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RESEARCH ARTICLE
www.lpr-journal.org
On-Demand Subwavelength-Scale Light Sculpting Using
Nanometric Holograms
Xiliang Zhang, Yanwen Hu, Xin Zhang, Zhen Li,* Zhenqiang Chen, and Shenhe Fu*
Spatially or temporally structured light has attracted considerable attention for
its intriguing beam characteristics, which have found extensive applications
in classical and quantum optics. Extending structured light from macroscale
and microscale to nanometricscale brings more prospects both for
fundamental and applied science. However, sculpting light at the
subwavelength scale remains a challenge since its transverse structure is
fragile in the nanometric scale. Here a novelholography for arbitrary light
sculpting at the subwavelength scale is demonstrated. A wave phenomenon
of diffractive focusing from an amplitude-only nanometric (50-nm-thick) film
is introduced, and use of the induced high-spatial-frequency waves as carriers
to encode information of an object is considered. Using this technique,
nanometric holograms are designed and fabricated for generating the
well-defined eigen modes including the zero-order Bessel beam, vortex beam,
vector beam, Airy beam, as well as an arbitrary light pattern, with feature sizes
on the deep-subwavelength scale. The broadband performance of the
hologram is examined, and a white-light nondiffracting beam at the
deep-subwavelength scale is realized. This demonstration paves a way toward
on-demand light sculpting at the nanometric scale, which may find
applications such as optical super-resolution imaging, nanoparticle
manipulation, and precise measurements.
1. Introduction
A propagating light beam contains fundamentally physical pa-
rameters such as amplitude, phase, polarization, wavevector, co-
herence, topology, and so forth. These parameters mainly deter-
mine the propagation dynamics of light in space or time. They
X. Zhang, Y. Hu, X. Zhang, Z. Li, Z. Chen, S. Fu
Department of Optoelectronic Engineering
Jinan University
Guangzhou 510632, China
E-mail: tlzh268@jnu.edu.cn; fushenhe@jnu.edu.cn
X. Zhang, Y. Hu, X. Zhang, Z. Li, Z. Chen, S. Fu
Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Com-
munications
Guangzhou 510632, China
Z. Li, Z. Chen, S. Fu
Guangdong Provincial Engineering Research Center of Crystaland Laser
Technology
Guangzhou 510632, China
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/lpor.202300527
DOI: 10.1002/lpor.202300527
can be carved spatially or temporally,[1,2]
using modulating devices including the
digital micromirror device,[3] spatial light
modulator,[4] anisotropic wave plate,[5]
and other metamaterial (metasurface)
elements.[6–11 ] Hence, numerous spatial
or temporal (or spatiotemporal) struc-
tures of light with unusual properties
can be generated.[1,12–15 ] One example is
the light beam, which can be precisely
sculpted to carry both spin and orbital an-
gular momenta, that is, the vector-vortex
beam.[16–20 ] This structured light is
characterized by a helical wavefront and
exhibits inhomogeneous polarization,
leading to intriguing applications in the
emulations of quantum processes.[21,22 ]
Another featured examples include
the Bessel beam,[23–25 ] Airy beam,[26–30 ]
and recently reported pendulum-type
beam,[31] which propagates (accelerates)
along arbitrary trajectory in 3D space
without diffraction and disintegration.
The structured light has been applied to
control nanostructures (particles),[32,33 ]
Bose–Einstein condensates,[34] electric
currents,[35] etc., and led to intriguing
spin-orbit couplings when the structured light meets structured
materials.[36,37 ] Therefore, light sculptings are crucial in many as-
pects of scientific research.
While many investigations on light sculptings were imple-
mented, the transverse dimension of the mostly studied light
patterns remains at macroscale or microscale. This “large-scale”
light pattern is uncompetitive in nanotechnologies such as na-
nomicroscopy, nanoparticle manipulation, nanofabrication. On
the other hand, the subwavelength structured light leads to
prominent spin-orbit interactions,[38] which strongly depend
not only on material structures but also on the spatial struc-
tures of light, bringing more prospects for the fundamental
and applied science.[39,40 ] Nevertheless, the far-field generation
and arbitrary manipulation of light on the deep-subwavelength
scale remain challenging. Possible solutions have been demon-
strated to address this problem. For instance, tightly focusing
the structured light with high-numerical-aperture lenses is com-
monly used to produce and control the subwavelength-scale
light fields.[41,42 ] However, due to the inevitable spin-orbit in-
teractions of light in tightly focusing condition,[38] the inci-
dent state cannot be maintained at the focal plane. The effects
of mutual conversions between spin (polarization) and orbital
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(phase) terms take place,[43,44 ] leading to longitudinal polariza-
tion component.[36,41,42 ] One may also exploit effect of optical su-
peroscillation, which is a phenomenon of wave that oscillates at
local frequency faster than its highest Fourier one, to realize deep-
subwavelength light patterns.[45–47 ] Yet for many years, the chal-
lenges have been generally to remove the unwanted strong side-
lobes from the superoscillatory light patterns.[25,48 ] In addition,
photonic structures such as subwavelength angular gratings,[49]
waveguide arrays,[50] metamaterials,[51] can significantly squeeze
the light field into extremely small scale; however, they only sup-
port several specific light modes that are difficult to be tuned;[52]
if these subwavelength modes emit from the structure to free
space, they exhibit serious diffraction and expand rapidly dur-
ing propagation. We emphasize that the diffraction limit restricts
spot size of light to about half the wavelength. A tradeoff between
spot size and diffraction of light significantly hinders subwave-
length generation of the nondiffracting beams.
