital coding elements have better broadband performance with the phase difference of around 45° from 12 to 18 GHz, which ensures that
broadband holography based on the proposed digital coding metasurface can be accomplished over a wide working frequency.
III. RESULTS
To demonstrate the performance of broadband holography
based on digital coding metasurface, five kinds of broadband metasurfaces superposing with the phase-only holograms of letters “S,”
“E,” “U,” “X,” and “Z” are, respectively, proposed. Then, the holograms of the above-mentioned letters should be calculated. In practice, the near-field imaging area is usually close to the feed and the
metasurface in microwave holography, resulting in that the imaging
field distribution will be interfered with by the incident wave. The
holograms are optimized by a modified Gerchberg–Saxton (GS)
algorithm, which considers the effect of the incident wave to adaptively iterate the corresponding perfectly matched phase distributions. As a proof of concept, the optimized holograms of letters
“S,” “E,” “U,” “X,” and “Z” at the initial imaging locations of
320 mm with the center frequency of 15 GHz are calculated by the
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FIG. 3. The calculated holograms and the corresponding configuration of the designed metasurface. (a)–(e) The optimized holograms by a modified GS algorithm superposing letters “S,” “E,” “U,” “X,” and “Z,” respectively. (f )–(k) The coding elements distributions of five metasurfaces with letters “S,” “E,” “U,” “X,” and “Z,” respectively.
reconstructed from 12 to 18 GHz. The concrete relation between
the locations, the effective sizes of holographic images, and the
working frequency are described as follows:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(x x1 )2 þ (y y1 )2 þ z12 z1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2πf2
(x x2 )2 þ (y y2 )2 þ z22 z2 ,
¼
c
2πf1
c
(1)
where f1 and f2 are two different working frequencies, c is the propagation speed of EM waves in free space, (x, y) are the coordinates
of the coding elements, and (xi , yi , zi ) represent the coordinates of
15 April 2025 02:04:53
above modified GS algorithm, as shown in Figs. 3(a)–3(e).
According to the above-optimized holograms, five corresponding
coding metasurfaces are, respectively, designed as Figs. 3(f )–3( j),
each of which consists of 30 × 30 elements with a total size of
300 × 300 mm2 (15 × 15 λ2).
The above digital coding metasurfaces are simulated by the
time-domain solver of CST Microwave Studio with the openboundary condition. Meanwhile, a standard waveguide working
from 12 to 18 GHz is served as an exciting source, normally placed
at a distance of 180 mm from the center of the metasurface and
thus illuminating five metasurfaces, respectively. The simulated
near-field results are depicted in Figs. 4(a)–4(e). As can be
observed, letters “S,” “E,” “U,” “X,” and “Z” can be clearly
FIG. 4. Full-wave simulated results.
(a)–(e) The intensity distributions of
letters “S,” “E,” “U,” “X,” and “Z” from
12 to 18 GHz at different locations,
respectively.
J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
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FIG. 5. The prototype of metasurface
and experimental setup. (a) The metasurface sample corresponding to the
hologram of the letter “U.” (b) The
near-field experimental setup in microwave anechoic chamber.
the holographic images at the working frequency of fi . According
to the above relationship, the sizes of the holographic image and
the distance between the metasurface and the holographic images
vary with the working frequency. After the optimization, the locations of relatively good holographic results are selected as 160, 240,
280, 320, 340, 380, and 460 mm corresponding to 12, 13, 14, 15,
16, 17, and 18 GHz, respectively. It is noticeable that the locations
and the effective sizes of holographic images have a gradually
enlarging tendency with the increase of working frequencies. As
shown in Fig. 4, the relative bandwidth of the proposed broadband
holography based on the digital coding metasurface is 40% with
high imaging quality.
To experimentally verify the performance of broadband holography based on digital coding metasurfaces, two kinds of broadband digital coding metasurfaces, respectively, integrating the
holograms of letters “U” and “X” are fabricated and measured, one
fabricated sample of which is exhibited in Fig. 5(a). The above
broadband metasurfaces with the effective size of 300 × 300 mm2
(15 × 15 λ2) composed of 30 × 30 digital coding elements are fabricated by the printed circuit board (PCB) technology. The samples
are measured in the microwave anechoic chamber for the nearfield, and the experimental environment is shown in Fig. 5(b). A
standard waveguide working from 12 to 18 GHz serves as a transmitter and the experimental probe connected with the vector
network analyzer serves as a receiver. Meanwhile, the polarized
state of a standard waveguide is set as vertical polarization and the
polarized state of the experimental probe is horizontal. The
15 April 2025 02:04:53
IV. EXPERIMENTAL VERIFICATION
standard waveguide is vertically placed on the center of the acrylic
board used to support samples, with a distance of 180 mm away
from samples. The distance between samples and the experimental
probe is set as the different distances varied with the working frequency according to the simulated results in Fig. 4. The scanning
plane is parallel to the samples with an effective area of 300
× 300 mm2.
