Nanoscale
PAPER
Cite this: Nanoscale, 2018, 10, 4237
Received 25th September 2017,
Accepted 28th December 2017
DOI: 10.1039/c7nr07154j
rsc.li/nanoscale
Complete amplitude and phase control of light
using broadband holographic metasurfaces†
Gun-Yeal Lee,
a
Gwanho Yoon,
b
Seung-Yeol Lee,
c
Hansik Yun,
a
Jaebum Cho,
a
Kyookeun Lee,
a
Hwi Kim,
d
Junsuk Rho
b,e
and Byoungho Lee *
a
Reconstruction of light profiles with amplitude and phase information, called holography, is an attractive
optical technology with various significant applications such as three-dimensional imaging and optical
data storage. Subwavelength spatial control of both amplitude and phase of light is an essential require-
ment for an ideal hologram. However, traditional holographic devices suffer from their restricted capabili-
ties of incomplete modulation in both amplitude and phase of visible light; this results in sacrifice of
optical information and undesirable occurrences of critical noises in holographic images. Herein, we have
proposed a novel metasurface that is capable of completely controlling both the amplitude and phase
profiles of visible light independently with subwavelength spatial resolution. The full, continuous, and
broadband control of both amplitude and phase was achieved using X-shaped meta-atoms based on the
expanded concept of the Pancharatnam-Berry phase. The first experimental demonstrations of the com-
plete complex-amplitude holograms with subwavelength definition at visible wavelengths were achieved,
and excellent performances with a remarkable signal-to-noise ratio as compared to those of traditional
phase-only holograms were obtained. Extraordinary control capability with versatile advantages of our
metasurface paves a way to an ideal holography, which is expected to be a significant advancement in the
field of optical holography and metasurfaces.
Introduction
Holography is an optical technique that reconstructs the
wave front of electromagnetic waves with both amplitude
and phase information to display three-dimensional (3D)
images.
1
Holography ha s be en an attractive topic ever since
it has been used to realize ultimate 3D displays and optical
data storage.
2– 4
However, conventional dig ital holography
techniques, which are based on typical optoelectronic
devices such as spatial light modulators and digital micro-
mirror devices, have been suffering from several issues, such
as low resolution, narrow viewing a ngle, and severe noises
generated from undes irable diffraction or ders and twin
images, due to their large pix el size as compared to the oper-
ating wavelengths. More importantly, conventional holo-
graphy techniques are usually based on the amplitude- or
phase-only modulation scheme with incomplete approxi-
mations o f object images. In p rinciple, a complex-amplitude
modulation, which means independent modulation of
both amplitude and phase of light, is required to perfectly
reconstruct the profile of light. However, for convention al
devices, operating mechanisms of both amplitude- an d
phase-modulation fundamentally interfere with each
other; this causes challenges for indepen dent and full
control of them. Althoug h there are a few reports on
complex-amplitude modulation schemes applied to the
convent ional optoel ectronic devices, they still suffer from
issues including twin image generation, huge optical system
size, and limited modulation ranges.
5– 9
Hence, de spite its
significance, impleme ntation of high quality complex-
am plitud e modu lation scheme has not been demonstrated
to date.
Metasurfaces, which are planar optical elements with the
composition of artificially fabricated photonic atoms, have
attracted extensive interest owing to their numerous function-
† Electronic supplementary information (ESI) available: Supplementary texts
with details of numerical simulations, device fabrication, optical measurement,
and hologram design. Supplementary Movies S1–S3. See DOI: 10.1039/
c7nr07154j
a
School of Electrical and Computer Engineering and Inter-University Semiconductor
Research Center, Seoul National University, Gwanak-gu Gwanak-ro 1, Seoul 08826,
Republic of Korea. E-mail: byoungho@snu.ac.kr
b
Department of Mechanical Engineering, Pohang University of Science and
Technology (POSTECH), Nam-gu Cheongam-ro 77, Pohang 37673, Republic of Korea
c
School of Electronics Engineering, College of IT Engineering, Kyungpook National
University, buk-gu daehakro 80, Daegu 702-701, Republic of Korea
d
Department of Electronics and Information Engineering, Korea University, Sejong-ro
2511, Sejong 339-700, Republic of Korea
e
Department of Chemical Engineering, Pohang University of Science and Technology
(POSTECH), Nam-gu Cheongam-ro 77, Pohang 37673, Republic of Korea
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alities and potentials to modify electromagnetic
characteristics.