In this article, we introduce theoretically and experimentally
a holographic technique for arbitrary light sculpting at the sub-
wavelength scale, without an accompany of the longitudinal com-
ponent. Specifically, the amplitude and phase information of an
object is carried by delicate high-spatial-frequency waves which
are excited by edge diffraction of an ultrathin film. A proper de-
sign of a nanometric sophisticated film allows to manipulate
the high-spatial-frequency waves in the reciprocal space such
that the object waves can be recovered at the subwavelength
scale. This holographic technique depends on the high-spatial-
frequency wave carriers, very distinct from conventional holog-
raphy which is based on zero-order diffractive wave and hence
operates at large-scale beam size. We present nanometric holo-
grams and demonstrate arbitrary light sculpting at the subwave-
length scale, both in the scalar and vector frameworks.
2. Theoretical Model and Experimental Scheme
To realize holographic light manipulation on the deep-
subwavelength scale, we exploit the novel concept of diffractive
focusing effect induced by a sharp truncation to the incident light
wave.[53] The diffractive focusing is originating from an internal
structure of the initially truncated light, which causes focusing
diffractive wavevectors in the phase space, as first revealed
by a rectangular wavefunction in the quantum mechanics.[54]
Such a concept has been recently extended to different settings
including plasmonics, optics and hydrodynamics.[55,56 ] We st ar t
by considering truncating an incident plane wave using a non-
transparent film of negligible thickness. The truncated light field
at the interface immediately introduces a local discontinuity in
phase and amplitude distributions, which can be represented by
a step function, as illustrated in Figure 1a. The sharply truncated
light is then diffracted into different orders in the far field (the
propagating ones) and partially converted to the non-propagating
(evanescent) waves in the near field. The diffractive waves having
wavenumbers comparable to the incident one can propagate
freely to the far-field region,[57] with a large bending angle.
In this work, we concentrate on the propagating higher-order
diffractive components with different high-spatial frequencies.
We therefore define them as the high-spatial-frequency waves
featured by spatial frequencies kxand ky, with respect to co-
ordinates xand y, respectively. Essentially, the appearance of
the high-spatial-frequency waves is explained by a giant phase
gradient of the initially truncated light wave. In this scenario,
the high spatial frequencies can be expressed as
(kx,k
y)=𝜕Φ(x, y)
𝜕x
x+𝜕Φ(x, y)
𝜕y
y(1)
where Φ(x, y) is the spatial phase distribution of the truncated
light field.
xand
ydenote unitary vectors associated with the co-
ordinates xand y, respectively. Clearly, interfacial discontinuity
of the truncated light gives rise to an abrupt phase change, re-
sulting in significant high-spatial-frequency waves. As an illus-
tration, Figure 1b presents the resulting continuous diffractive
components from a step truncation function, whereas Figure 1c
depicts the high-spatial-frequency waves in a form of cosine func-
tion with different frequencies. The higher-order diffractive com-
ponent has a larger spatial frequency but with a relatively weaker
amplitude. If the spatial wavevectors (kx,k
y) are arranged to ex-
hibit cylindrical symmetry (in phase) with respect to the on-
axis position, a constructive diffraction-limit light spot in the
deep-subwavelength scale can be realized.[24] This fact implies
that the light field initially truncated by an appropriate trunca-
tion function significantly shrinks in the course of propagation.
Such a working principle enables to manipulate the high-spatial-
frequency waves in reciprocal space for a subwavelength-scale
structured light. Based on the diffractive focusing, we subse-
quently generate nanometric holograms to truncate the incident
light field, arbitrarily sculpting light at the deep subwavelength
scale. This requires to satisfy two conditions. First, the designed
hologram should be thinned to a nanometric scale, which causes
a sufficiently sharp truncation to the incident light and induces
pronounced high-spatial-frequency waves propagating into the
far field. Second, the complex amplitude and phase information
of a desired light field is carried by the high-spatial-frequency
waves (kx,ky). We report a nanometric holographic technique for
encoding the light field. The nanometric hologram is produced
by a two-beam interference, that is, a superposition between a
converging spherical wavefront E(x, y, zf)=exp(−i2𝜋r∕𝜆)andan
arbitrary object wave O(x, y, zf)=A(x, y, zf)exp[i𝜙(x, y, zf)], where
Aand 𝜙represent, respectively, the desired complex amplitude
and phase distributions of the object wave. The amplitude A
is normalized to unitary while the phase 𝜙is in a range be-
tween 0 and 2𝜋.zfdenotes a converging distance at which the
two waves interfere coherently, 𝜆is a carrier wavelength and
r=(x2+y2+z2
f)1∕2. The resulting holographic pattern is written
as
M=2Acos 2𝜋r∕𝜆+𝜙(x, y, zf)(2)
The spherical wavefront that is encoded into the ultrathin holo-
gram is utilized to globally manipulate the high-spatial-frequency
waves such that they exhibit cylindrical symmetry in the recipro-
cal space, and contribute to constructive wave interfering at the
subwavelength scale. The object wave form O(x, y) can be given
either by direct analytical solutions to the electromagnetic wave
equation such as the typical Gaussian mode, Laguerre–Gaussian
mode, Bessel mode, vortexing mode, or by using numerical al-
gorithm to calculate the indirect phase distribution of an arbi-
trary object. The value of function M(x, y) changes continuously
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Figure 1. Working principle for the nanometric hologram and experimental characterization. a) An incident wave is diffracted at the edge of an ultrathin
interface, leading to propagating high-spatial-frequency waves and non-propagating evanescent (surface) waves. b) Continuous distribution of high-
spatial-frequency components (right panel) obtained from a step truncation function to incident wave (left panel). c) Illustration of the high-spatial-
frequency waves in a cosine form. d) Structure of the nanometric hologram. e,f) Geometric layouts of designed and fabricated holograms for the
zero-order Bessel beam. g) Experimental setup. BS: beam splitter; OB: objective lens; TL: tube lens; M: mirror; CCD: charge-coupled device.
