††thanks: These two authors contributed equally††thanks: These two authors
contributed equally

# Probing optical anapoles with fast electron beams

Carlos Maciel-Escudero  Materials Physics Center, CSIC-UPV/EHU, Donostia-San
Sebastián, 20018, Spain  CIC NanoGUNE BRTA and Department of Electricity and
Electronics, EHU/UPV, Donostia-San Sebastián, 20018, Spain  Andrew B.
Yankovich  Department of Physics, Chalmers University of Technology, 412 96,
Gothenburg, Sweden  Battulga Munkhbat  Department of Physics, Chalmers
University of Technology, 412 96, Gothenburg, Sweden  Department of Photonics
Engineering, Technical University of Denmark, DK–2800, Kgs. Lyngby, Denmark
Denis G. Baranov  Department of Physics, Chalmers University of Technology,
412 96, Gothenburg, Sweden  Center for Photonics and 2D Materials, Moscow
Institute of Physics and Technology, Dolgoprudny 141700, Russia  Rainer
Hillenbrand  CIC NanoGUNE BRTA and Department of Electricity and Electronics,
EHU/UPV, Donostia-San Sebastián, 20018, Spain  IKERBASQUE, Basque Foundation
for Science, 48011 Bilbao, Spain  Eva Olsson<EMAIL_ADDRESS>Department of Physics, Chalmers University of Technology, 412 96, Gothenburg,
Sweden  Javier Aizpurua<EMAIL_ADDRESS>Materials Physics Center, CSIC-
UPV/EHU, Donostia-San Sebastián, 20018, Spain  Donostia International Physics
Center DIPC, 20018 Donostia-San Sebastián, Spain  Timur O. Shegai
<EMAIL_ADDRESS>Department of Physics, Chalmers University of Technology,
412 96, Gothenburg, Sweden

###### Abstract

Optical anapoles are intriguing charge-current distributions characterized by
a strong suppression of electromagnetic radiation. They originate from the
destructive interference of the radiation produced by electric and toroidal
multipoles. Although anapoles in dielectric structures have been probed and
mapped with a combination of near- and far-field optical techniques, their
excitation using fast electron beams has not been explored so far. Here, we
theoretically and experimentally analyze the excitation of optical anapoles in
tungsten disulfide (WS2) nanodisks using Electron Energy Loss Spectroscopy
(EELS) in Scanning Transmission Electron Microscopy (STEM). We observe
prominent dips in the electron energy loss spectra and associate them with the
excitation of optical anapoles and anapole-exciton hybrids. We are able to map
the anapoles excited in the WS2 nanodisks with subnanometer resolution and
find that their excitation can be controlled by placing the electron beam at
different positions on the nanodisk. Considering current research on the
anapole phenomenon, we envision EELS in STEM to become a useful tool for
accessing optical anapoles appearing in a variety of dielectric
nanoresonators.

##  I Introduction

Anapoles are particular charge-current distributions giving rise to an optical
phenomenon characterized by strong suppression of electromagnetic radiation
[1]. This phenomenon is typically understood as the interference between the
electromagnetic (EM) field produced by the Cartesian electric multipole with
the EM field of the toroidal multipole. When this interference is destructive,
the system yields a non-radiating current configuration known as the optical
anapole state [2]. Excitation of the anapole in a polarizable nanostructure
greatly suppresses its scattering cross-section thus providing invisibility to
nanoobjects [3], which offers promising applications in nanophotonics [4, 5,
6, 7, 8]. Additionally, optical anapoles concentrate EM fields inside the
nanoresonators serving to enhance nonlinear harmonics generation[9], four-wave
mixing [10], Raman scattering [11, 12], and photothermal nonlinearities [13].

Intense experimental and theoretical efforts have been devoted to identify
optical anapole states in different dielectric nanostructures. However, the
detection of ideal optical anapoles is complicated and usually requires the
suppression of other multipole resonances. Typically, this suppression is
achieved by engineering the nanoresonator geometry and by structuring the
incident illumination [8, 5, 4]. Complementary to far-field characterization,
understanding how anapoles are excited by localized probes can be of paramount
importance to control and realize the full potential of these non-radiating
states. An interesting technique of such kind, to probe anapoles, is Electron
Energy Loss Spectroscopy (EELS) in Scanning Transmission Electron Microscopy
(STEM) due to its ability to access not only electric dipole modes, but also
quadrupoles and higher-order modes that do not, or weakly, couple to far-field
radiation.

EELS in STEM employs a tightly focused electron beam that allows for mapping
the optical properties of a material with tens of meV energy resolution and
down to atomic scale spatial resolution while simultaneously relating this
information to the samples precise size, shape and structure [14, 15]. For
example, EELS has been used to characterize and map localized plasmons in
different nanostructures [16, 17, 18, 19], to probe electronic excitations
such as excitons in Transition Metal Dichalcogenide (TMDC) materials [20], to
predict optical toroidal modes in silver heptamer cavities[21], and to map
photonic modes of dielectric silicon nanocavities [22]. Recently, EELS has
also shown to be a useful technique to resolve strong light-matter
interactions with unprecedented spatial and spectral resolution[23, 24, 25,
26, 27]. However, a detailed study of optical anapoles excited by fast
electrons is still pending.