10–14
The applied areas of metasurfaces have
been rapidly expanding with noticeable examples including
negative index materials and unusual nonlinear optical
materials.
15–19
Recently, metasurfaces are expected to pave the
path for high quality spatial light modulators that can over-
come the limitations of conventional optical components. A
number of metasurfaces have been investigated as holographic
devices with control of phase,
20–30
polarization,
31
and both
components of light.
32–35
Furthermore, the development of a
simultaneous control of amplitude and phase of light has
been attempted in some studies, and plasmonic metasurfaces
with V-shaped meta-atoms proposed; however, they have
limited modulation ranges, sophisticated fabrication require-
ments, as well as low efficiency.
36
Metasurfaces with C-shaped
meta-atoms have been demonstrated with terahertz waves,
37
but fabrication difficulty with their convoluted modulation
schemes makes it hard to implement their scalable design
for visible light. A reflective metasurface with single nanorods
has been proposed to control both the amplitude and phase of
near-infrared waves by changing the length and rotation of the
nanrods.
38
However, the scheme of changing the length of the
nanorod is solely based on the resonant property of the struc-
tures, which cannot be applied to broadband operations;
moreover, this sort of modulation schemes based on the
changes of the structure lengths require very precise control of
the geometries at the nanoscale due to high susceptible reso-
nances, which result in high inaccuracy and fabrication
difficulties. Other types of metasurfaces have also been
suggested, but within theoretical considerations with low prac-
ticality or restricted capabilities.
39,40
As a result, none of the
metasurfaces have achieved the complete control of complex-
amplitude in visible range with subwavelength resolution and
broadband.
In this study, an advanced holographic metasurface has
been proposed and experimentally demonstrated that enables
full and broadband complex-amplitude modulation of visible
light with subwavelength spatial resolution, which can
achieve the most complete holograms reaching to ideal holo-
graphy. As a building block, an X-sha ped meta-atom is intro-
duced based on the expanded concept of th e Pancharatnam-
Berry phase. The X-shaped meta-atom, which is made of poly-
crystalline silicon (Poly-Si), ena ble s that full ranges of both
amplitude and phase can be mapped and tailored by
tuning th e orientations of i ts two arms. Furthermore,
the metasurface provides broadband and chiral
operations du e to the great feature of the Pancharatnam-
Berry phase.
17,20,22,25,27,29,31,42–49
Duetosimpleandintuitive
design strategy, the proposed metasurface is resistant to fab-
rication errors and shows high efficiency in the mid-visible
region (40% at 532 nm). To the be st of our knowledge, this is
the first time that the completely complex-amplitude modu-
lated holograms have been experimentally realized for visible
light with subwavelength spatial resolutions, and this is
expec ted to be a significant adva ncement in op tical holo-
graphic t echnology and metamaterials.