from −2 to 2 A, which poses a great challenge to generate a holo-
gram mask with a nanometric thickness. To overcome this prob-
lem, we binarize the interference pattern M(x, y) according to an
amplitude-related bias function cos[𝜋q(x, y)], where q(x, y) is rele-
vant to the amplitude distribution A(x, y). We note that this tech-
nique was originally proposed for phase-only holography.[ 58,59]
We apply it for producing the binary amplitude-only hologram
with nanometric thickness. The spatial position of the construc-
tive and destructive fringes of the interference pattern M(x, y)
satisfies the relationship: cos[2𝜋r∕𝜆+𝜙(x, y)] =cos[𝜋q(x, y)]. Ac-
cordingly, we rewrite the amplitude mask as:
M=1
21+sgn cos( 2𝜋r
𝜆+𝜙)−1
2cos(𝜋q) (3)
where sgn(⋅) represents a signum function. The resulting binary
hologram is composed of spatially shaped apertures with differ-
ent structure geometries, manifesting information of the original
object. Another issue is to address how q(x, y) is associated with
the desired amplitude A(x, y). For this purpose, we expand the
binary function M(x, y) according to the Fourier series represen-
tation
M=1
21+
m=+∞
m=−∞ sin(m𝜋q)
mexp [im (2𝜋r∕𝜆+𝜙)](4)
where mdetermines order of diffraction. Here we focus on the
first-order diffraction (m=±1) and set A=sin(𝜋q), that is, q=
1∕𝜋arcsin(A). We further simplify Equation (3) using the paraxial
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wave condition, that is, r≃zf+(x2+y2)∕(2zf). With these con-
ditions, Equation (3) can be rewritten as:
M=1
21+sgncos 𝜋(x2+y2)
𝜆zf
+𝜙−1
2cos (arcsin A)
(5)
where we have removed the term 2𝜋zf∕𝜆, since the binary holo-
gram M(x, y) is recorded only in the transverse plane. The ad-
vantages of the developed holography are that the hologram en-
codes both the spherical wavefront and full information of the ob-
ject. The resultant holographic element is able to reproduce the
object pattern in the far field and provides a manner for deep-
subwavelength light sculptings.
To fabricate the nanometric hologram, we consider using an
extremely thin gold film deposited onto a 0.3-mm-thick glass sub-
strate. The gold film has a thickness of only 50 nm. Another 10-
nm-thick chromium film is utilized as an adhesion layer between
the metallic film and the substrate, see Figure 1d. The ultra-
violet lithography is used to generate a hologram mask, and then
the focused ion beam (FIB) is used to etch the mask to obtain
the final hologram pattern. Note that the substrate, together with
the adhesion layer, only acts as a holder for the nanometric holo-
gram and does not modulate the incident light. We emphasize
that the thickness of the holograms is an important issue for
realizing subwavelength-scale light sculpting since it requires
constructive contributions from the high-spatial-frequency prop-
agating waves. Smoothing the truncation function would lead to
negligible high-spatial-frequency wave effect. We take the Bessel
beam as an example to illustrate the 50-nm-thick hologram. The
specific phase function 𝜙of the Bessel beam is given by Equa-
tion (6). Figure 1f shows a fabricated nanometric hologram for
the zero-order Bessel beam, which matches well to the calculated
pattern as depicted in Figure 1e. The complex amplitude of inci-
dent light is freely transmitted through the hologram apertures,
while it is cut sharply near the edges. The emerging light from
the hologram is represented as E0×M(x, y), where E0denotes an
initial amplitude.
Figure 1g displays an experimental setup to characterize the
nanometric hologram. A linearly polarized He-Ne laser operat-
ing at a wavelength of 𝜆=632.8 nm is weakly focused into the
hologram from the substrate side. The sample is placed at a posi-
tion of z=0, where zdenotes propagation distance. The emerg-
ing light field from the hologram is modulated and detected by
a microscopy system, which is comprised of an objective lens
(Nikon, CFI EPI 150×, numerical aperture (NA) 0.9), tube lens,
and a charge-coupled device (CCD) with a pixel size of 1.4 μm.
In order to observe the holographic reconstruction and evolution
along distance, the objective lens is mounted to a precise stage
which can be electrically controlled and moved along z-axis with
a step size about 20 nm.
3. Results and Discussions
3.1. Subwavelength Generation of the Bessel Beam
We design and fabricate a nanometric hologram for generat-
ing the nondiffracting beam at the deep subwavelength scale.
This beam is an eigenmode to the free-space Helmholtz wave
equation,[23] featured by the Bessel function. The required phase
distribution for the nanometric hologram is
𝜙(x, y)=2𝜋−2𝜋
𝜆⋅x2+y2(6)
Figure 1e and 1f show the theoretical and experimental layouts
of the Bessel-beam hologram, respectively, with a radius setting
as 𝜌=20 μm. We study reconstruction of the Bessel beam at the
subwavelength scale. Figure 2a presents theoretical and experi-
mental intensity distributions of the diffracted light fields in the
y–zplane. As expected, the generated light pattern remains non-
diffracting during propagation along distance up to z=25 μm.