Here we present a numerical and experimental analysis of optical anapoles and
anapole-exciton hybrids in WS2 nanodisks using EELS. We first identify optical
anapole states in model high-index dielectric nanodisks by calculating the
electron energy losses experienced by a focused electron beam traveling in
aloof trajectory in the vicinity of the nanodisk. Destructive interference
between electric and toroidal Cartesian multipoles induced in the nanodisk
manifests as a dip in the electron energy loss (EEL) spectra. Besides being
widely used as an excitonic platform, multilayer WS2 possesses a high
refractive index [28] which provides a possibility to excite optical anapole
states. To experimentally reveal and map anapole excitations in EELS, we thus
fabricate WS2 nanodisks and compare experimental EEL spectra with numerical
calculations. By varying the nanodisk dimensions the anapoles supported by the
WS2 nanodisk can be tuned to match the resonance of an excitonic transition of
WS2 leading to anapole-exciton hybridization. The emergence of this light-
matter interaction regime shows the advantage of using TMDCs instead of other
conventional high-index materials. Finally, we show the possibility to
spatially map optical anapoles and to control their excitation by placing the
electron beam at different positions on the nanodisk, demonstrating the
potential of EELS to access these special non-radiating charge-current
distributions.

##  II Results

###  II.1 Theoretical prediction of optical anapoles in EEL spectra

Figure 1: Theoretical description of optical anapoles excited by fast electron
beams. (a) Sketch of the system under study. The blue cylinder represents the
high-index dielectric nanodisk with dielectric function $\varepsilon=18$,
thickness $d=55\,\mathrm{nm}$ and radius $R$. The green ray represents the
focused electron beam ($e$ is the elementary charge) traveling along the
$z$-direction with velocity $v$ at a distance $b$ (impact parameter) with
respect to the nanodisk center. The contour plot in (b) shows the EEL
probability $\Gamma(\omega)$ calculated as a function of both the nanodisk
radius $R$ and the energy loss experienced by the electron beam. White dotted
and gray dashed lines are guides to the eye and mark the position of the first
two peaks and four dips in the EEL spectra respectively. (c) Simulated EEL
probability spectrum (blue line) on a nanodisk with $R=250\,\mathrm{nm}$. The
red dots mark the spectral dip positions. (d) Amplitude of the induced dipole
moment in the nanodisk. (e) Amplitude of the induced quadrupole moment in the
nanodisk. The field plots on the right of panels (d) and (e) depict the
amplitude of the total electric field $|{\bf{E}}(\omega)|$ inside the disk at
the plane $z=0$ (half of the nanodisk height), for energies: (A)
$1.2575\,\mathrm{eV}$ and (B) $1.52\,\mathrm{eV}$. The scale bar is
$100\,\mathrm{nm}$. The maximum value of $|{\bf{E}}(\omega)|$ in each case is:
(A) $5\times 10^{8}\,\mathrm{V/m}$ and (B) $4\times 10^{8}\,\mathrm{V/m}$. The
inset next to panel (c) illustrates a top view of the nanodisk probed by the
electron beam. (f) Sketch of the anapole states formed by the electric and
toroidal dipoles and by the electric and toroidal quadrupoles.

We begin our study by describing the general features appearing in the EEL
spectra of a model high-index dielectric nanodisk that can exhibit optical
anapole states[29]. Figure 1(a) illustrates a sketch of the system under
study: a dielectric disk is excited by an electron beam traveling in aloof
trajectory close to the disk. We choose a disk of variable radius $R$,
thickness $d=55\,\mathrm{nm}$ and permittivity $\varepsilon=18$. The electron
beam travels with velocity $v=0.7c$ ($200\,\mathrm{eV}$, $c$ being the speed
of light in vacuum) along the $z$-axis at a distance $b=1.1R$ with respect to
the nanodisk center (impact parameter). We calculate numerically the EEL
probability $\Gamma(\omega)$ using the classical dielectric theory[14, 30] as
specified in Methods and Supplementary Materials S1.

Figure 1(b) shows the calculated $\Gamma(\omega)$ spectra for different
nanodisk radius $R$ in the energy range of $0.5\,\mathrm{eV}$ to
$2.5\,\mathrm{eV}$. One can recognize in the spectra peaks (white dotted
lines) and dips (gray dashed lines) that monotonously shift to higher energies
when the nanoresonator radius $R$ is reduced from $300\,\mathrm{nm}$ to
$100\,\mathrm{nm}$. We associate the peaks to different nanoresonator modes
excited by the fast electron beam at the nanodisk (see Supplementary Materials
S2). Here we focus on the underlying physics of the spectral dips as they are
related to the optical anapole states excited at the disk, as detailed below.

