RESEARCH ARTICLE
www.advmat.de
Bidirectional Vectorial Holography Using Bi-Layer
Metasurfaces and Its Application to Optical Encryption
Hyeonhee Kim, Joonkyo Jung, and Jonghwa Shin*
asymmetric responses, such as asymmetric wettability,[1,2] chemical reactivity,[3,4] or
reflection,[5,6] involves utilizing different
materials or structures on each side of
the system. This straightforward approach
serves as a basis for more complex applications.
In addition to these basic constructs,
systems also possess a subtler and often surprising property—the asymmetric
transport of matters and energy. This
phenomenon, in which the direction
of incidence influences the quantity or
other properties of what is being transported, is exemplified by the electric diode.
The unidirectional electric conduction
of diodes has made them indispensable
components of modern electronic circuits
and devices. Building upon this concept,
studies have endeavored to extend asymmetric transport to a diverse range of
matters such as liquids[2,7,8] or ions.[9–11]
Furthermore, the directional asymmetry
of energy and information flow has attracted considerable research interest owing to its unique physics and potential applications. Examples include the diode-like
one-way transmission of elastic/acoustic waves[12–16] and
heat.[17–20] In the realm of optics, controlling the amplitude,
phase, or polarization of transmitted light, depending on the
direction of incidence holds significant implications for various
applications in optical science and engineering. This level of
control is highly sought after for its utility in a wide range of
fields. Furthermore, enhanced functionality can be achieved by
designing the asymmetry of light transmission at a pixel-wise
level with wavelength-scale spatial resolutions across an optical
interface. This will enable precise spatial manipulation of light
with exceptional resolution. The resulting thin optical systems
can serve as completely different devices depending on the
incidence direction of light. For example, they can function as a
magnifying lens with front-side illumination and a polarization
camera with back-side illumination, as shown in Figure 1.
Most optical systems, except for special cases such as magnetooptic, nonlinear, and temporally modulated devices, adhere to
Lorentz reciprocity.[21] Reciprocal systems are typically deemed
unsuitable for achieving asymmetric transmission because the
transmission coefficients, including their phases, remain the
same when the input and output modes are swapped (that is
when the direction of incidence is reversed).[22,23] However, the
The field of optical systems with asymmetric responses has grown significantly
due to their various potential applications. Janus metasurfaces are noteworthy
for their ability to control light asymmetrically at the pixel level within thin
films. However, previous demonstrations are restricted to the partial control
of asymmetric transmission for a limited set of input polarizations, focusing
primarily on scalar functionalities. Here, optical bi-layer metasurfaces
that achieve a fully generalized form of asymmetric transmission for
any input polarization are presented. The designs owe much to the theoretical
model of asymmetric transmission in reciprocal systems, which elucidates the
relationship between front- and back-side Jones matrices in general cases. This
model reveals a fundamental correlation between the polarization-direction
channels of opposing sides. To circumvent this constraint, partitioning
the transmission space is utilized to realize four distinct vector functionalities
within the target volume. As a proof of concept, polarization-directionmultiplexed Janus vectorial holograms generating four vectorial holographic
images are experimentally demonstrated. When integrated with computational
vector polarizer arrays, this approach enables optical encryption
with a high level of obscurity. The proposed mathematical framework and
novel material systems for generalized asymmetric transmission may pave
the way for applications such as optical computation, sensing, and imaging.
1. Introduction
A system of materials may respond differently, depending on the
direction of the stimulus. These asymmetric responses can be
observed in various systems, such as electrical, optical, chemical, or mechanical devices. Such effects have captivated many researchers due to their academic intrigue and potential for many
useful applications. A common yet effective method for achieving
H. Kim, J. Jung, J. Shin
Department of Materials Science and Engineering
KAIST
Daejeon34141, Republic of Korea
E-mail: qubit@kaist.ac.kr
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adma.202406717
© 2024 The Author(s). Advanced Materials published by Wiley-VCH
GmbH. This is an open access article under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs License, which permits
use and distribution in any medium, provided the original work is
properly cited, the use is non-commercial and no modifications or
adaptations are made.
DOI: 10.1002/adma.202406717
Adv. Mater. 2024, 36, 2406717
2406717 (1 of 14)
© 2024 The Author(s). Advanced Materials published by Wiley-VCH GmbH
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Figure 1. Schematics of a device featuring asymmetric transmission. a) Device operating as a magnifying lens for back-side illumination. b) Device
operating as a polarization camera for front-side illumination. The colors represent the polarization states of light, as described in a subsequent section.
massive plurality of modes in free space presents an opportunity
to achieve “apparent asymmetric transmission” without violating
reciprocity. By leveraging additional degrees of freedom, such as
incidence angle or polarization, the asymmetric transport of energy and information can be realized within reciprocal systems
using numerous intriguing methods. For example, by restricting
incident light to a specific polarization and designing the system
such that the polarization of the transmitted light is orthogonal
to that of the incident beam, transmission coefficients may appear different when the sample is flipped without adjusting the
incident light than when it is in its original state.[24] This is because reciprocity only dictates that the transmission of the flipped
sample aligns with that of the original configuration when the
polarization of the incident beam is also adjusted to match the
initial output polarization. Therefore, through careful design of
the optical system’s response to different polarizations, asymmetric transmission can be achieved without violating Lorentz reciprocity.
The innovative approach of cross-polarized transmission,
which involves using orthogonal input and output polarizations
for asymmetric transmission, has paved the way for incorporating asymmetric transmission in reciprocal systems. However,
this has proven challenging in natural materials owing to their
limited optical anisotropy.[25] Metasurfaces, thin film-like 2D arrays of nanostructures at a subwavelength scale, have emerged
as a revolutionary optical platform. These structures offer control over the fundamental properties of light, such as amplitude, phase, and polarization, across various wavelength ranges
with unprecedented degrees of freedom, overcoming the limitations inherent in natural materials.[26–28] In particular, metasurfaces have proven their superiority as polarization optics compared to conventional optics, enabling complex manipulation
of polarization[29–31] and multiplexing various functions owing
to their polarization-sensitive responses.[32–37] This unique capability has potential applications in various optical fields, such
as optical computations,[38–40] quantum optics[41–45] or optical
imaging.[46–49]
Initially, research on metasurface-based asymmetric transmission focused on the asymmetric transport of energy[50–53] where
transmitted intensities varied for the front- and back-side illumi-
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nations. More recently, the focus has shifted toward precise phase
control of transmitted electromagnetic waves. This precise phase
control is significant because it enables greater flexibility and efficiency in designing optical devices without compromising transmitted energies. These advancements have resulted in the development of metasurfaces with bidirectional functionalities, commonly referred to as Janus metasurfaces. These innovative structures are currently being explored for applications, such as bidirectional optical communications,[54–56] holograms,[54,55,57–66] or
optical encryptions.[59,67,68] Despite these innovations, the feasibility of realizing optical devices with independent and arbitrary
asymmetric functionalities for front-side and back-side illuminations, as described in Figure 1, is debatable. Most previous
demonstrations have been restricted to controlling asymmetric
transmission with limited input polarization states and scalar
functionalities. Therefore, achieving full control of asymmetric
transmission remains a challenging task.