The nondiffracting characteristic is a direct result of coherent su-
perposition of the propagating high-spatial-frequency waves. Af-
ter a distance of 25 μm, the high-spatial-frequency waves gradu-
ally separate in space during propagation. As a result, the sub-
wavelength Bessel wave form cannot maintain at all. The gener-
ated Bessel wave form is confirmed by the theoretical (Figure 2b)
and experimental (Figure 2c) measurements at a distance of
z=20 μm. The full width at half maximum (FWHM) of the in-
tensity profile is measured as 349 nm, very close to the optical
diffraction limit, see result in Figure 2d. These results indicate
that the original phase information 𝜙of the zero-order Bessel
beam has been correctly encoded into the nanometric hologram
that is able to recover the target at the subwavelength scale. Ac-
cording to a definition of the NA for the zero-order nondiffract-
ing Bessel beam,[60] that is, NA =0.358𝜆∕FWHM, we can fur-
ther calculate the resulting numerical aperture of the nanomet-
ric hologram as NA =0.65. Such a high NA is difficult to be
achieved with conventional axicon devices, since the light bend-
ing angle is seriously restricted by the total internal reflection
angle of the axicons. We examine other nanometric hologram
with a larger radius and obtain similar results. We increase the
radius to 𝜌=25 μmand𝜌=30 μm, with outcomes illustrated
in Figures 2e–h and 2i–l, respectively. It is seen that increas-
ing the radius of the hologram leads to a longer distance for
the nondiffracting Bessel beam propagation. Despite variation
of the hologram size, the nondiffracting Bessel beam structure
can be also recovered in the subwavelength scale. The zero-order
Bessel profiles are experimentally observed, see measurements
recorded at z=20 μm in Figure 2g,k, in accordance with the
simulations in Figure 2f,j, respectively. The FWHM values of the
Bessel profiles are measured as 362 and 378 nm, for the cases of
𝜌=25 μmand𝜌=30 μm. It means that changing the radius of
the nanometric hologram slightly alters its numerical aperture.
We demonstrate that the nanometric hologram exhibits broad-
band characteristic, which enables recovering the subwavelength
Bessel beams at different colors. Particularly note that the white-
light nondiffracting beams were previously demonstrated both
theoretically and experimentally.[61,62] However, these beams so
far have been only generated in a large spatial scale, while produc-
ing such a white-light nondiffracting beam at the subwavelength
scale is not reported. Regarding this issue, we first investigate the
broadband performance of the nanometric hologram by illumi-
nating with different color laser beams. We replace the 632.8 nm
laser with 532 and 405 nm laser sources, while keeping the ex-
perimental setup unchanged. Figure 3a–d and 3e–h presents the
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Figure 2. Subwavelength generation of the zero-order Bessel beam. Three nanometric holograms are designed and fabricated, with radius setting as:
𝜌=20 μm(a–d);𝜌=25 μm (e–h); and 𝜌=30 μm (i–l). a,e,i) Theoretical and experimental intensity distributions of light field in the y−zplane. The
holograms are placed at z=0. b,c,f,g,j,k) The recovered light patterns at a distance of z=20 μm. d,h,l) Cross-sections of normalized intensity profiles
along x-axis at y=0. The data is recorded at z=20 μm. Red curves denote the experiments, while blue curves represent the simulations. In color bars,
H: high; L: low.
reconstructed light patterns both theoretically and experimen-
tally at these two different colors. In these experiments, we utilize
a nanometric hologram with a radius of 𝜌=25 μm. Evidently, the
recovered light beams exhibit nondiffracting propagation prop-
erty. The dispersion effect of the nanometric hologram does not
affect the reconstruction of the subwavelength Bessel beams, dis-
tinct from most diffractive elements which usually depend on
the illumination wavelength. Figures 3b,c and 3f,g displays cor-
responding intensity distributions for the two color lasers, veri-
fying the Bessel wave forms. The FWHM values of the central
main lobes are measured as 328 nm for 𝜆=532 and 296 nm for
𝜆=405 nm, indicated in Figure 3d,h, respectively. From these
results, together with the outcome in Figure 2e, we find that the
subwavelength feature size of the generated Bessel light beam is
proportional to the considered wavelength.
Based on the broadband property of the nanometric hologram,
we discuss possibility for generating a white-light nondiffracting
beams at the subwavelength scale. We hence modify the exper-
imental setup by using an incoherent white light source, rather
than the coherent laser beam. An optical spectrometer is used
to characterize the white light source, with its spectrum mainly
ranging from 380 to 1100 nm, as illustrated in Figure 3j. The
measured spectral intensity is nearly invariant within the visible
wavelengths. More details for the white-light illumination refer
to Section SA, Supporting Information. The recovered light pat-
tern after the nanometric hologram is precisely recorded from z
=0–20 μm, with the help of a nano-displacement stage. From
the measurement shown in Figure 3i, we observe a Bessel-like
pattern having a bright (white) main lobe at the center, propagat-
ing along distance without significantly diffraction. The central
bright spot of the reconstructed light pattern exhibits no disper-
sion. This is because the high-spatial-frequency waves induced by
hologram diffraction of all frequency components of the white-
light source contribute equally to the central position. On the
other hand, the central main lobe is surrounded by a series of
circular rings at the off-center region, which exhibit diffraction-
induced dispersion, as observed from Figure 3k,l, recorded at
z=10 μmandz=20 μm, respectively. Each Bessel ring has clear
spectral separation in the transverse plane, with red color at the
inner radius of the ring. The wavelength-dependent separation
in the Bessel ring can be measured as small as 100 nm. Such
a fine spatial separation may find potential applications in pre-
cision measurement.[63] The outcomes in Figure 3m,n further
show that the FWHM value of the white-light beam is at the deep-
subwavelength scale, and slightly increases with propagation dis-
tance. We emphasize that this is the first time, to our knowledge,
to demonstrate a white-light weakly diffracting beam at the sub-
wavelength scale.