The anapole phenomenon originates from the destructive interference between
the electric and toroidal Cartesian moments inside the nanodisk with identical
amplitude and far-field patterns. To corroborate anapole excitation with fast
electron beams, we thus calculate the EEL probability $\Gamma(\omega)$ for a
$250\,\mathrm{nm}$ radius disk (Fig. 1(c)) and perform multipole decomposition
of the current density ${\bf{J}}_{\mathrm{ind}}({\bf{r}})$ induced at the
nanoresonator by the electron beam. The red points in Fig. 1(c) mark a series
of dips revealed in the EEL spectra. The induced current density
${\bf{J}}_{\mathrm{ind}}({\bf{r}})$ can be described by the series of exact
multipole moments induced in the disk. In the long-wavelength approximation
one can write each multipole moment as a superposition of the so called
Cartesian multipole moments [31, 32, 33]. For example, the spherical electric
dipole moment ${\bf{P}}_{\mathrm{sph}}(\omega)$ in the long-wavelength
approximation is described by the superposition of the electric and toroidal
Cartesian dipole moments:
${\bf{P}}_{\mathrm{sph}}(\omega)\approx{\bf{P}}_{\mathrm{car}}(\omega)+ik_{0}{\bf{T}}_{\mathrm{car}}(\omega)$,
where $k_{0}=\omega/c$ is the wave number in vacuum. When the contributions of
the electric and toroidal Cartesian dipole moments are out-of-phase
(${\bf{P}}_{\mathrm{car}}(\omega)=-ik_{0}{\bf{T}}_{\mathrm{car}}(\omega)$),
that is, they interfere destructively, the electric spherical dipole moment
${\bf{P}}_{\mathrm{sph}}(\omega)$ approaches zero. This is the condition for
the excitation of optical anapole states [3]. In Supplementary Materials S3,
we provide further details on the calculations of the spherical and Cartesian
multipoles as well as on the multipole expansion in the long-wavelength
approximation. In order to corroborate anapoles excitation in the high-index
dielectric disk, we calculate the dipole and quadrupole moments of the induced
current density ${\bf{J}}_{\mathrm{ind}}({\bf{r}})$ inside the
$250\,\mathrm{nm}$ disk.

Figure 1(d) shows calculated amplitudes of the electric spherical
$|{\bf{P}}_{\mathrm{sph}}(\omega)|$ (black dashed line) dipole moment, as well
as the Cartesian electric $|{\bf{P}}_{\mathrm{car}}(\omega)|$ (green line) and
scaled toroidal $|ik_{0}{\bf{T}}_{\mathrm{car}}(\omega)|$ (magenta) dipole
moments. From the $|{\bf{P}}_{\mathrm{sph}}(\omega)|$ spectrum, we recognize a
dip at around $1.25\,\mathrm{eV}$ (marked with A). The appearance of the dip
is a consequence of the Cartesian dipole and toroidal dipole moments having
the same amplitude but opposite phase (green and magenta lines intersect at an
energy marked with A in Fig. 1(d)). Most importantly, by comparing the EEL
(Fig. 1(c)) and the spherical dipole moment (blacked dashed line in Fig. 1(d))
spectra, we find that the dip in $|{\bf{P}}_{\mathrm{sph}}(\omega)|$
corresponds to the first dip in $\Gamma(\omega)$, indicated by the fist gray
dashed lines in Figs. 1(c) and (d). This corroborates that the first resonance
dip revealed in the EEL spectra of the nanodisk belongs to an optical anapole
state excited by the fast electron beam. The distribution of the electric
field plot at energy $1.2575\,\mathrm{eV}$ around the disk (right panel of
Fig. 1(d)) shows the anapole near-field pattern inside the disk, revealing
regions of intense fields inside the nanodisk and two opposite vortices
typically found in the optical phenomena involving anapoles. We refer to this
anapole as the first electric dipole (ED) anapole state. We note that the
ideal anapole (zero in the EEL probability) cannot arise due to higher-order
multipolar contributions to the energy loss and thus, an “attenuated dip” can
be observed in the EEL spectra.

Analogously, we can understand the dip at $1.52\,\mathrm{eV}$ in the EEL
spectrum (marked with B in Fig. 1(c)) as due to the destructive interference
between electric and toroidal quadrupole current distributions with identical
far-field patterns. To demonstrate this, we calculate the electric spherical
$\hat{\mathbb{Q}}_{\mathrm{sph}}(\omega)$, Cartesian electric
$\hat{\mathbb{Q}}^{(\mathrm{e})}_{\mathrm{car}}(\omega)$ and toroidal
$\hat{\mathbb{Q}}^{(\mathrm{T})}_{\mathrm{car}}(\omega)$ quadrupole moments of
the induced current density ${\bf{J}}_{\mathrm{ind}}({\bf{r}})$. In the long-
wavelength approximation, one finds that the spherical electric quadrupole
moment has the following form
$\hat{\mathbb{{Q}}}_{\mathrm{sph}}(\omega)\approx\hat{\mathbb{Q}}^{(\mathrm{e})}_{\mathrm{car}}(\omega)+3ik_{0}\hat{\mathbb{Q}}^{(\mathrm{(T})}_{\mathrm{car}}(\omega)$
(see Supplementary Materials S3) and thus, the condition for the excitation of
electric quadrupole (EQ) anapole states is
$\hat{\mathbb{Q}}^{(\mathrm{e})}_{\mathrm{car}}=-3ik_{0}\hat{\mathbb{Q}}^{(\mathrm{T})}_{\mathrm{car}}$.
In Fig. 1(e) we show the amplitude of
$|\hat{\mathbb{Q}}_{\mathrm{sph}}(\omega)|$ (black dashed line),
$|\hat{\mathbb{Q}}^{(\mathrm{T})}_{\mathrm{car}}(\omega)|$ (green line) and
$|3ik_{0}\hat{\mathbb{Q}}^{(\mathrm{T})}_{\mathrm{car}}(\omega)|$ (magenta
line). From the green and magenta spectra we clearly see that the Cartesian
and toroidal quadrupole moments sustain the same amplitude but opposite phase
at $1.52\,\mathrm{eV}$, which confirms that the dip at $1.52\,\mathrm{eV}$ in
the EEL spectra corresponds to the excitation of the first EQ anapole state.
We note that the EQ anapole states in the disk can not be excited using plane
wave illumination at normal incidence, as we show in Supplementary Materials
S4. The difference in the properties of the first ED and the first EQ anapoles
excited by the fast electron beam can be observed in the right panel of Fig.
1(e), where we show the near-field pattern induced at $1.52\,\mathrm{eV}$
(marked with B) inside the disk. Notice that the field pattern of the first EQ
anapole exhibits two additional vortices compared to the field pattern of the
first ED anapole (see right panel of Fig. 1(d)). This increase in the number
of vortices can be attributed to the quadrupolar distribution of the induced
current density ${\bf{J}}_{\mathrm{ind}}({\bf{r}})$ inside the disk, as
sketched in Fig. 1(f). Finally, we note that subsequent dips in the EEL
spectrum (marked C and D in Fig. 1(c)) belongs to the excitation of higher-
order anapole states such as the second ED anapole (marked C) and the second
EQ anapole (marked D) states.