Results and discussion
Theory of the metasurface with X-shaped meta-atoms
A schematic depicting the mechanism of the X-shaped meta-
atoms is represented in Fig. 1a. At first, the key principle of
the proposed meta-atom, the Pancharatnam-Berry phase, has
been discussed. The Pancharatnam-Berry phase, or geometric
phase, is one of the most useful phenomena to describe the
phase profile of scattered light by spin-rotation coupling. The
geometric-phase metasurfaces commonly consist of a unit-cell
of a rectangular nanorod, which is composed of plasmonic or
dielectric materials. As shown in the left side of Fig. 1a, elec-
tric dipole moments are induced parallel to the major axis of
the nanorod when the circularly polarized light (σ) is normally
incident to the nanorod. Herein, the parameter σ is selected as
+1 or −1 for right or left circular polarization, respectively. The
orientation angle (θ
1
with respect to x-axis) of the nanorod
leads to time delay of the dipole excitation; this makes relative
phase delay among the nanorods according to their own orien-
tation angles. As a result, the scattered light with opposite
Fig. 1 Schematic of an X-shaped meta-atom (a) describing the operat-
ing mechanism of the structures. Rotation of the single nanorod with
orientation angle θ
1
(or θ
2
) leads to the phase variance 2σθ
1
(or 2σθ
2
)ina
cross-polarized component of transmitted light according to the
Pancharatnam-Berry phase. The superposition of the two nanorods with
different orientation angles θ
1
and θ
2
implements the X-shaped struc-
ture, which has the amplitude 2 cos(θ
2
− θ
1
) and phase σ(θ
1
+ θ
1
)ina
cross-polarized component of transmitted light. η
σ
and η
−σ
are the coup-
ling coefficients of co- and cross-polarized light, respectively. (b)
Schematic of a unit cell of the proposed metasurface. An X-shaped
meta-atom consists of Poly-Si on a glass substrate with thickness t and
the unit cell period P. (c) Top view of the unit cell showing longer length
L, width w, orientation angles of its arms θ
1
and θ
2
, and their disparity α.
For the metasurfaces designed at the operating wavelength λ
d
=
532 nm, X-shaped meta-atoms have L = 290 nm, w = 65 nm, t =
128 nm, and P = 350 nm. (d) Simulation results that show the distri-
bution of electric fields and polarization vectors. Colours represent the
real part of cross-polarized electric fields (E
−σ
), and black arrows in the
figures represent the magnitudes and directions of the polarization
vectors at each position. The upper figure has the angular disparity α =
60°, whereas the lower figure has α = 90°. Other geometric parameters
of both structures are identica l. Scale bar, 50 nm.
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handedness (−σ) experiences a relative phase shift (2σθ
1
),
which is only proportional to the orientation angle. The geo-
metric phase is a purely geometrical effect, which can lead to
broadband characteristics whose tendency of phase shift is
independent of the wavelength of light.
In this regard, the concept of geometric phase can be
expanded. If two nanorods with different orientation angles (θ
1
and θ
2
) are overlapped, they will construct an X-shaped struc-
ture whose arms direct to the angles θ
1
and θ
2
. Speculating
that the X-shaped structure can be modelled by two indepen-
dent electric dipoles, the behaviour of the X-shaped structure
is allowed to be analysed by the superposition of the geometric
phase. The phase components of cross-polarized waves scat-
tered by these electric dipoles are just proportional to their
orientation angles, but with the same amplitude components.
Hence, the complex-amplitude of the cross-polarized wave
(E
cross
) radiated from the X-shaped structure can be simply
expressed as follows:
E
cross
/ e
j2σθ
2
þ e
j2σθ
1
¼ðe
jσðθ
2
θ
1
Þ
þ e
jσðθ
2
θ
1
Þ
Þe
jσðθ
1
þθ
2
Þ
¼ 2 cosðθ
2
θ
1
Þe
jσðθ
1
þθ
2
Þ
ð1Þ
According to eqn (1), the complex-amplitude E
cross
can be
separated into the amplitude and phase component. The
amplitude A and phase ϕ of the total cross-polarized wave can
be expressed as 2 cos(θ
2
− θ
1
) and σ( θ
1
+ θ
2
), respectively. That
is, the amplitude of scattered light can be determined by the
difference between two orientation angles, whereas the phase
of scattered light can be determined by the summation of two
orientation angles. Thus, we confirm that the complex-ampli-
tude modulation can be realized from the double electric
dipoles. However, in the case of an actual X-shaped structure,
higher order modes, such as magnetic dipoles and electric
quadrupoles, rather than the electric dipole modes can be
excited when a circularly polarized light illuminates on the
backside of the structure. However, we have found that these
higher order modes can be suppressed, and only double elec-
tric dipoles are dominantly generated around the specific reso-
nance. This resonance can occur with accurately designed geo-
metric parameters such as thickness, length, and width of the
X-shaped structure. Therefore, the proposed X-shaped struc-
ture can modulate the incoming light with the full coverage of
complex-amplitude domain according to eqn (1).