3.2. Subwavelength Generations of Arbitrary Structured Beams
We turn attention to generate arbitrary structured light beams
including the typical vortex beam and vector beam, using the
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Figure 3. Broadband performance of the nanometric hologram and subwavelength generation of a white-light nondiffracting beam. The hologram with a
radius of 𝜌=25 μm is illuminated by two laser sources: a–d) 𝜆=532 nm and e–h) 𝜆=405 nm. a,e) Theoretical and experimental intensity distributions of
light fields in the y–zplane. b,c,f,g) Illustrate the recovered light patterns at a distance of z=20 μm. d,h) The corresponding cross-sections of normalized
intensity profiles along x-axis at y=0. Red curves denote the experiments, while blue curves represent the simulations. i) Intensity distribution of the
white-light nondiffracting beam in y–zplane. It is obtained by white-light illumination, whose spectrum is depicted in (j). k,l) The reconstructed light
patterns at the distances of z=10 and 20 μm. m,n) The corresponding cross-sections to (k,l) showing the normalized intensity profiles along x,aty=0.
In color bars, H: high; L: low.
same holographic principle. These spatially structured beams
have been drawing considerable attention.[1,2 ] Nevertheless, pro-
ducing them at deep-subwavelength scale remains challenging
since their structures tend to disintegrate at the subwavelength
scale. To generate a subwavelength vortex beam, we encode the
following vortex wavefront into a nanometric hologram
𝜙(x, y)=2𝜋−2𝜋
𝜆×x2+y2+𝓁𝜑(7)
where 𝜑=arctan(y∕x) is an azimuthal angle and 𝓁is a topologi-
cal charge of the vortex beam. Here the Bessel profile is also en-
coded, in order to generate a non-diffracting vortex beam at the
deep-subwavelength scale. We design and fabricate the nanomet-
ric holograms with different topological charges. The geomet-
ric layouts are presented in Section SB, Supporting Information.
Figure 4a–d presents the results for 𝓁=1, whereas similar re-
sults for 𝓁=2 can be found in the Section SC, Supporting Infor-
mation. Figure 4a presents both the theoretical and experimen-
tal light patterns, showing clear nondiffracting hollow structures
(higher-order Bessel forms) along distance. We further charac-
terize the recovered light pattern with a measurement at z=20
μm, see Figure 4b, showing the first-order Bessel-like structure.
Such a beam structure guarantees the nondiffracting propaga-
tion. To verify the vortex wavefront, another plane wave beam is
introduced in the setup to interfere with the reconstructed light
field. The resulting interference pattern is displayed in Figure 4c.
A clear dislocation in the fringes (see the white dashed line) man-
ifests the vortex phase. The FWHM value of the main lobe is mea-
sured as 263 nm, at the position of z=20 μm, as indicated in
Figure 4d; while the peak-to-peak distance is measured as 526
nm, smaller than an optical wavelength (𝜆=632.8nm).These
results confirm a subwavelength generation of the nondiffract-
ing vortex beam using the designed nanometric hologram. We
demonstrate that the nanometric hologram is able to sculpt vec-
torial light beam at the subwavelength scale. Unlike the scalar
beams whose phase can be described by scalar functions and en-
coded directly into the nanometric holograms, the vectorial char-
acteristics of light cannot be written directly into the nanomet-
ric hologram. However, such a spatially varying polarization state
can be carried by an incident beam and recovered at the subwave-
length scale after light passing through an appropriately designed
nanometric hologram. In this scenario, we demonstrate the zero-
order (𝓁=0) nanometric hologram by illuminating it with a vec-
tor beam, which can be realized by inserting a q-plate into the
setup. Specifically, setting a topological charge of the q-plate as
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Figure 4. Subwavelength generations of the Bessel vortex beam and vector beam. a–d) A nondiffracting vortex beam with a topological charge of 𝓁=1
is realized at the deep-subwavelength scale, using a first-order (𝓁=1) Bessel hologram with radius being 𝜌=20 μm. The hologram is illuminated
by a linearly polarized plane wave beam. e-h) A nondiffracting spirally polarized vector beam (the polarization angle 𝛼=𝜋∕4) is realized at the deep-
subwavelength scale, using a zero-order (𝓁=0) Bessel hologram with radius being 𝜌=20 μm. The hologram is illuminated by the vector beam (𝛼=
𝜋∕4). a,e) Theoretical and experimental intensity distributions of light fields in the y–zplane. b,f) The recorded light patterns at a distance of z=20 μm.
c) Plane-wave interference pattern and g) horizontal polarization component for verifying vortex phase and vector state of light, respectively. d,h) The
corresponding cross-sections of the intensity profiles to (b,f). In color bars, H: high; L: low.
q=1∕2, a linearly polarized laser beam can be coherently con-
verted to a vector beam expressed as[17]
E0(x, y)=f0(x, y)[cos(𝜑+𝛼)
x+sin(𝜑+𝛼)
y](8)
where f0(x, y)=x2+y2∕W0exp[−(x2+y2)∕W2
0] denotes a
Laguerre–Gaussian envelope with Gaussian duration being W0.