The possibility to probe optical anapole states with fast electron beams turns
EELS into a promising tool for fundamental studies of optical phenomena
involving anapoles. To experimentally verify our numerical calculations we
fabricate high-index TMDC WS2 nanodisks with various radii and performed
electron energy loss spectroscopy to spatially resolve their optical behavior.

###  II.2 Fabrication of WS2 nanodisks

We synthesize WS2 nanodisks by transferring a mechanically exfoliated WS2
flake onto a $50\,\mathrm{nm}$ thick SiN membrane and performing a combination
of e-beam lithography and dry etching. This process enables the creation of
donut-shaped etched patterns with isolated nanodisks at their center with
selected radii (see Methods and Supplementary Materials S5 for additional
details). The thickness of the nanodisk determines its optical response to a
probing fast electron, therefore we experimentally measure the disk thickness
using three independent methods: EELS, tilted view STEM imaging, and the
combination of optical reflectivity and transfer-matrix fitting (Supplementary
Materials S6). From the three methods, we find a disk thickness of around
$d\approx 70\,\mathrm{nm}$.

Figure 2: Fabrication of WS2 nanodisks. (a) Plan view HAADF STEM images of
nine WS2 nanodisks with radii ranging from $88\,\mathrm{nm}$ to
$295\,\mathrm{nm}$. Disk radii are shown at the top of each image and a scale
bar of $200\,\mathrm{nm}$ stands for all images. (b)-(d) 53∘ tilted HAADF STEM
images of the nanodisks with radii $110\,\mathrm{nm}$, $240\,\mathrm{nm}$ and
$295\,\mathrm{nm}$, respectively. (e)-(g) 53∘ tilted SE STEM images
simultaneously acquired of the three nanodisks shown in panels (b)-(d). (h)
Atomic resolution HAADF STEM image taken from the center of the largest
($295\,\mathrm{nm}$) disk.

In Fig. 2(a) we show high-angle annular dark-field (HAADF) STEM images of nine
WS2 nanodisks of different size, demonstrating the ability to precisely
synthesize isolated nanodisks with controllable radii ranging from around
$88\,\mathrm{nm}$ to $295\,\mathrm{nm}$. Simultaneously acquired $53^{\circ}$
tilted HAADF and secondary electron (SE) STEM images of nanodisks with various
radii (Figs. 2(b)-(g)) reveal the morphology of the nanoresonators and the
residual resist material that remains on top of the WS2 nanodisks after
fabrication, as indicated in Fig. 2(e). High-angle annular dark-field STEM
images are dominated by mass-thickness Z-contrast [34] and thus, the brightest
regions reveal the position and shape of the WS2 nanodisks below the primarily
low-Z residual resist material. To identify the size and morphology of both
the WS2 nanodisks and the residual material, we use SE image contrast which is
sensitive to surface topography [35]. From Figs. 2(b)-(g) we observe two main
features of the WS2 nanodisks: (i) the edges show small vertically aligned
surface variations and (ii) a tapered side surface with larger radii at the
base. These variations of the WS2 nanodisk radius are small compared to the
average nanodisk radius, and thus modeling our nanodisks as perfect disks is
an adequate description of the system. The residual resist could lead to minor
shifts in energy of the disk modes, but does not alter the excitation of the
nanoresonator modes and anapole states. Therefore, the resist has not been
included in our model calculations. We address the reader to Supplementary
Materials S7, where we provide further details on the chemical composition of
the fabricated samples. In Fig. 2(h) we show an atomic-resolution HAADF STEM
image from the center of a nanodisk, revealing that the single crystalline
atomic structure of the WS2 flake is preserved after the nanodisk fabrication
process.