In response to this challenge, we propose a novel strategy
for achieving full control over the asymmetric transmission
of light in optical systems. Our approach involves a generalized mathematical framework for the asymmetric transmission of an optical system, clearly defining the relationship between the transmission coefficients of the reciprocal system for
front- and back-side illuminations with respect to general elliptical polarization. This generalization enables a tailored design of systems capable of generalized asymmetric transmission for any polarization. Building on our recent study demonstrating that bi-layer metasurfaces can achieve complete linear
control of coherent light,[69] we developed thin film-like structures that fully control asymmetric transmission. These structures enable the customization of both co- and cross-polarized
transmission coefficients. Our research also highlights a fundamental constraint on the polarization-direction-multiplexing capability of asymmetric transmissions in passive and reciprocal
thin film systems. Specifically, the simultaneous design of four
arbitrary vector functionalities for four independent polarizationdirection illumination conditions proved restricted. To circumvent this limitation, we proposed a novel approach based on partitioning the transmission space and achieved independent and
distinctive vector functionalities for four different illumination
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conditions within the maximum target volume. We experimentally demonstrated polarization-direction-multiplexed Janus vectorial holograms, generating unique vectorial holograms based
on the direction of incidence and input polarization. Furthermore, we propose a novel optical encryption algorithm that integrates our Janus metasurfaces with computational vector polarizer arrays. This integration significantly enhances the security
of metasurface-based optical encryptions, presenting new possibilities in secure communication technologies.
2. Results
2.1. Generalization of Asymmetric Transmission
For asymmetric transmission in a reciprocal system, we focus on
orthogonal input–output polarization as an additional degree of
freedom. The effect of an optical system on the amplitude, phase,
and polarization of incident light can be effectively captured using the Jones matrix.[24,32,33,69,70] This matrix relates input and output lights through matrix multiplication based on two polarization states as a basis. The Jones matrices for the front- and backside illuminations are correlated based on reciprocity.[24] For the
x- and y-polarization basis, we suppose the front-side Jones maf
= [A, B; C, D]. In that
trix of an optical system is expressed as Txy
case, the back-side Jones matrix when the system is flipped beb
comes Txy
= [A, −C; −B, D], where the subscript xy denotes the
x- and y-polarization basis and the superscripts f and b represent the front- and back-side illuminations, respectively. Similarly, for the right- and left-handed circular polarization (RCP
and LCP) basis, if the front-side Jones matrix of a system is exf
= [A′ , B′ ; C′ , D′ ], then the back-side Jones matrix
pressed as TRL
b
becomes TRL = [A′ , C′ ; B′ , D′ ], where the subscript RL denotes
the RCP and LCP basis and the superscripts f and b represent the
front- and back-side illuminations, respectively. Notably, in both
cases, while the diagonal elements (co-polarized transmission
coefficients) remain constant, the off-diagonal elements (crosspolarized transmission coefficients) are interchanged, with or
without sign conversion.
Most previous studies leveraged the interchange of crosspolarized transmission coefficients to achieve asymmetric transmission with specific cross-polarized input–output channels,
such as x-polarized input and y-polarized output,[55–62,71] or RCP
input and LCP output.[54,63–66] By strategically designing these offdiagonal elements and minimizing the impact of diagonal elements, studies have developed devices that offer distinct functionalities for front- and back-side illuminations within these specific cross-polarization channels. However, the relationship between the front- and back-side Jones matrices under arbitrary
elliptical polarization bases is not as straightforward as merely
interchanging off-diagonal elements.[24] This complexity has resulted in limited exploration of asymmetric transmission relative
to general elliptical polarization bases, and a comprehensive expression for this phenomenon remains undefined. This knowledge gap has impeded progress in defining the clear boundaries
of what kinds of asymmetric functionalities can or cannot be integrated within a single device.
Furthermore, previous studies have primarily focused on manipulating only the off-diagonal elements of the Jones matrix.
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However, to fully leverage the vector nature of electromagnetic
fields, a deliberate and harmonious design of both diagonal and
off-diagonal elements is necessary. Although a noteworthy exception in which co- and cross-polarized transmissions are utilized concurrently has been proposed,[67] this example still falls
short of achieving full control over the asymmetric transmission. Therefore, a comprehensive understanding of asymmetric
transmission and the simultaneous designability of co- and crosspolarized transmissions can create an intriguing avenue for further inquiry and innovation in the realm of metasurface-enabled
asymmetric transmission.
To address these issues, we developed a generalized representation of the Jones matrices for front- and back-side illuminations
with arbitrary elliptical polarization bases, in alignment with the
case of the x- and y-polarization basis. This involves a simple interchange of off-diagonal elements with a sign conversion. Differentiating between reversing the direction of illumination and
flipping the optical system itself is crucial; the latter scenario involves reversing the direction of illumination with a coordinate
rotation (refer to Figure S1, Supporting Information for the details).
In our generalization, we consider an arbitrary orthogonal
pair of elliptical polarizations, 𝜆 and 𝜆⟂ -polarizations, defined
as |𝜆⟩ = [ cos 𝜒; sin 𝜒ei𝜃 ] and |𝜆⟂ ⟩ = [ sin 𝜒; − cos 𝜒ei𝜃 ] in the xand y-polarization basis. Using these polarizations as the basis,
the front-side Jones matrix of an optical system is expressed as
f
= [a, b; c, d], where the subscript 𝜆𝜆⟂ represents the 𝜆- and
T𝜆𝜆
⊥
𝜆⟂ -polarization basis. A schematic of this matrix as a linear network connecting the input and output ports (from left to right)
relative to this basis, with the matrix elements corresponding to
the transmission coefficients for the co- and cross-polarization
channels is shown in Figure 2a.