Based on the theoretical analysis, the X-shaped meta-atoms
were implemented using dielectric materials. A schematic of
the proposed unit cell is shown in Fig. 1b. The meta-atom con-
sists of poly-Si on a glass substrate with the thickness of t. The
metasurface is then composed of periodically arranged square
lattices of X-shaped meta-atoms with the period P for both x-
and y-directions. The proposed structure is designed to
operate in the visible light with the wavelength of 532 nm;
thus, the period (P = 350 nm) is set to be shorter than the
wavelength of light. Since the period is even shorter than the
wavelength in the glass substrate with the refractive index of
1.45, there are no diffraction orders in both transmission and
reflection. The thickness of poly-Si (t = 128 nm) is chosen to
compose a Fabry–Perot resonator with a low quality-factor,
which not only enhances the modulation efficiency but also
allows broadband operations. Fig. 1c shows the top view of the
unit cell. Each pixel has its own orientation angles (θ
1
and θ
2
)
about the x-axis. The angular disparity between the orientation
angles is defined as α. Considering both the fabrication feasi-
bility and modulation efficiency, other parameters, such as the
length of the nanorod (L = 290 nm) and the width of the
nanorod (w = 65 nm), were also carefully designed. Although
only a transmission-type metasurface has been discussed
herein, we have confirmed that a reflection-type metasurface
can also be implemented in the same manner in the visible
region (see the ESI Part 1†).
Verification with numerical simulations
The capability of the X-shaped meta-atom is verified by a com-
mercial tool (COMSOL) based on the finite element method
(FEM) (see the ESI Part 2† for details). Electric field maps of
the X-shaped meta-atom with normal incidence of circular
polarization were calculated first, as shown in Fig. 1d. Herein,
two cases of X-shaped structures with α = 60° and 90° are con-
sidered as examples (for other cases, see Fig. S4 and S5†). In
the figure, colours represent the real part of cross-polarized
electric fields (E
−σ
), whereas the black arrows represent the
magnitude and directions of electric polarization vectors. It is
noticeable that we have allowed the values of α to be in the
range from 60° to 90° because a meta-atom having an α
smaller than 60° is not appropriate to apply the superposition
mechanism of the X-shaped structure due to severe overlap of
two nanorods, which is not suitable for our theoretical
approach. As shown in Fig. 1d, it can be confirmed that the
electric dipoles are dominantly induced along the arms of the
X-shaped meta-atom in the defined range; this means that the
speculation of our theoretical approach is practically valid (see
Fig. S4 and S5† for details).
Fig. 2 shows the cross-polarized transmission coefficient
(t
cross
) as a function of the orientation angle (θ
1
) and the
angular disparity (α) calculated from both theoretical calcu-
lations and FEM simulations. Herein, t
cross
is defined as the
ratio of complex-amplitude of the cross-polarized transmission
(E
cross
) to incident light (E
in
), as depicted in Fig. 2a. Fig. 2b–d
present the results of theoretical calculations based on eqn (1)
that models the X-shaped meta-atom as double electric dipoles
whose directions are parallel to the major axes of two arms.
Corresponding FEM simulation results for the actual X-shaped
meta-atom are presented in Fig. 2e–g. To compare the results
in detail, they are represented separately in each component
i.e. the amplitude (Fig. 2b and e) and phase (Fig. 2c and f ).
Fig. 2d and g describe all the t
cross
in the complex domain
whose x- and y-axes mean the real and imaginary part of the
complex-amplitude, respectively. As expected, both results of
modelling and simulations show a strong agreement. The
angular disparity is related with the amplitude, whereas the
orientation angle is related with the phase relying on the eqn
(1). In addition, the simulation indicates that the maximum
efficiency, which is defined as the efficiency for the maximized
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amplitude, reaches 49% at the wavelength of 532 nm. As a con-
sequence, we can confirm that our theoretical approach is
fairly accurate, and both amplitude and phase of transmitted
and cross-polarized light can be fully described by the orien-
tation angles of the two arms of the X-shaped meta-atom with
high efficiency.