###  II.3 Probing optical anapoles in WS2 nanodisks using EELS

To experimentally investigate the optical response of WS2 nanodisks to a fast
electron beam, we performed monochromated STEM EELS experiments using a
$200\,\mathrm{keV}$ electron beam with less than $1\,\mathrm{nm}$ spatial
resolution and $20\,\mathrm{meV}-40\,\mathrm{meV}$ energy resolution (see
Methods). In Fig. 3(a) we show the collected EEL spectra as a function of
nanodisk radius as obtained when an aloof electron beam passes outside
($b<R+5\,\mathrm{nm}$) the edge of each nanodisk shown in Fig. 2(a). From the
EEL spectra we observe a low-loss signal composed of multiple sharp peaks and
dips (see Fig. 3(a)). The number of peaks and dips decreases steadily as the
disk size is reduced and their position shifts monotonously to higher energies
in agreement with our theoretical prediction (Fig. 1(b)). Importantly, EEL
spectra of the WS2 disks exhibit a spectral peak at around $1.95\,\mathrm{eV}$
(bright stripe in Fig. 3(a)) present in all the nanoresonators. Notice that
above this energy the EEL signal dampens and blurs. For a better quantitative
comparison, we show in Figs. 3(b) and 3(c) the EEL spectra extracted from Fig.
3(a) for the $268\,\mathrm{nm}$ (blue spectrum) and $110\,\mathrm{nm}$ (red
spectrum) radius nanodisks, respectively. We clearly distinguish the peak at
$1.96\,\mathrm{eV}$ which we attribute to the excitation of the A-exciton
absorption band of WS2 (for further details and discussion see Supplementary
Materials S1), as identified in the EEL spectrum of an unpatterned WS2 flake
shown by the green lines in Figs. 3(b) and (c).

To better understand the measured EEL spectra, we numerically calculate the
EEL probability $\Gamma(\omega)$ for different WS2 nanodisks with radius
ranging from $88\,\mathrm{nm}$ to $295\,\mathrm{nm}$ (Fig. 3(d)). In contrast
to the numerical simulations shown in Fig. 1, we performed these calculations
shown in Figs. 3(d)-(f) with a permittivity function of the disk that includes
the A-exciton absorption band of WS2 (see bright stripe in Fig. 3(d) and
Supplementary Materials S1). We find a good agreement between the experimental
and simulated spectra (Figs. 3(a) and 3(d)) in the number, position, and
dispersion of peaks and dips across the complete disk radii range (notice that
the appearance of the A-exciton in the EEL spectrum for every disk radii is
also consistent between experiments and simulations). Above
$1.96\,\mathrm{eV}$ the EEL signal is better resolved in the simulated than in
the experimental spectra (region between $2\,\mathrm{eV}-2.5\,\mathrm{eV}$ in
Figs. 3(a) and 3(d)). We attribute this blurring in the experimental signal to
the excitation of B- and C-exciton absorption bands of WS2 that are not
included in the simulations.

To check whether the dips in the experimental spectra are due to the
excitation of optical anapoles, we analyze the EEL signal of the
$268\,\mathrm{nm}$ disk radius (blue line in Fig. 3(b)). To that end, we
extract from Fig. 3(d) the corresponding simulated spectrum and plot it in
Fig. 3(e) (solid blue line). One can observe that both experimental and
simulated results show two attenuated dips between $1\,\mathrm{eV}$ and
$1.5\,\mathrm{eV}$, marked with A and B in Fig. 3(b) and (e). As we discussed
in Fig. 1, these two attenuated dips can be associated to the disk first ED
and the first EQ anapole states. We have verified that the dips in this energy
range are not caused by the intrinsic losses in WS2. Specifically, we simulate
the spectrum of the model disk with $R=268\,\mathrm{nm}$, $d=70\,\mathrm{nm}$
and artificial permittivity $\varepsilon=18$ (mimicking the WS2 without the
A-exciton resonance at $1.96\,\mathrm{eV}$). The spectrum is shown in Fig.
3(e) (thin blue line). By comparing the solid and the thin blue lines we can
observe that for low energies the first two spectral dips (marked with A and
B) appear nearly at the same energy for both types of disk (compare solid and
thin blue lines between $0.5\,\mathrm{eV}-1.5\,\mathrm{eV}$). This confirms
the excitation of optical anapoles in the WS2 disk by the fast electron beam.
We note that the differences between the solid and the thin blue spectra in
Fig. 3(e) are a direct consequence of the appearance of the A-exciton
resonance at $1.96\,\mathrm{eV}$ (identified in the EEL spectrum of a WS2
flake shown by the green lines in Fig. 3(e)).

Figure 3: Electron energy loss spectra of the WS2 nanodisks. The contour plot
in (a) shows the experimental EEL spectra of the nine disks displayed in Fig.
2(a). Blue solid line in (b) and red solid line in (c) show the EEL spectra
for disks with $R=268\,\mathrm{nm}$ and $R=110\,\mathrm{nm}$, respectively.
Green lines in panels (b) and (c) show EEL spectra from an unpatterned WS2
flake. The contour plot in (d) shows the simulated EEL probability
$\Gamma(\omega)$ as a function of both the nanodisk radius $R$ and the energy
loss experienced by the electron beam. Blue solid line in (e) and red solid
line in (f) show the EEL spectra for disks with $R=268\,\mathrm{nm}$ and
$R=110\,\mathrm{nm}$, respectively. Thin blue and thin red spectra correspond
to $\Gamma(\omega)$ obtained with disks of artificial permittivity
$\varepsilon=18$. Green lines in panels (e) and (f) show calculated
$\Gamma(\omega)$ for a WS2 flake of $70\,\mathrm{nm}$ thickness (see
Supplementary Materials S1). White dashed lines in panels (a) and (d) are
guides to the eye indicating anti-crossing of the first ED anapole and the
A-exciton. Green curves in (a) and (b) were scaled to be consistent with the
relatives heights in (e) and (f).