By changing the basis to the x- and y-polarizations, the frontside Jones matrix can be expressed as follows:
[ ][
]
]
] a b ⟨𝜆|
[
AB
= |𝜆⟩ ||𝜆⊥ ⟩
c d ⟨𝜆⊥ ||
CD
[
f
=
Txy
(1)
At this point, reciprocity indicates that if the direction of incidence is reversed and the polarization states under consideration are time-reversed or in conjugate forms compared with
those used for front-side illumination, the system exhibits the
same transmission behaviors. Thus, the Jones matrix for this
reciprocal scenario becomes T𝜆r∗ 𝜆∗ = [a, c; b, d], where the super⊥
script r represents the reciprocal scenario and the subscript 𝜆∗ 𝜆∗⊥
∗
represents the 𝜆∗ - and 𝜆⊥ -polarization basis, defined as |𝜆∗ ⟩ =
[ cos 𝜒; sin 𝜒e−i𝜃 ] and |𝜆∗⊥ ⟩ = [sin 𝜒; − cos 𝜒e−i𝜃 ]. Similarly, this
reciprocal Jones matrix can be expressed relative to the x- and
y-polarization basis as follows:
r
=
Txy
[
[ ][
]
]
⟩ ] a c ⟨𝜆∗ |
[
AC
⟨ ∗
= |𝜆∗ ⟩ ||𝜆∗⊥
BD
bd
𝜆⊥ ||
(2)
Note that the Jones matrices for the front-side illumination and
its reciprocal scenario are transposes of each other only when
represented in conjugate polarization bases, as indicated using
Equations 1,2. Such a straightforward relationship for general elliptical polarization bases was not apparent in previous studies
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Figure 2. Generalized asymmetric transmission. a) Schematics of the optical system for the front- and back-side illuminations (upper panel) and network
representations of their Jones matrices (lower panel). “F” and “B” denote the front- and back-sides of the optical system, respectively. b) Polarization
bases for generalized asymmetric transmission on the Poincaré sphere. c) Schematics of the unit cell structure of bi-layer metasurfaces, with crosssections of the upper (subscript B) and lower (subscript A) layers shown in the right panels. p: period; h: height of posts; lM,m : length of the major
(M) and minor (m) axes; 𝜃: orientation angle. d) Scanning electron microscopy images of the fabricated metasurface. e) Numerical validation of the
generalized asymmetric transmission, with the elements of the Jones matrices for the front- and back-side illuminations relative to the 𝜆𝜆⟂ - and 𝜆′ 𝜆′⊥ polarization bases, respectively. f) Experimental validation of the generalized asymmetric transmission. Tf and Tb represent the Jones matrices for the
front- and back-side illuminations, respectively. The kets represent the polarization of incident light, whereas the bras represent the passing polarization
of the polarizer.
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since the same polarization basis was utilized for front- and backside illuminations.
However, in this fixed coordinate system, the representation of
the handedness of polarization states is contingent upon the direction of incidence owing to the reversed propagation direction.
For example, the RCP is represented as [ √1 ; √i ] for front-side il2
2
lumination and [ √1 ; √−i ] for reversed back-side illumination. To
2
2
eliminate any confusion, we rotated the coordinate around the
x-axis for the back-side illumination, ensuring consistent notation of polarization states regardless of the direction of incidence.
This reversed illumination condition with the coordinate rotation
is effectively the same configuration as flipping the system itself;
therefore, throughout this study, we equate flipping the system
with reversing the direction of illumination with the coordinate
rotation around the x-axis (refer to Figure S1, Supporting Information for the comparisons). Considering this coordinate rotation, the back-side Jones matrix is derived by multiplying the matrix Q = [1, 0;0, −1] on both sides of the transpose of the Jones
matrix of the reciprocal scenario as follows:
b
=
Txy
r
QTxy
Q
[
| ′⟩
= |𝜆 ⟩ |𝜆⊥
|
′
] [ a −c]
−b d
[
⟨𝜆′ |
⟨ ′|
𝜆⊥ |
|
]
(3)
where |𝜆′ ⟩ = [ cos 𝜒; − sin 𝜒e−i𝜃 ] and |𝜆′⊥ ⟩ = [− sin 𝜒; − cos 𝜒e−i𝜃 ]
denote the newly introduced polarizations (refer to Text S1, Supporting Information for the details). By changing the basis of
Equation 3, the back-side Jones matrix relative to the 𝜆′ - and
𝜆′⊥ -polarization basis is expressed as T𝜆b′ 𝜆′ = [a, −c; − b, d], ob⟂
tained by interchanging the off-diagonal elements of the frontside Jones matrix relative to the 𝜆- and 𝜆⟂ -polarization basis with
a sign conversion, as shown in Figure 1a. In summary, we established a generalized relation between polarization bases for
asymmetric transmission, ensuring the presence of two orthogonal polarization bases for the front- and back-side illuminations.
In this setup, co-polarized transmission coefficients remain consistent, whereas cross-polarized transmission coefficients are interchanged with a sign conversion. This generalization clearly illustrates the performance boundary of the asymmetric transmission of passive and reciprocal optical systems. It also provides an
intuitive mathematical framework for designing various asymmetric optical devices in subsequent sections.
In Figure 2b, the polarizations of |𝜆⟩, |𝜆⟂ ⟩, |𝜆′ ⟩ and |𝜆′⊥ ⟩ are
represented on the Poincaré sphere with their corresponding polarization ellipses and the Stokes parameters. Notably, the two
points on the Poincaré sphere for |𝜆⟩ and |𝜆′ ⟩ (likewise, |𝜆⟂ ⟩ and
|𝜆′⊥ ⟩) are mirror symmetric to each other with respect to the S1 -oS3 plane. This symmetry indicates that their polarization ellipses
have the same ellipticity and handedness, but the major axes are
rotated in opposite directions. This geometric relationship provides a key insight. For any basis with an orthogonal pair of polarizations on the S1 -o-S3 plane, the front- and back-side Jones
matrices follow the simple relation of interchanging off-diagonal
elements with a sign conversion for the same polarization basis,
regardless of the direction of incidence. The representative examples include the x- and y-polarization basis or RCP and LCP
polarization basis (in this case, |𝜆′⊥ ⟩ is defined as LCP with a 𝜋
phase delay). In addition, the orientation of this mirror plane can
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be modified by rotating the axis along which the system is flipped
(refer to Text S1 and Figure S2, Supporting Information for the
details).
Recent advancements in dielectric metasurfaces have enabled
the realization of arbitrary Jones matrices using bi-layer arrays
with supercell structures, called universal metasurfaces, as in
Figures 2c,d.[69] To demonstrate the proposed generalized asymmetric transmission, we randomly selected a basis with an orthogonal pair of polarizations (𝜒 = 2𝜋/5 and 𝜃 = 𝜋/6) and
designed universal metasurfaces to operate at a wavelength of
915 nm with a randomly selected Jones matrix (refer to Experimental Section and Text S2, Supporting Information for the
details). The Jones matrices retrieved from simulations for the
front- and back-side illuminations are shown in Figure 2e. As expected, the retrieved diagonal elements were identical and the retrieved off-diagonal elements were interchanged with a sign conversion.