Experimental demonstrations of X-shaped metasurfaces
To experimentally demonstrate the extraordinary capability
and versatility of the proposed metasurface, metasurfaces com-
posed of X-shaped meta-atoms were fabricated according to
the geometric parameters by standard electron beam lithogra-
phy process (see the ESI Part 3† for details). In this section, we
have characterized two different categories of the metasur-
faces. The first category was a set of metasurfaces with a peri-
odic array of identical X-shaped meta-atoms to measure trans-
mission characteristics of the unit cell. The other category was
used for validating the performance of full complex-amplitude
holographic metasurfaces using X-shaped meta-atoms as com-
pared to that of a phase-only holographic metasurface.
Herein, four devices belonging to the first category consist
of identical X-shaped meta-atoms with four types of angular
disparities: α = 60°, 70°, 80°, and 90°. Fig. 3a–d represent their
field-enhanced scanning electron microscopy (FE-SEM)
images. According to the images, it is possible to confirm the
feasibility of the proposed structures at the nanoscale. The
samples were then illuminated from the bottom by a laser
with the free-space wavelength (λ
d
) of 532 nm. On the trans-
mitted side, a cross-polarized circular analyser comprising a
quarter waveplate and a linear polarizer was used to filter and
measure the cross-polarized component of transmitted light.
Using the oppositely directional circular analyser comprising a
quarter waveplate and a linear polarizer, the cross-polarized
component of transmitted light can be measured. The results
are shown in Fig. 3e with the simulation results. The intensity
values in Fig. 3e are normalized by the case of α = 60°.
According to the graph, both experiments and simulations
indicate that the intensity of t
cross
sinusoidally decreases when
α increases from 60° to 90°, and finally, it reaches zero at α =
90°. For the maximum case of the experimental results, we
measured a maximum efficiency of 40% in cross-polarized
transmission. The measured efficiency is a bit smaller than its
corresponding simulated values (49%) because of slight differ-
ences between the geometry of the designed and fabricated
structures.
The second category of our metasurfaces was prepared for
validating the functionalities of full complex-amplitude meta-
surface holograms. As abovementioned, extraordinary capa-
bility of X-shaped meta-atoms can satisfy the requirement of
ideal complex-amplitude holograms. We designed the compu-
ter-generated holograms (CGHs) for right circularly polarized
light with normal incidence. As shown in Fig. 4a, the CGHs
were designed to generate the letters “SNU” in 3D space. The
letters “S”, “U”, and “N” are displayed on different image
planes in the Fresnel region, which are at z =0μm, 80 μm, and
150 μm, respectively. It is noticeable that one of the image
Fig. 2 Theoretical and numerical analyses of cross-polarized transmissions of an X-shaped meta-atom. (a) Schematic of a unit cell of an X-shaped
meta-atom. Cross-polarized transmission coefficient t
cross
is defined as the ratio between the complex amplitude of cross-polarized component of
transmitted light and that of incident light. Results of (b–d) analytical calculations and (e–g) FEM simulations for t
cross
. (b and e) Variation in the
amplitude component of t
cross
for different orientation angles θ
1
and disparities α . (c and f ) Variation in the phase component of t
cross
for different
orientation angles θ
1
and disparities α. (d and g) Accessible range of t
cross
plotted in the complex domain. The different colours of the lines represent
the cases of different orientation angles, and the colour bar is represented on the right side of the graphs.
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planes is located at z =0μm, which is directly on the metasur-
face plane, to show the unique performance of complex-ampli-
tude holograms. For conventional phase-only holograms, only
phase information of object images remains, whereas the
amplitude information of them is set to be identical.