####  II.3.1 Anapole-exciton hybridization

The coexistence of an excitonic resonance and the dispersive anapoles in the
same object allows these resonant features to couple and hybridize with each
other when varying the nanodisk radius $R$. To explore this aspect, we trace
the first ED anapole state upon decreasing the nanodisk radius from
$268\,\mathrm{nm}$ to $110\,\mathrm{nm}$ (white dashed line in Fig. 3(a) and
(d)) until it reaches the energy of the A-exciton resonance, where a splitting
(anti-crossing) of the dip is produced. This behavior is clearly shown in Fig.
3(f), where we plot the simulated spectrum of the $110\,\mathrm{nm}$ disk
radius (solid red line, extracted from Fig. 3(d)). For comparison, we also
plot the spectrum of the model disk with artificial permittivity
$\varepsilon=18$ (thin red line). By comparing the spectra of both type of
disks, one can observe that the attenuated anapole dip at $2\,\mathrm{eV}$
(thin red line) splits into two dips at $1.86\,\mathrm{eV}$ and
$2.16\,\mathrm{eV}$ in the solid red line. Due to the hybrid nature of these
dips, we refer to them as the lower anapole-exciton-hybrid (lower AE-hybrid)
and the upper anapole-exciton-hybrid (upper AE-hybrid). We can also see a peak
in between the two dips which originates by the excitation of excitons that do
not couple to the anapole. The splitting of the dips, together with the anti-
crossing feature, are signatures of the coupling between the first ED anapole
state and the A-exciton, consistent with previous observations in far-field
optical spectroscopy of WS2 nanodisks [29].

The anti-crossing observed, and fully identified in Fig. 3(d) resembles the
typical situation of coupling between an EM mode confined in an optical cavity
and a dipolar excitation. The anapole, however, is not an EM mode of the disk,
but instead is the result of interference between at least two resonant modes
excited by the electron beam [36, 37]. To explain the coupling between the
first ED anapole and the A-exciton, we implement an analytical model of the
response of the coupled system based on temporal coupled mode theory (TCMT).
Within this framework, we model the anapole-exciton system using an effective
$3\times 3$ Hamiltonian containing the eigenfrequencies of two EM modes, whose
far-field interference produces the anapole dip, coupled to a third non-
radiating mode representing the A-exciton of WS2. We use this model and apply
the following procedure to reproduce the simulated and experimental EEL
spectra. First we reproduce the simulated spectra of the model disk with
$\varepsilon=18$ and find the eigenfrequencies of the two EM modes producing
the first ED anapole dip. We then use these values to reproduce the
experimental and simulated EEL spectra of the WS2 disks (Figs. 3(a) and (d))
and find the coupling strengths between each EM mode and the A-exciton. By
diagonalizing the effective $3\times 3$ Hamiltonian of the system, we find the
eigenfrequencies of the new hybrid modes. The results obtained with this
procedure are shown in Supplementary Materials S8, where we describe in detail
the coupled-mode model. The analysis reveals a clear anti-crossing between the
hybrid modes as a function of the inverse of the nanodisk radius, $1/R$,
indicating that the two electromagnetic modes are strongly coupled to the
A-exciton resonance. The two dips that result from the coupling between the
two modes and the A-exciton correspond to the lower and upper AE-hybrids.

###  II.4 Real-space mapping of optical anapole states

An advantage of EELS in STEM is its ability to acquire spectral information of
a sample with subnanometer spatial resolution. Typically, this is achieved by
scanning the sample area with the fast electron beam, thus obtaining spectral
information of the sample at different beam positions (see Methods). In Fig. 4
we apply this capability to spatially resolve disk modes and anapoles states
excited in the WS2 disk. Specifically, we collect the EEL signal as a function
of the impact parameter $b$. The cylindrical symmetry of the nanodisk along
the $z$-axis, together with the trajectory of the probing electron beam,
yields an EEL signal that depends only on the impact parameter. Therefore, we
represent the spatial distribution of the EEL signals obtained from the WS2
nanodisks by a 2D-EEL line profile showing the energy loss as a function of
impact parameters for each energy.

In Fig. 4 we show experimental and simulated 2D-EEL line profiles for
nanodisks with $R=268\,\mathrm{nm}$ (Figs. 4(a) and 4(b)) and
$R=110\,\mathrm{nm}$ (Figs. 4(f) and 4(g)). The line profiles for the
$R=268\,\mathrm{nm}$ nanodisk reveal a low-loss EEL signal confined to an
annular region with a maximum at the edge of the nanodisk (see region between
$0.5\,\mathrm{eV}$ to $1.5\,\mathrm{eV}$ in Figs. 4(a) and Fig. 4(b)). We show
in Fig. 4(e) the simulated spectrum for a beam that is close to the nanodisk
edge (blue dashed line in Fig. 4(a)). We recognize the fist ED and EQ anapole
dips at around $1\,\mathrm{eV}$ and $1.25\,\mathrm{eV}$, respectively. The
electric field distribution inside the nanodisk associated to these energies
(see Figs. 4(c) and 4(d)) corroborate the nature of these dips. Interestingly,
when the electron beam passes through the nanodisk center ($b=0$) the EEL
signal becomes nearly zero, as shown in Figs. 4(a) and Fig. 4(b). In this
case, the electron beam is not able to efficiently excite the disk modes due
to the cylindrical symmetry of the disk.