Furthermore, we experimentally demonstrated the generalized asymmetric transmission by designing four different holograms for four independent co- and cross-polarization transmission channels, defined with 𝜒 = 𝜋/6 and 𝜃 = 𝜋/4. The required
phase profiles were designed based on the gradient-descent optimization method[72,73] (refer to Experimental Section for details).
As shown in Figure 2f, for the front-side illumination with 𝜆and 𝜆⟂ -polarizations, four unique images—a dog, cat, sheep, and
rat—were successfully measured for each polarization channel
(see Experimental Section for the details). On the contrary, for
the back-side illumination with 𝜆′ - and 𝜆′⟂ -polarizations, while
the same images—the dog and rat—were measured through the
co-polarization channels, the measured images for the crosspolarization channels—the cat and sheep—were interchanged.
Additionally, if the metasurface is illuminated from the front-side
with 𝜆′ - and 𝜆′⟂ -polarizations, overlapped images are generated
since 𝜆′ - and 𝜆′⟂ -polarizations can be regarded as the mixture of
𝜆- and 𝜆⟂ -polarizations (See Figure S4, Supporting Information).
Note that all images captured during back-side illumination were
flipped upside down because the phase profiles of holograms
were also flipped upside down when flipping the metasurface.
2.2. Polarization-Direction-Multiplexed Janus Vectorial
Holograms
The generalized form derived in the previous section offers a
clear and intuitive framework for understanding asymmetric
transmission in passive and reciprocal systems. Consider an opf
=
tical system characterized by the Jones matrix given as T𝜆𝜆
⊥
[a, b; c, d]. In the 𝜆- and 𝜆⟂ -polarization basis, the Jones matrix reveals the constraint imposed by reciprocity on the system’s asymmetric transmission under 𝜆- and 𝜆⟂ -polarization incidences. Specifically, the co-polarized transmission coefficients
remain invariant, while the cross-polarized transmission coefficients are interchanged for the flipped system under 𝜆′ - and
𝜆′⊥ -polarization incidences. For the front-side illumination with
𝜆- and 𝜆⟂ -polarizations, the output field E is given as E 𝜆𝜆𝜆 =
⊥
𝜆
[a; c] and E 𝜆𝜆⊥ = [b; d], where the superscript 𝜆(𝜆⟂ ) represents
⊥
the input 𝜆(𝜆⟂ )-polarization and the subscript represents the basis. Conversely, for the back-side illumination with 𝜆′ - and 𝜆′⊥ ′
polarizations, the output field E is given as E 𝜆𝜆′ 𝜆′ = [a; −b] and
⊥
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𝜆′
E 𝜆⊥′ 𝜆′ = [−c; d], where the superscript 𝜆′ (𝜆′⊥ ) represents the input
⊥
𝜆′ (𝜆′⊥ )-polarization and the subscript represents the basis.
These four output fields share common elements, demonstrating their interdependence. This interdependence highlights a
lack of degrees of freedom necessary to achieve four independent vector field distributions, each requiring independent control over both components of the output electric fields under four
different polarization-direction conditions of illumination. Furthermore, the analysis revealed that the co-polarized transmission coefficients remain unchanged when the direction of illumination is reversed, indicating symmetry. Consequently, polarization manipulation has received less attention in the field of
Janus metasurfaces. Most previous studies have focused primarily on scalar functionalities using cross-polarized transmission
channels, where the polarization profile of output fields was homogeneous and fixed orthogonally to the input polarization.
However, as previously mentioned, controlling the polarization of electromagnetic waves is crucial for enabling various polarization-related applications. To address the constraint
associated with Janus metasurfaces, we proposed a different
polarization-direction multiplexing approach. This technique enables a single metasurface to operate independently under different polarization-direction illumination conditions. By using
the proposed polarization-direction-multiplexed Janus vectorial
holograms, four independent asymmetric vector functionalities,
in which spatially-varying complex polarization profiles are required, can be designed. The concept is based on the spatial partitioning of the transmission space into upper and lower halfspaces, with only the upper half-space serving as the active target spatial channel, whereas the lower half-space is blocked or
ignored, as shown in Figure 3a.
This approach maximizes the available target spatial volume
for vector functionalities up to half of the transmission space by
utilizing the aforementioned spatial flipping of output fields accompanied by system flipping. For example, if the element a(x,
y) of the Jones matrix is designed to generate an image in the upper half-space for front-side illumination, the image will shift to
the lower half-space when the system is flipped for back-side illumination, thereby leaving the upper half-space vacant. In contrast, the same element a(x, y) can be designed to generate an
image in the upper half-space for back-side illumination. In this
case, this image will shift to the lower half-space for front-side
illumination, with the empty upper half-space. By designing a(x,
y) such that two images are generated in the upper and lower
half-spaces simultaneously, the desired image can be placed exclusively in the target spatial channel for both directions of illumination while blocking or ignoring information in the lower
half-space. That is, a(x, y) can be designed to achieve different
functionalities in the target spatial channel (upper half-space) for
front- and back-side illuminations without crosstalk. Similarly, by
designing other elements—b(x, y), c(x, y), and d(x, y)—four independent vector functionalities can be realized within the target
spatial channel using a single optical system. Furthermore, the
ability to design arbitrary vector functionalities for the input 𝜆′ and 𝜆′⊥ -polarizations suggest that arbitrary vector functionalities
can be designed for any other orthogonal pair of input polarizations. This indicates that the input polarizations for front- and
back-side illuminations do not have to be correlated, and any in-
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put polarizations for the back-side illumination, represented as
𝜂- and 𝜂⟂ -polarizations in Figure 3a, can be considered.
To experimentally validate our proposed polarizationdirection-multiplexed Janus vectorial holograms, we designed
and fabricated a Janus metasurface capable of generating four
distinct vectorial holographic images. Specifically, under the
front-side illumination with 𝜆- and 𝜆⟂ -polarizations, the metasurface generates the images of a butterfly and grasshopper,
respectively. On the other hand, the images of a ladybug and
beetle were generated for the back-side illumination with 𝜂- and
𝜂⟂ -polarizations, as described in Figure 3a. To maximize the
efficiency, each constituent unit cell was designed to possess a
unitary Jones matrix. Subsequently, the Janus metasurface was
optimized using gradient-descent optimization (Experimental
Section).