Therefore, it is impossible to describe the images directly on
the metasurface plane. On the other hand, complex-amplitude
holograms have both amplitude and phase information, which
is capable of describing the reconstructed images on arbitrary
planes including the surface of metasurfaces. Therefore, the
proposed example can definitely prove whether the given meta-
surfaces modulate the phase, amplitude, or both. Calculated
CGHs with a sample size of 210 μm × 210 μm and a pixel size
of 350 nm × 350 nm are shown in the upper side of Fig. 4d.
Any approximations or algorithms, such as random phase
injection, that should be used in conventional phase-only
holograms are not employed to obtain the expected amplitude
and phase profiles, and the back-propagation of the desired
image profiles is taken into account according to the Fresnel
diffraction theory. The optical microscopy image and FE-SEM
images of the fabricated devices possessing the designed
CGHs are shown in Fig. 4b and c, respectively. Fig. 4d shows
the obtained holographic images at each z-plane in both simu-
lations and experiments. Optical microscopy setup with the
cross-polarized analyser was used to measure the holographic
images (see the ESI Part 4† for details and Fig. S1† for the
illustration of the setup). It is noteworthy that the holographic
images of both simulations and experiments have almost iden-
tical profiles without any significant noises; this demonstrates
the great capability of the metasurface for generating holo-
graphic images in 3D space. Moreover, the letter “S” recon-
structed on the image plane very close to the metasurface is
purely described; this indicates that the amplitude profiles as
well as the phase profiles are correctly implemented. A signal-
to-noise ratio (SNR), which is defined as the ratio of the
maximum intensity in the holographic image to the standard
deviation of the background noise,
36
has been used to evaluate
the image quality. For the experimentally reconstructed image
in Fig. 4d, the SNR is 211.3 where the background area is set
to the size of 32 μm×32μm. This is a remarkable record since
the SNRs reported in previous studies have only the values
around 50 although approximation algorithms are used in
them that improve the image quality, but sacrifice the original
wavefronts.
36,44
For comparison, the phase-only metasurface with uniform
amplitude profiles was also designed, and the other conditions
were the same as those of the sample shown in Fig. 4d. Due to
the deficient expressiveness of phase-only holograms, multipli-
cation of randomly valued phase profiles should be employed
to improve the image quality of the phase-only holograms (see
the ESI Part 5† for details). Calculated phase profile of the
phase-only CGH is shown in the upper side of Fig. 4e. Both cal-
culated and measured holographic images in Fig. 4e show that
the letter “S” cannot be formed at the metasurface plane as
properly as the other letters “N” and “U” are displayed due to
severe noises around the images. Upon comparing the holo-
graphic images of Fig. 4d and e, we conclude that the complex-
amplitude hologram can overcome the speckle noise problem
of typical phase-only holograms, significantly expand the
range of reconstructed image plane, and simplify the compli-
cated calculation processes of the phase-only CGHs that often
involve iterative algorithms.
Moreover, one of the attractive properties of the proposed
metasurface is the broadband characteristic. As proved in the
theoretical approach, the nature of the X-shaped meta-atoms
originates from the geometric phase, which only depends on
the orientation of the structure. In addition, the broadband
characteristic of the proposed metasurface is more improved
using all-dielectric materials, which have less sensitive reso-
nance properties as compared to plasmonic materials with
sharp plasmonic resonances.
41
Therefore, it is expected that
Fig. 3 Experimentally measured cross-polarized transmissions (t
cross
)of
the X-shaped meta-atoms in several angular disparities. (a–d) FE-SEM
images of the metasurfaces composed of regularly patterned X-shaped
unit-cells with the angular disparities α = 60°, 70°, 80°, and 90° for (a),
(b), (c), and (d), respectively. Scale bar of inset, 50 nm. (e) Results of both
simulations and experiments for the cross-polarized transmittance as a
function of the angular disparity α. Blue circles indicate the experimental
results, whereas the red-crossed points and curve are for the FEM simu-
lation results. The results are normalized to the transmittance for the
case of α = 60°, which is designed to have the maximum transmittance.
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