Figure 4: Spatially-resolved EEL of WS2 nanodisks. (a) Simulated and (b)
experimental EEL spectra recorded along the impact parameter $b$ of a disk
with $268\,\mathrm{nm}$ radius as depicted in the schematics above the
spectra. Blue dashed lines indicate $b=268\,\mathrm{nm}$. White dashed lines
indicate the first ED (at $1.048\,\mathrm{eV}$) and the first EQ (at
$1.276\,\mathrm{eV}$) anapole states. Panels at the right of (b) show the
amplitude of the total electric field $|{\bf{E}}(\omega)|$ at the plane $z=0$
for the energies (c) $1.048\,\mathrm{eV}$ and (d) $1.276\,\mathrm{eV}$. The
scale bar is $100\,\mathrm{nm}$. (e) Simulated $\Gamma(\omega)$ spectra for
the WS2 disk (solid blue line), the model disk with $\varepsilon=18$ (thin
blue line) and a WS2 flake of $70\,\mathrm{nm}$ thickness. (f)-(j) same as
(a)-(e) but for the $R=110\,\mathrm{nm}$ nanodisk. The scale bars in panels
(h) and (j) are $50\,\mathrm{nm}$. We used for the calculation of
$\Gamma(\omega)$ an impact parameter equal to $b=1.05R$.

Finally, the line profile obtained from the $R=110\,\mathrm{nm}$ nanodisk
reveals an EEL signal that is spatially confined to an annular region from
half the disk radius to significantly outside of the nanodisk. The calculated
electric field distributions at the spectral dips (around $1.75\,\mathrm{eV}$
and $2.25\,\mathrm{eV}$ as indicated in Fig. 4(j)) display a clear ED anapole-
like field pattern (Figs. 4(h) and 4(i)). These field distributions reveal
that the first ED anapole is hybridized with the A-exciton absorption band
(bright stripe around $1.95\,\mathrm{eV}$) to produce the anapole-exciton
hybrids. These results open up the possibility for future EELS experiments on
systems exhibiting more complicated spatial behavior of the isolated anapoles
or anapole-exciton hybrids by, for example, breaking the cylindrical symmetry
of the system.

##  III Conclusion

In summary, we demonstrated that electron energy loss spectroscopy can be
applied to probe optical anapole states in high-index dielectric
nanoresonators. To that end, we calculated the electron energy loss
probability of high-index dielectric nanodisks and showed that the prominent
dips in the the EEL spectra are associated with the excitation of optical
anapoles in the disk. We experimentally verified our theoretical prediction by
performing EELS of WS2 nanodisks and revealed optical anapoles and anapole-
exciton hybrids excitation within the same nano object. Additionally, we
demonstrated that EELS in STEM allows for spatial mapping of WS2 nanodisk
modes, isolated anapoles and anapole-exciton hybrids with subnanometer
resolution. By locating the electron beam at specific positions along the WS2
nanodisk, we can effectively control the modes excitation and thus the
formation of the optical anapole.

Our results show that EELS in STEM is a powerful tool to study dark scattering
states and their complex interactions with the electronic structure of
dielectric materials beyond what is possible using optical techniques. We
anticipate our results will enable new possibilities for studying of higher-
order and magnetic anapole states in dielectric nanoresonators with
subnanometer spatial resolution.

## Methods

###  III.1 Sample fabrication

The multilayer WS2 ($\sim 70\,\mathrm{nm}$) flake was mechanically exfoliated
from bulk crystal (HQ graphene) onto polydimethylsiloxane (PDMS) stamps using
the scotch-tape method, and then transferred onto a $50\,\mathrm{nm}$ thick
silicon nitride (SiN) membrane TEM grid (TEMwindows.com) with an all dry-
transfer method. The fabrication of WS2 nanodisks was achieved using our
previously developed method with a combination of e-beam exposure of a
positive resist and dry etching [38, 39, 29]. In brief, nanopatterning WS2
($\sim 70\,\mathrm{nm}$) flake into the nanodisks was carried out by first
spin coating a positive ARP 6200.13 resist at $4000\,\mathrm{rpm}$ for
$1\,\mathrm{min}$, followed by soft-baking at $120^{\circ}\,\mathrm{C}$ for
$5\,\mathrm{min}$. To fabricate the nanodisks on a thin SiN membrane by dry
etching, the sample was exposed with donut-shaped patterns with various inner
and outer diameters using a Raith EPG5200 electron beam lithography system
($100\,\mathrm{keV}$) to make a resist mask for further dry etching (see
Supplementary Materials S4). It is worth mentioning that the inner diameter of
the donut pattern defines the diameters of the nanodisks. Then, the sample was
developed with $n$-amyl acetate for $4\,\mathrm{min}$ and dried gently with
nitrogen gas. Subsequently, the sample was etched using dry reactive ion
etcher (RIE) with CHF3 gas. A complete etching of WS2 nanodisks was ensured by
performing STEM diffraction, atomic resolution STEM imaging, EELS and energy
dispersive spectroscopy (EDS) chemical analysis inside the etched donut-shaped
patterns.