The numerical efficiencies, defined as the ratio of the power
of an image in the target spatial channel to the input power,
of the four vectorial holographic images were ≈31.9%, 52.8%,
44.0%, and 34.4%, assuming an ideal metasurface with unity
transmission. In our Janus vectorial hologram configuration, the
efficiency within the target spatial volume was constrained to
≈50%. This was attributed to the design of each element in
the Jones matrix generating two distinct holographic images in
the upper and lower half-spaces for front- and back-side illuminations. However, efficiency can be redistributed by prioritizing desired vector functionalities; assigning higher weights
during optimization to more critical functions can lead to increased efficiency at the cost of reduced efficiencies for less
critical functions. Furthermore, the efficiency can be enhanced
by utilizing flexibly designed nanostructures based on neural
networks,[35,36] instead of employing a set of nanostructures, or a
structural library, with discretely selected optical responses, as in
our case.
Throughout this work, we visualize polarization and intensity
using false color by mapping the normalized Poincaré sphere
into the CIELAB color space, as shown in Figure 3b. In this visualization, the azimuth and elevation angles represent the polarization, whereas the radius represents the intensity, with the
maximum intensity represented by a radius of one. The target
and the measured holographic images in the upper half-space
(refer to Figure S5, Supporting Information for the optimized
and measured images in the full transmission space) are shown
in Figure 3c, according to which the target and measured images
closely align. The degradation and speckle noise in the measured
images can be attributed to fabrication and measurement imperfections as well as the characteristics of the laser source used.
2.3. Integration of Janus Metasurfaces with State-of-the-Art
Hologram Techniques
Advancements in modern hologram techniques have significantly expanded the capacity to store information within a single
device. Our proposed Janus vectorial holograms can be designed
to integrate seamlessly with these advanced metasurface-based
hologram techniques. As exemplified, we incorporated two stateof-the-art hologram techniques: multi-plane holograms[69,74–77]
and multichannel holograms with nonseparable polarization
transformation,[72] as schematically described in Figures 4a,b.
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Figure 3. Polarization-direction-multiplexed Janus vectorial holograms. a) Schematics of Janus vectorial holograms created by a single bi-layer metasurface. The shaded regions indicate non-target spatial channels. b) Mapping of CIELAB color space onto the normalized Poincaré sphere. The conversion
relationship is expressed as (L* , a* , b* ) = (50∙(S3 + 1), 100∙S1 , 100∙S2 ). c) Experimental demonstration of Janus vectorial holograms. The upper and
lower rows represent the target and measured polarization images, respectively. Tf and Tb represent the Jones matrices for the front- and back-side
illuminations, respectively. Kets represent the polarization of incident light; |H⟩ for x-polarization; |V⟩ for y-polarization; |D⟩ for diagonal polarization;
and |A⟩ for anti-diagonal polarization.
Unlike traditional far-field holograms, which generate a single target image at the far-field plane, multi-plane holograms
generate multiple images at various positions within the Fresnel
diffraction regime. This unique feature enables the continuous
modification of diffracted patterns based on wave propagation,
rendering multi-plane holography a prominent approach for creating 3D holographic images.[69,74,77] Our proposed Janus metasurfaces can further enhance the storage capacity of information
in multi-plane holograms by introducing additional degrees of
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freedom through the polarization-direction of illumination. Our
experimental demonstrations showed that Janus metasurfaces
can store multiple vectorial holographic images in both the farfield and the Fresnel diffraction regimes under different illumination conditions (Experimental Section). Figure 4a illustrates
the schematic of the designed device for a specific incidence condition (front-side illumination with 𝜆-polarization). Specifically,
the device was designed to generate vectorial holographic images
of a butterfly, grasshopper, ladybug, and beetle in the far-field
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Figure 4. Integration of Janus vectorial hologram and state-of-the-art hologram techniques. a) Schematics of multi-plane holograms. b) Schematics
of multichannel holograms with nonseparable polarization transformation. The shaded regions represent non-target spatial channels. c) Experimental
demonstration of multi-plane holograms. The upper and lower rows represent the measured polarization images in the far-field regime and Fresnel
diffraction regime of z0 = 1 mm, respectively. d) Experimental demonstration of multichannel holograms with nonseparable polarization transformation,
with each panel displaying the measured intensity image under various incidence conditions. Tf and Tb represent the Jones matrices for the front- and
back-side illuminations, respectively. Kets represent the polarization of incident light; |H⟩ for x-polarization; |V⟩ for y-polarization; |D⟩ for diagonal
polarization; |A⟩ for anti-diagonal polarization; |R⟩ for RCP polarization; and |L⟩ for LCP polarization.
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regime, and a dog, sheep, cat, and rat in the Fresnel regime for
four different incidence conditions: front-side illumination with
x- and y-polarizations, and back-side illumination with diagonal
and anti-diagonal polarizations.
The measured vector images for four different incidence conditions are presented in Figure 4c, showing close alignment
with the target values (refer to Figure S6, Supporting Information). Notably, crosstalk between different channels is increased
slightly, a phenomenon that was barely observed in the far-field
only holograms in Figure 3c. This degradation is likely due to the
increased complexity of holograms (refer to Text S3, Supporting
Information for the detailed discussions on crosstalk). Although
the same input polarization was considered for the holographic
images in the far-field and Fresnel diffraction regimes, the system can be designed to operate with distinct input polarizations
for different imaging planes. Increasing the number of stored
images may impact the quality and complexity of the holographic
images.
Conventionally, polarization-multiplexed holograms are designed to generate only two target images for an orthogonal pair
of input polarizations. In such configurations, deviations from
the designated input polarizations often result in the observation of overlapped images of two targets. However, leveraging
the vector nature of electromagnetic fields can significantly expand this capability, enabling the creation of multiple target images for various input polarizations beyond an orthogonal pair
of polarizations within a single device. This advanced approach,
known as multichannel holograms with nonseparable polarization transformation,[72] enables more complex image storage.
Similarly, our Janus metasurfaces can further enhance the capacity for storing information in multichannel holograms. We experimentally demonstrated direction-multiplexed multichannel
holograms with nonseparable polarization transformation using
Janus metasurfaces (refer to the Experimental Section for details). Figure 4b presents a schematic of the designed device under front-side illumination. The device was particularly designed
to generate the letters “A”, “B”, “C”, and “D” for the front-side illumination with x-, y-, diagonal and anti-diagonal polarizations,
and the Greek letters “𝛼”, “𝛽”, “𝛾”, and “𝛿” for the back-side illumination with x-, y-, RCP, and LCP polarizations, respectively.