Owing to cylindrical symmetry of the zero-order Bessel hologram
(see Figure 1d), we expect that the original vector state of light can
be reconstructed at the subwavelength scale. We set a polariza-
tion angle to be 𝛼=𝜋∕4. In this case a spirally polarized vector
beam is generated for illuminating the hologram. Figure 4e
shows the recovered vector light pattern which propagates with-
out diffraction along the distance. The experiment matches well
with the simulation. Note that the simulation is performed ac-
cording to the vectorial wave equation ∇×∇×E−k2E=0, with
an input E(x, y, z =0) =E0(x, y)×M(x, y). Figure 4f presents
intensity distribution of the generated vector beam at z=20
μm, showing a well reconstructed first-order Bessel structure.
Its vectorial feature is revealed by measuring the horizontal
polarization component as illustrated in Figure 4g. Particularly
note that the resulting FWHM value of the main lobe is 263 nm
and the peak-to-peak width is 532 nm, indicated in Figure 4h.
This is the same as those for the first-order vortex beam. We
attribute this phenomenon to their identical topological charge,
which results in an identical first-order (𝓁=1) Bessel profile,
as revealed by the theory in ref. [24]. This also happens when
considering other nanometric holograms with different radiuses
(NA), as adjusted from results in Figures S3 and S5, Supporting
Information. More results for subwavelength vector beam ma-
nipulations using other nanometric holograms are presented in
Section SD, Supporting Information.
We theoretically investigate subwavelength generation of other
kind of structured light (the Airy beam) which propagates along
a curve line rather than a straight line in space. The phase profile
of the Airy beam is a cubic function modulated by the Gaussian
envelope.[29] Using the same technique, we design the nanomet-
ric hologram and obtain the recovered Airy pattern as shown in
Figure S6, Supporting Information. We measure the widths of
the main lobe and side lobe of the Airy profile as 432 and 306
nm, respectively. This indicates a generation of the Airy beam
with deep-subwavelength feature size. The self-accelerating and
nondiffracting of the Airy main lobe following a parabolic trajec-
tory in space are observed. These results show that our technique
can be also applied to the self-accelerating structured light.
We finally encode an arbitrary object expressed as O(x, y)2
into the nanometric hologram and recover it in the far field
with feature size on the subwavelength scale. However, unlike
the studied cases of light which are well-defined in phase, the
phase distribution of the complex function O(x, y) is not given
explicitly. An advanced Gerchberg–Saxton (GS) algorithm is de-
veloped in this work,[64] in order to numerically calculate the de-
sired phase. More details about the advanced GS algorithm re-
fer to Section SF, Supporting Information. We consider encod-
ing the English symbols “JNU” and a Chinese symbol to illus-
trate this point. We launch these objects into the algorithm and
obtain their corresponding phase functions presented in numer-
ical forms. We then encode the phases into holograms, marked
as Ma(x, y)andMb(x, y), with their layouts shown in Figure 5a,b,
respectively. We simulate reconstructions of the objects accord-
ing to the Helmholtz wave equation, with inputs E(x, y, z =0) =
E0×Ma,b, see calculated outcomes in Figure 5e,f, respectively.
Even though there are some speckles in the strokes of the sym-
bols which are resulted from insufficient resolution of the nano-
metric holograms, we observe clear reconstructions of the target
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Figure 5. Arbitrary light sculpting at the subwavelength scale. Typical nanometric holograms designed to encode the objects: The English symbols “JNU;”
A Chinese symbol; 1D grating of light; and 2D square lattice of light. An advanced Gerchberg–Saxton algorithm is developed to calculate the phases of
these objects. The output phases from the algorithm are then encoded into the holograms with geometric layouts shown in (a–d), respectively. e–h) The
corresponding diffracted light patterns numerically recorded at a distance of z=30 μm. The holograms are illuminated by plane wave beam. In color
bar, H: high; L: low.
objects in the far field. While the overall size of the recovered
pattern is larger than the wavelength, the stroke weight for these
characters is measured as 500 nm. Other examples including
the one-dimensional (1D) grating structure and two-dimensional
(2D) square lattice of light are further presented for holographic
wave manipulations. Figure 5c,d shows their hologram struc-
tures, Mc(x, y)andMd(x, y), while Figure 5g,h depicts the corre-
sponding diffracted light fields at z=30 μm, showing clear re-
constructions of the grating structure and square lattice in the
far field. The period of the structures is measured as 684 nm for
1D grating and 868 nm for 2D lattice, while their line widths are
measured as 235 and 185 nm, respectively. The periodic struc-
tures of light with ultrahigh spatial resolution may find potential
applications in spatial precise measurements and superresolu-
tion microscopy.[63,64] These results argue that an arbitrary object,
in addition to the well-defined structures of light, can be encoded
by the nanometric hologram and recovered in the far field with
feature size at deep-subwavelength scale.
4. Conclusion
We have demonstrated both theoretically and experimentally a
novel holography for arbitrary light sculpting at the subwave-
length scale. The holographic principle is based on a wave phe-
nomenon of diffractive focusing induced by edge diffraction of
a nanometric (50-nm-thick) mask.[53,54 ] The excited high-spatial-
frequency waves from the diffraction of the mask are considered
as carriers on which the phase and amplitude information of an
arbitrarily given object are encoded. Note that this holography
is contrary to the conventional ones that usually happen in the
macroscale or microscale. Using this nanometric hologram, in-
cident light can be focused into the diffraction-limit (nanometric)
regime, while the target object can be recovered at the focal plane
with deep-subwavelength feature size. As illustrations, we have
designed and experimentally fabricated nanometric holograms
for encoding the Bessel beam, vortex beam, vector beam, and Airy
beam, as well as the beams having arbitrary structures. High-
quality images have been reconstructed from the holograms,
which in turn verifies the validity of our proposed holography. We
have further shown the broadband performance of the nanomet-
ric holograms and realized for the first time the white-light non-
diffracting beam at the deep-subwavelength scale. The generated
subwavelength nondiffracting beams might be used in potential
applications such as optical nanoparticle manipulation,[65] super-
resolution imaging,[42] and spatial precise measurements.[63] Our
work also provides a new manner for controlling structured light
propagation at the subwavelength scale, which remains difficult
to be achieved.