First, the probe is moved to a distance of 240 mm from the
metasurface and the intensity of the metasurface with the letters
“U” and “X” at 13 GHz is, respectively, measured by the probe
automatically moving along the x–y plane. Similarly, the probe is
successively moved to 280, 320, 340, 380, and 460 mm when the
working frequency is set from 14 to 18 GHz. It should be noted
that the distance between the metasurface and the probe at 12 GHz
is 160 mm, less than 180 mm, and, hence, the intensity of the metasurface at 12 GHz is unable to be measured due to the experiment
limitation. All measured results are demonstrated in Fig. 6. The
intensity distributions of the letter “U” from 13 to 18 GHz are
clearly shown in Fig. 6(a), and Fig. 6(b) displays the intensity distributions of the letter “X” from 13 to 18 GHz. We can observe that
the deviation exists between the measured and the simulated
results. Limited by the accuracy of the manufacturing technology
and the characteristic of the used substrate, the imperfect fabrication and a slight deformation of samples will cause the actual phase
deviation. In particular, for higher working frequencies, the
imaging effect is slightly different from the simulation because
higher tolerance for the accuracy of the fabricated samples is
required. Moreover, the performance of the waveguide used as the
feed and the imperfect alignment between the waveguide and the
metasurface can affect the measured results. The deviation between
FIG. 6. The measured results in microwave anechoic chamber. (a) and (b)
The intensity distributions of letters “U”
and “X” from 13 to 18 GHz at the distance of 240, 280, 320, 340, 380, and
460 mm, respectively.
J. Appl. Phys. 130, 235103 (2021); doi: 10.1063/5.0064675
Published under an exclusive license by AIP Publishing
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the probe position and the metasurface center can exist in the measured process because the measuring probe is installed manually.
To a certain extent, the deviation can be decreased by the advanced
fabricated technology and precise position matching.
Hence, the relative bandwidth of the proposed broadband
holography based on the digital coding metasurface is at least
33.33% with high imaging quality. Moreover, the realized imaging
efficiency of the letters “U” and “X” is calculated to be 54.8% and
49.2% at a center frequency of 15 GHz based on the definition of
imaging efficiency that the fraction of incident energy that contributes to the transmitted holographic image.45,46 In general, the proposed metasurface accomplishes the function of broadband
holography with good performance.
V. CONCLUSION
ACKNOWLEDGMENTS
This work was supported in part from by the National Key
Research and Development Program of China under Grant Nos.
2017YFA0700201, 2017YFA0700202, and 2017YFA0700203, the
National Natural Science Foundation of China (NNSFC) under
Grant Nos. 61871127, 61735010, 61731010, 61890544, 61801117,
61722106, 61701107, 61701108, 61701246, and 61631007, the State
Key Laboratory of Millimeter Waves, Southeast University, China
(K201924), the Fundamental Research Funds for the Central
Universities under Grant No. 2242018R30001, the 111 Project
under Grant No. 111-2-05, and the Fund for International
Cooperation and Exchange of the National Natural Science
Foundation of China (NNSFC) under Grant No. 61761136007.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts of interest to disclose.
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding authors upon reasonable request.
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To summarize, we have demonstrated broadband holography
with the realized maximum imaging efficiency of 54.8% based on
the digital coding metasurface in the microwave region. The
adopted broadband digital coding metasurface holograms can be
optimized by a modified GS algorithm taking the incident field
into account. Thus, the proposed broadband digital coding metasurface holography realizes the broadband performance of a relative
bandwidth of 40% with excellent imaging quality. The digital
coding metasurface can greatly simplify the design process and
bridge the physical world and the digital world. We believe that the
proposed broadband digital coding metasurface holography may
have potential applications in microwave imaging systems and
holographic data storage.
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