In Figure 4d, the measured intensity profiles show good agreement with the optimized images (see Figure S8, Supporting Information). The apparent crosstalk in this demonstration is attributed to the hologram technique itself (refer to Text S3, Supporting Information). Similarly, the number of stored images can
be increased at the cost of the quality and complexity of the holographic images.
2.4. Optical Encryption Based on Janus Vectorial Holograms
with High-Security Level
Numerous studies have explored the application of metasurfaces
in optical encryption, recognizing their potential to significantly
enhance security levels. Metasurfaces offer two main advantages
in optical encryption. First, their capacity for multichannel operation, utilizing polarization,[37,78–81] wavelength,[81–83] orbital angular momentum,[82,84,85] and direction[59,67,68] as multiplexing
methods, enables selective access to ciphertexts. Selective access
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ensures that users can view ciphertexts only when specific predetermined conditions are satisfied, thereby enhancing security.
Second, the high degrees of freedom offered by metasurfaces in
controlling polarization, phase, and amplitude enable the creation of highly complex ciphertexts, further enhancing security
levels.
Polarization is particularly valuable in this context owing to its
inherently multi-dimensional nature, enabling the storage of vast
amounts of information or the concealment of data awaiting decryption. By leveraging our Janus metasurfaces, we introduced
an advanced optical encryption scheme with an extremely highsecurity level. In this scheme, ciphertexts are accessible only under the correct conditions of input polarization and direction of
illumination, requiring a complex polarization filtering process
for decryption.
Our proposed polarization-direction-multiplexed Janus holograms, shown in Figure 5a, utilize computational vector polarizers (VPs) comprising arrays of pixelated virtual polarizers to
achieve high-security optical encryption. The encryption mechanism can be understood geometrically based on the Poincaré
sphere, as shown in Figure 5b. A polarizer enables the transmission of desired polarization while blocking its undesired orthogonal counterpart; for example, an x-polarizer transmits xpolarization and blocks y-polarization. Malus’ law states that only
the energy corresponding to the desired polarization can be transmitted when an arbitrary polarization is introduced.[86]
On the Poincaré sphere, an orthogonal pair of desired and undesired polarizations of the polarizers form an axis, such as the
S1 -axis for the x-polarizer. A great circle on the sphere perpendicular to the axis given by the polarizer, such as the great circle on the S2 -o-S3 -plane for the x-polarizer, represents the polarization states that possess the same amount of the desired
and undesired polarizations in terms of energy. The great circle
divides the Poincaré sphere into two hemispheres. One hemisphere is closer to the desired polarization, containing a larger
amount of the desired polarization compared with the undesired
one, whereas the other hemisphere contains a larger amount of
the undesired polarization. Therefore, polarizations on these two
hemispheres can be viewed as representing “relatively high” and
“relatively low” intensities after the light passing through the polarizer. These intensities are denoted as “1” and “0” states in this
study, rendering this division useful for optical encoding.
Expanding on this concept, if we consider three polarizers (p1 ,
p2, and p3 ) with mutually perpendicular axes on the Poincaré
sphere (such as x-, diagonal, and RCP polarizers), the Poincaré
sphere is divided into eight octants, as described in Figure 5b.
Each octant exhibits a unique intensity pattern with respect to
the three polarizers. For example, polarizations in the “011” octant show the intensity pattern of “relatively low” for the first xpolarizer, “relatively high” for the second diagonal polarizer, and
“relatively high” for the third RCP polarizer, as shown in the inset
of Figure 5b. This configuration enables the storage of 3-bit information using electromagnetic wave polarization. To maintain
uniform intensity differences between the “1” and “0” states for
the three polarizers, we only utilized the eight polarizations selected as the vertices of the inscribed cube, which are aligned with
the three axes of the polarizers. By incorporating more polarizers,
higher-density information can be stored in light polarization using a finely segmented Poincaré sphere.
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Figure 5. Optical encryption based on Janus vectorial holograms. a) Schematics of optical encryption utilizing a Janus metasurface that generates a
ciphertext with a pixelated vector polarization pattern. b) Encryption and decoding mechanisms involving polarization and polarizers. c) Experimental
demonstration of optical encryption. The left and right panels indicate the measured raw data of the Stokes parameters and computationally decoded
images with the appropriate VPs, respectively.
By employing polarization as an information carrier, three
pixelated binary images can be encrypted into a single vectorial hologram with uniform intensity and complex polarization profiles in a pixelated pattern, as shown in Figure 5a.
For each pixel, three polarizers—p1 , p2 , and p3 —are randomly selected, and three computational VPs were defined
as arrays of these three polarizers for all pixels. When this
vectorial hologram is computationally decoded using the appropriate VPs as keys, three images can be retrieved, as
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shown in Figure 5a, demonstrating the hologram’s encryption
capabilities.
As mentioned previously, Janus metasurfaces have the unique
ability to generate different vectorial holograms for various
polarization-direction illumination conditions, enabling highsecurity optical encryption when combined with our novel encryption mechanism. Decryption is successful only when the incidence direction, input polarization, and appropriate VP are satisfied, ensuring that the correct information is extracted from the
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metasurface. To demonstrate this capability experimentally, we
designed and fabricated Janus metasurfaces capable of producing four distinct vectorial holograms generating 8-by-8 and 10by-10 pixelated polarization patterns for the front- and back-side
illuminations with x- and y-polarizations. These polarization patterns, or ciphertexts, can be decoded by predefined VPs as decoding keys.
The fabricated samples were measured, and the hidden images were successfully retrieved from measurements using the
predetermined computational VPs (Experimental Section). The
hidden images in the 3-bit storage configuration were independently designed without any crosstalk. Figure 5c presents the
measured and retrieved results of the holograms generating 10by-10 pixelated polarization patterns (refer to Figure S9, Supporting Information for the results of the holograms generating 8-by8 pixelated patterns and Figure S10, Supporting Information for
the raw measured data and optimized polarization patterns).
The raw measured data are shown on the left panels of
Figure 5c, including the Stokes parameters and polarization patterns for the front- and back-side illuminations with the designed input x- and y-polarizations. These raw measurements effectively conceal any discernible clues regarding the hidden images, demonstrating the robustness of our proposed encryption
method. Conversely, upon the application of the correct computational VPs, all the hidden images were well extracted as shown
in the right panels, and all these results are in good agreement
with the ground truth binary images (see Figure S11, Supporting
Information). We assessed quantitatively the effect of noise (refer
to Text S4, Supporting Information). The calculated accuracy of
the output polarization pixels of 12 decoded images is 85.9%. The
performance of the optical encryption can be further improved by
refined experimental processes and advanced design methodologies such as neural network-based flexible nanostructure design
and fabrication-conscious design.[87]
The hidden images hold significant potential for various applications. Each hidden image can serve as true information on its
own; some images represent true information, whereas others
act as decoys; each hidden image stores a fragment of the complete information.