We point out that the reported nanometric hologram is
distinct from the superoscillatory masks. A superoscillatory
mask, in principle, is able to create arbitrarily small light spots,
accompanied by strong side lobes around the central main
lobe;[45–47 ] while the presented nanometric hologram produces
a diffraction-limit light field without generation of significant
side lobes. Moreover, the superoscillatory mask cannot en-
code information of light and only acts as a focusing element;
whereas our hologram mask allows us to encode the phase,
amplitude, and polarization information of the structured light.
Despite differences among them, they share a common char-
acteristic that relies on the constructive interference of many
high-spatial-frequency propagating waves emitting from the
masks.
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Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
This work was supported by the National Natural Science Foundation of
China (11974146, 62175091), the Key-Area Research and Development
Program of Guangdong Province (2020B090922006), and the Guangzhou
Science and Technology Project (202201020061).
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
The data that support the findings of this study are available from the cor-
responding author upon reasonable request.
Keywords
high-spatial-frequency waves, holography, light field manipulation, sub-
wavelength nondiffracting structured light
Received: June 8, 2023
Revised: August 3, 2023
Published online:
[1] A. Forbes, M. de Oliveira, M. R. Dennis, Nat. Photonics 2021,15, 253.
[2] Y. Shen, X. Wang, Z. Xie, C. Min, X. Fu, Q. Liu, M. Gong, X. Yuan,
Light: Sci. Appl. 2019,8, 90.
[3] Y. Ren, R. Lu, L. Gong, Ann. Phys. 2015,527, 447.
[4] X. Wang, J. Ding, W. Ni, C. Guo, H. Wang, Opt. Lett. 2007,32, 3549.
[5] Y.Liu,Z.Liu,J.Zhou,X.Ling,W.Shu,H.Luo,S.Wen,Opt. Lett. 2017,
42, 3447.
[6] N. Yu, F. Capasso, Nat. Mater. 2014,13, 139.
[7] N. Meinzer, W. L. Barnes, I. R. Hooper, Nat. Photonics 2014,8, 889.
[8] D. Lin, P. Fan, E. Hasman, M. L. Brongersma, Science 2014,345, 298.
[9] F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, X. Chen, ACS Photonics
2016,3, 1558.
[10] A. H. Dorrah, F. Capasso, Science 2022,376, 367.
[11] C. Li, S. Liu, B. Yu, H. Wu, C. Rosales-Guzmán, Y. Shen, P. Chen, Z.
Zhu, Y. Lu, Laser Photonics Rev. 2023,17, 2200800.
[12] A. Chong, W. H. Renninger, D. N. Christodoulides, F. W. Wise, Nat.
Photonics 2010,4, 103.
[13] A. Chong, C. Wan, J. Chen, Q. Zhan, Nat. Photonics 2020,14, 350.
[14] C. Wan, Q. Cao, J. Chen, A. Chong, Q. Zhan, Nat. Photonics 2022,16,
519.
[15] A. Zdagkas, C. McDonnell, J. Deng, Y. Shen, G. Li, T. Ellenbogen, N.
Papasimakis, N. I. Zheludev, Nat. Photonics 2022,16, 523.
[16] G. Milione, H. I. Sztul, D. A. Nolan, R. R. Alfano, Phys. Rev. Lett. 2011,
107, 053601.
[17] S.Fu,C.Guo,G.Liu,Y.Li,H.Yin,Z.Li,Z.Chen,Phys. Rev. Lett. 2019,
123, 243904.
[18] Z. Ren, L. Kong, S. Li, S. Qian, Y. Li, C. Tu, H. Wang, Opt. Express 2015,
23, 26586.
[19] X. Yi, Y. Liu, X. Ling, X. Zhou, Y. Ke, H. Luo, S. Wen, D. Fan, Phys. Rev.
A2015,91, 023801.
[20] Y. Shen, Z. Wang, X. Fu, D. Naidoo, A. Forbes, Phys.Rev.A2020,102,
031501R.
[21] A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque,
K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C.
Marquardt, G. Leuchs, R. W. Boyd, E. Karimi, Optica 2017,4,
1006.
[22] T. Stav, A. Faerman, E. Maguid, D. Oren, V. Kleiner, E. Hasman, M.
Segev, Science 2018,361, 1101.
[23] J. Durnin, J. J. Miceli Jr, J. H. Eberly, Phys. Rev. Lett. 1987,58,
1499.
[24] Y. Hu, S. Fu, H. Yin, Z. Li, Z. Li, Z. Chen, Optica 2020,7, 1261.
[25] Y. Hu, S. Wang, J. Jia, S. Fu, H. Yin, Z. Li, Z. Chen, Adv. Photonics 2021,
3, 045002.
[26] Y. Zhu, Z. Dong, F. Wang, Y. Chen, Y. Cai, Opt. Lett. 2022,47, 2846.