Our proposed optical encryption algorithm can be securely implemented using a dual-channel method for secret transmission.
For example, a metasurface is physically delivered through the
first channel, whereas detailed instructions regarding the necessary incidence conditions are delivered through the second channel. Successful decryption of the information is contingent upon
precise matching of the metasurface, instructions, and decryption key (the VP). Even if one or two of these components are
leaked to eavesdroppers, the encrypted information remains secure. The security level can be enhanced when more pixels or
polarization modulations are further considered.[78,86]
3. Conclusion
We introduced a novel approach to asymmetric transmission by
developing a generalized formulation that established a clear correlation between the roles of co- and cross-polarized transmission
coefficients for the front- and back-side illuminations. This correlation was visible when using two related polarization bases.
We numerically and experimentally demonstrated that thin film-
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like structures can achieve complete control over asymmetric
transmission by designing metasurfaces with customized co- and
cross-polarized transmission coefficients.
Furthermore, we experimentally demonstrated that the simultaneous designability of co- and cross-polarized transmission
enabled polarization-direction-multiplexed Janus vectorial holograms to inscribe four different vector functionalities within a
single metasurface. In addition, we seamlessly integrated our
proposed Janus vectorial holograms with modern advanced hologram techniques, such as multi-plane holograms and multichannel holograms with nonseparable polarization transformation. Finally, we introduced a novel optical encryption scheme in
which our Janus metasurfaces combined with the computational
VPs provide a heightened level of security.
In the future, we envision significant potential for enhancing the performance of Janus metasurfaces by integrating them
with various active metasurface techniques, full-space light modulation, and nonreciprocal optical systems. Many active metasurface techniques are based on electrical modulation,[88,89] mechanical reconfiguration,[90–92] or phase-change materials.[59,68,93]
These active metasurfaces inherently enable asymmetric transmission when external stimuli are applied. Notably, the asymmetric transmission facilitated by active metasurfaces may differ qualitatively from that achieved by Janus metasurfaces, as it
relies on the dynamic optical properties of the system, whereas
the latter depends on the static optical properties. Therefore, we
anticipate a synergistic combination of Janus and active metasurfaces.
Furthermore, light modulation in full-space presents a promising technique in which both transmission and reflection spaces
are of interest.[58,63,94] For example, an optical system capable of
diffusing white light in reflection mode while maintaining transparency in transmission mode can be utilized in transparent display or augmented reality technologies.[94] Janus metasurfaces
can be further enhanced with functionalities of full-space light
modulation.[58,63]
Finally, recent advancements in nonlinear[95,96] and space-time
metasurfaces[97,98] are noteworthy since they could provide nonreciprocal asymmetric transmission. These advancements could
potentially enable the full utilization of the transmission space
for polarization-direction-multiplexed Janus vectorial holograms
when combined with our Janus metasurfaces. Overall, we believe
that the extended functionalities offered by our Janus metasurfaces hold promise for applications across various scientific and
engineering disciplines.
4. Experimental Section
Design of Universal Metasurfaces: The unit cell structure of universal
metasurfaces (Figure 2), operating at a wavelength of 915 nm, was composed of a SiO2 substrate, Si nanoposts, and a SU-8 spacer layer, as
shown in Figure 2c. The lateral size was set at 450 nm, and the heights
of Si nanoposts in the lower and upper layers and the SU-8 spacer layer
were 790, 700, and 1300 nm, respectively. For fabrication feasibility, the
lengths of the major and minor axes of the nanoposts were restricted
to a range of 100–350 nm. The complex refractive indices of the constituent materials were assumed to be 1.45 for SiO2 , 3.61 + 0.0066i for
Si, and 1.56 for SU-8 polymer. For numerical demonstration, commercial
FDTD software from Ansys Lumerical Inc. was utilized. We randomly generated an arbitrary matrix and decomposed it to obtain related structural
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parameters of the universal metasurfaces (see Text S2, Supporting Information for the details). Using the obtained structural parameters, the universal metasurfaces were designed with sub-cells of 11-by-11 clusters of
bi-layer structures.
Fabrication of Bi-Layer Metasurfaces: The first layer of amorphous
Si, with a thickness of 790 nm, was deposited on quartz glass using
plasma-enhanced chemical vapor deposition. For electron-beam (e-beam)
lithography, an adhesion layer (AR 300–80, Allresist), e-beam resist (ARP 6200.04, Allresist), and conductive polymer (AR-PC 5090.02, Allresist)
were spin-coated. Then, alignment-marks were patterned using e-beam
lithography, followed by metal deposition of Cr with 20 nm thickness and
Au with 50 nm thickness using e-beam evaporation and lift-off process. For
the patterning of nanopost structures on the lower layer, the e-beam lithography process was employed. An alumina hard mask with a thickness of
60 nm was deposited by e-beam evaporation, and the lift-off process was
performed. To achieve vertical sidewalls and a high aspect ratio, the deep
reactive ion etching technique, known as pseudo-Bosch dry etching, was
utilized. Then, the first layer was coated by spin-coating SU-8 polymer with
a 1.7 μm thickness to encapsulate the first layer and provide a flattened
surface for the deposition of the second layer. The second layer of amorphous Si, with a thickness of 650 nm, was deposited by radio-frequency
sputtering. Nanopost structures on the second layer were patterned using
a process similar to that of the first layer. For experimental demonstration,
pixels of Janus metasurfaces were composed of 3-by-3 clusters of bi-layer
structures.
Design of Scalar Holograms: All holograms demonstrated in this work
were optimized using gradient-descent optimization (refer to Text S5,
Supporting Information for the details). For optimization of a multifunctional device with ∑
various incidence conditions, the total loss function
was set as Ltot = i L(i) , where Ltot is the total loss function, and L(i)
is the loss function of the i-th function of a metasurface. For the optimization of scalar holograms (Figure 2), the loss function given as L(i) =
2
(i) ∗,(i)
(i) ∗,(i) 2
1 ∑ ∑
+ Epq,y ty | − I(i) ) , was used where N is the nump
q (|Epq,x tx
N2
ber of spatial points in the kx and ky domain in the far-field plane, the
subscripts p and q represent the indices of spatial points in the kx and ky
(i)
(i)
domain, Ex and Ey are the x- and y-components of the output electric
field in the far-field regime for the i-th incidence condition, I(i) is the in-
tensity profile of the i-th holographic image, the superscript * represents
(i)
(i)
conjugation, and tx and ty represent the x- and y-components of the target polarization of the i-th holographic image. Intuitively, the first term of
the loss function could be understood as a term for inserting a polarizer
to pass the desired polarization. Then, through the optimization, this intensity of the desired polarization got closer to the target intensity profile.
Design of Polarization-Direction-Multiplexed Janus Vectorial Holograms:
For optimization of Janus vectorial holograms that generate four vectorial holographic images in the far-field regime with spatially varying polarization for different incidence conditions (Figures 3 and
2
∑ ∑ [ (i) 2
(i) 2
5), the loss function given as L(i) = N14
p
q (|Epq,x | − |tpq,x | )
2
(i) 2
(i) 2
(i) (i)
(i) (i) 2 ]
+(|Epq,y | − |tpq,y | ) + |Epq,y tpq,x − Epq,x tpq,y | , was used where N is the
number of spatial points in the kx and ky domain in the far-field plane, the
subscripts p and q represent the indices of spatial points in the kx and
(i)
(i)
ky domain, Ex and Ey are the x- and y-components of the output elec(i)
tric field in the far-field regime for the i-th incidence condition, and tx
(i)
and ty represent the x- and y-components of the target output field of the
i-th holographic image. The first and second terms of the loss function
could be intuitively understood as terms for matching the amplitude of xand y-polarization components, and the third term as a term for matching the∑relative phase between them. The total loss function was given as
Ltot = i L(i) . It is important to note that since only the upper half-space
was of interest, only the gradient information of the upper half-space was
considered during the optimization to maximize efficiency through the target spatial channel.
Design of Multi-Plane Janus Vectorial Holograms: For the optimization of multi-plane Janus vectorial holograms that generate
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eight vectorial holographic images in the far-field and the Fresnel diffraction regimes (Figure 4), two kinds of loss functions
were used. The first kind, used to optimize holograms for the far2
∑ ∑
(i)
(i) 2
(i) 2
field regime, was given as L1 = N14
p
q [(|Epq,x | − |tpq,x | )
2
(i)
(i)
2 2
(i)
(i)
(i)
(i)
2
+(|Epq,y | − |tpq,y | ) + |Epq,y tpq,x − Epq,x tpq,y | ], where N is the number of spatial points in the kx and ky domain in the far-field plane, the
subscripts p and q represent the indices of spatial points in the kx and ky
(i)
(i)
domain, Ex and Ey are the x- and y-components of the electric field in the
(i)
(i)
far-field regime for the i-th incidence condition, and tx and ty represent
the x- and y-components of the target output field of the i-th holographic
image in the far-field regime. The second kind of loss function, used to
optimize the holograms for the Fresnel diffraction regime, was given
∑ ∑
(j)
′,(j)
′,(j)
′,(j)
′,(j)
′,(j) ′,(j)
as L2 = a b [(|Eab,x |2 − |tab,x |2 )2 + (|Eab,y |2 − |tab,y |2 )2 + |Eab,y tab,x −
′,(j) ′,(j)
Eab,x tab,y |2 ], where the subscripts a and b represent the indices of spatial
′,(j)
′,(j)
points in the real domain of the Fresnel diffraction regime, Ex and Ey
are the x- and y-components of the electric field in the Fresnel diffraction
′,(j)
′,(j)
regime for the j-th incidence condition and tx and ty represent the
x- and y-components of the target output field of the j-th holographic
image in the Fresnel diffraction regime. The electric field in the Fresnel
diffraction regime was calculated using the angular spectrum method.[99]
∑ (i)
∑ (j)
The total loss function was given as Ltot = i L1 + j L2 . Note that
only the gradient information of the upper half-space was considered
during the optimization to maximize efficiency through the target spatial
channel.
Design of Multichannel Holograms with Nonseparable Polarization Transformation: For optimization of multichannel holograms with nonseparable polarization transformation (Figure 4), the loss function given as
2
∑ ∑
(i) 2
(i) 2
L(i) = N14 p q (|Epq,x | + |Epq,y | − I(i) ) , was used where N is the number of spatial points in the kx and ky domain in the far-field plane, the
subscripts p and q represent the indices of spatial points in the kx and ky
(i)
(i)
domain, Ex and Ey are the x- and y-components of the output electric
field in the far-field regime for the i-th incidence condition and I(i) is the
intensity profile∑
of the i-th holographic image. The total loss function was
given as Ltot = i L(i) .
Optical Characterization: Scalar holograms and multichannel holograms with nonseparable polarization transformation were characterized
using the setup shown in Figure S14 (Supporting Information). The polarization of incident light was controlled using a half-wave plate and a
quarter-wave plate. After passing through the device, the Fourier plane
was formed at the back-focal plane (BFL) of an objective lens (MPLFLN
10x, Olympus). To facilitate measurement, the Fourier plane was projected
onto a charge-coupled device (CCD) camera (CS505MU, Thorlabs) using
a 4-f system (LSB04, Thorlabs) with a focal length of 200 mm. For measuring scalar holograms, a linear polarizer and a quarter-wave plate were
placed in front of the CCD camera to pass only the desired elliptical polarization. Vectorial holograms were characterized by Stokes parameters,
which could be determined by four intensity measurements with the predefined configurations of a linear polarizer and a quarter-wave plate in
front of the CCD camera.[69,100] Holographic images in the Fresnel regime
could be measured directly by measuring the Fresnel diffraction regime
using a tube lens instead of a 4-f system as in Figure S14 (Supporting
Information).
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
This work was supported by the National Research Foundation
(NRF) grants (NRF-2021R1A2C2008687, NRF-2021M3H4A1A04086555,
© 2024 The Author(s). Advanced Materials published by Wiley-VCH GmbH
15214095, 2024, 44, Downloaded from https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202406717 by Huazhong University Of Sci & Tech, Wiley Online Library on [30/06/2025]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
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RS-2023-00283667) funded by the Ministry of Science and ICT (MSIT), Republic of Korea.
Conflict of Interest
The authors declare no conflict of interest.
Author Contributions
H.K. and J.J. contributed equally to this work. H.K. and J. J. conceived the
idea, and J.S. supervised the project. J.J. conducted the theoretical analyses. H.K. performed the numerical simulations and designed the samples.
H.K. and J.J. fabricated the samples and characterized them optically. H.K.,
J.J., and J.S. prepared the manuscript. All authors have accepted responsibility for the entire content of this submitted manuscript and approved its
submission.
Data Availability Statement
The data that support the findings of this study are available from the
corresponding author upon reasonable request.
Keywords
asymmetric transmission, Janus metasurface, optical encryption, vectorial
hologram
Received: May 10, 2024
Revised: August 26, 2024
Published online: September 13, 2024
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