[27] X. Zang, W. Dan, F. Wang, Y. Zhou, Y. Cai, G. Zhou, Opt. Lett. 2022,
47, 5654.
[28] N. K. Efremidis, Z. Chen, M. Segev, D. N. Christodoulides, Optica
2019,6, 686.
[29] G. A. Siviloglou, J. Broky, A. Dogariu, D. N. Christodoulides, Phys.
Rev. Lett. 2007,99, 213901.
[30] N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, Nature 2013,
494, 331.
[31] J. Jia, H. Lin, Y. Liao, Z. Li, Z. Chen, S. Fu, Optica 2023,10, 90.
[32] J. Glückstad, Nat. Photonics 2011,5,7.
[33] P. Samal, J. R. K. Samal, E. Gubbins, P. Vroemen, C. van Blitterswijk,
R. Truckenmüller, S. Giselbrecht, Adv. Mater. 2022,34, 2200687.
[34] K. C. Wright, L. S. Leslie, A. Hansen, N. P. Bigelow, Phys. Rev. Lett.
2009,102, 030405.
[35] A. Forbes, Nat. Photonics 2020,14, 656.
[36] H. Hu, Q. Gan, Q. Wen, Phys.Rev.Lett.2019,122, 223901.
[37] G. Guan, A. Zhang, X. Xie, Y. Meng, W. Zhang, J. Zhou, H. Liang,
Nanomaterials 2022,12, 2274.
[38] K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, A. V. Zayats, Nat. Pho-
tonics 2015,9, 796.
[39] J. Ni, C. Huang, L. Zhou, M. Gu, Q. Song, Y. Kivshar, C. Qiu, Science
2021,374, 418.
[40] R. Ma, R. F. Oulton, Nat. Nanotechnol. 2019,14, 12.
[41] H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, C. T. Chong, Nat. Pho-
tonics 2008,2, 501.
[42] X. Xie, Y. Chen, K. Yang, J. Zhou, Phys. Rev. Lett. 2014,113, 263901.
[43] Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, D. T. Chiu, Phys.
Rev. Lett. 2007,99, 073901.
[44] L. Du, A. Yang, A. V. Zayats, X. Yuan, Nat. Phys. 2019,15,650.
[45] M. V. Berry, S. Popescu, J. Phys. A: Math. Gen. 2006,39, 6965.
[46] F. M. Huang, N. I. Zheludev, Nano Lett. 2009,9, 1249.
[47] E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis,
N. I. Zheludev, Nat. Mater. 2012,11, 432.
[48] F. Qin, K. Huang, J. Wu, J. Teng, C. Qiu, M. Hong, Adv. Mater. 2017,
29, 1602721.
[49] P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser,
L. Feng, Science 2016,353, 464.
[50] Y. Liu, G. Bartal, D. A. Genov, X. Zhang, Phys.Rev.Lett.2007,99,
153901.
[51] F. Lemoult, N. Kaina, M. Fink, G. Lerosey, Nat. Phys. 2013,9, 55.
[52] C. Huang, C. Zhang, S. Xiao, Y. Wang, Y. Fan, Y. Liu, N. Zhang, G. Qu,
H. Ji, J. Han, L. Ge, Y. Kivshar, Q. Song, Science 2020,367, 1018.
[53] D. Weisman, S. Fu, M. Gonçalves, L. Shemer, J. Zhou, W. P. Schleich,
A. Arie, Phys.Rev.Lett.2017,118, 154301.
[54] W. B. Case, E. Sadurni, W. P. Schleich, Opt. Express 2012,20,
27253.
[55] D. Weisman, C. M. Carmesin, G. G. Rozenman, M. A. Efremov, L.
Shemer, W. P. Schleich, A. Arie, Phys.Rev.Lett.2021,127, 014303.
Laser Photonics Rev. 2023, 2300527 © 2023 Wiley-VCH GmbH
2300527 (9 of 10)
18638899, 0, Downloaded from https://wol-prod-cdn.literatumonline.com/doi/10.1002/lpor.202300527 by Jinan University, Wiley Online Library on [14/09/2023]. 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
www.advancedsciencenews.com www.lpr-journal.org
[56] Y.Hu,S.Fu,Z.Li,H.Yin,J.Zhou,Z.Chen,Opt. Commun. 2018,413,
136.
[57] J. Chen, Y. Hu, H. Yin, Z. Li, Z. Chen, S. Fu, Opt. Express 2022,30,
39510.
[58] W. Lee, Appl. Opt. 1979,18, 3661.
[59] I. Dolev, I. Epstein, A. Arie, Phys.Rev.Lett.2012,109, 203903.
[60] W. T. Chen, M. Khorasaninejad, A. Y. Zhu, J. Oh, R. C. Devlin, A. Zaidi,
F. Capasso, Light: Sci. Appl. 2017,6, e16259.
[61] P. Fischer, C. T. A. Brown, J. E. Morris, C. López-Mariscal, E. M.
Wright, W. Sibbett, K. Dholakia, Opt. Express 2005,13, 6657.
[62] H. Han, J. Ma, B. Tao, C. Xu, Y. Hu, J. Chu, Opt. Express 2022,30,
13148.
[63] G. H. Yuan, N. I. Zheludev, Science 2019,364, 771.
[64] Z. Zalevsky, D. Mendlovic, R. G. Dorsch, Opt. Lett. 1996,21, 842.
[65] M. Dienerowitz, M. Mazilu, K. Dholakia, J. Nanophotonics 2008,2,
021875.
Laser Photonics Rev. 2023, 2300527 © 2023 Wiley-VCH GmbH
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