###  III.2 Experimental STEM imaging and EELS

STEM experiments were performed at $200\,\mathrm{keV}$ and at room temperature
on a JEOL Mono NEO ARM 200F instrument. The microscope is equipped with a
Schottky field emission gun, double Wien filter monochromator, probe
aberration corrector, image aberration corrector, and Gatan Imaging Filter
continuum HR spectrometer. HAADF and SE STEM images were acquired with an
around $0.1\,\mathrm{nm}$ electron probe. The STEM image shown in Fig. 2(h)
was produced by summing a series of 50 images after the series was registered
based on cross correlation to correct for rigid image drifts between frames.
The resulting summed image was Fourier filtered to further enhance signal-to-
noise ratio and the WS2 signal. EDS experiments utilized a double detector
system with a collection solid angle of up to $1.6\,\mathrm{sr}$.

EELS experiments were performed with less than $1\,\mathrm{nm}$ spatial
resolution, $20\,\mathrm{meV}-40\,\mathrm{meV}$ energy resolution, a
$30\,\mathrm{pA}-50\,\mathrm{pA}$ beam current, a $21\,\mathrm{mrad}$ electron
probe convergence angle, and a $10\,\mathrm{mrad}$ EELS collection angle. The
EEL spectra shown in Figs. 3(a)-(c) were acquired from just outside the edge
of the WS2 nanodisks and are the sum of a series composed of $160,000$ spectra
using a $5\,\mathrm{meV}$ dispersion. Before summing the spectral series, a
high quality dark spectrum reference was subtracted from each spectra and the
spectra were energy-aligned based on the zero energy loss peak position. After
summing, the spectra were processed with the Richardson-Lucy deconvolution
algorithm using a reference spectrum acquired from the SiN window and only 5
iterations to ensure no introduction of known artifacts [40, 41].
Deconvolution was used to reduce intensity from the zero-loss peak tail in the
energy region of interest. Then the remaining tail of the zero-loss peak was
removed by fitting each spectrum in the $0.3\,\mathrm{eV}-0.5\,\mathrm{eV}$
range of interest to a power law function, extrapolating that function and
subtracting it from the spectrum.

The experimental EEL line profiles shown in Fig. 4 were each produced from
three spectrum images of the same sample area. Each spectrum image consisted
of $50\times 3500$ spatial pixels and $2048$ energy channels. To enhance
signal-to-noise ratio, each spectrum image was binned by $50$ in the $x$
direction and by $7$ in the $y$ direction to produce a line profile, and the
three profiles from each area were summed after the data processing mention
below. The spectra were processed with high quality dark spectrum reference
subtraction, energy-alignment, Richardson-Lucy deconvolution, and zero-loss
peak tail removal using the same details as the spectra mentioned above.
Additionally, the EEL line profiles were normalized based on their total
integrated EEL signal. The EEL intensity in the as-acquired data is modified
by scattering sources other than the low-loss optical and electronic signals
that we are interested in. For example, WS2 elastic diffraction scatters a
significant amount of electrons outside of the spectrometer collection
aperture, significantly reducing all the EEL signals when the electron beam
passes through the WS2 nanodisk as compared to when it passes outside the
nanodisk. Additionally, variations in the morphology and composition of the
residual resist modify the spatial variations in EEL signal intensity.
Normalizing each spectrum in the line profile to its own total integrated EEL
signal counteracts some of these effects and makes them more comparable to
simulations. The spectrum images were acquired in dual EELS mode with a
$15\,\mathrm{meV}$ dispersion to enable the collection of EELS data over a
larger range of energies and increase the inelastic energy range of the
normalization process. Splicing the two dual EEL spectra together allows each
spectra to extend to around $50\,\mathrm{eV}$ while still resolving the disk
modes and anapole states in the $0.5\,\mathrm{eV}-2.5\,\mathrm{eV}$ range.

###  III.3 Numerical simulations

We performed the numerical simulations shown in Figs. 1, 3 and 4 using the
Radio Frequency Module of COMSOL Multiphysics software [42]. This module
solves Maxwell’s equations in the frequency domain based on the Finite Element
Method (FEM). The nanodisk was modeled as a cylindrical structure of variable
radius $R$ and thicknesses $d=55\,\mathrm{nm}$ (Fig. 1) and
$d=70\,\mathrm{nm}$ (Figs. 3 and 4). The symmetry axis of the nanodisk is
parallel to the $z$-direction and the center of the nanodisk was located at
coordinates $(0,0,d/2)$. The probing electron traveling in the $z$-direction
was modeled as a line current (along the $z$-direction) located at a distance
$b$ (impact parameter) with respect to the nanodisk center. For numerical
calculations shown in Figs. 1 and 3, we located the electron beam trajectory
outside the nanodisk at an impact parameter $b=1.1\times R$. For simplicity,
numerical calculations shown in Fig. 1 were performed without considering any
substrate whereas in Figs. 3 and 4 the nanodisk is on top of a
$50\,\mathrm{nm}$ thick substrate layer characterized by the permittivity of
SiN $\varepsilon_{\mathrm{SiN}}=4.1853$. To ensure numerical convergence of
the calculated electron energy loss probability $\Gamma(\omega)$, the complete
structure (electron beam and nanodisk) was embedded in a homogeneous box
filled with air of depth, width and height equal to $L_{\mathrm{PML}}=12\times
R$. We use perfectly matched layers (PML, with thickness equal to $0.1\times
L_{\mathrm{PML}}$) for the boundaries of the simulation box, free triangular
elements for the the nanodisk mesh and free tetrahedral elements for all other
structures. The length of the line current that models the electron beam is
equal to $L_{\mathrm{PML}}$. Material permittivities and further details on
EEL probability calculations are provided in Supplementary Materials S1.

## Acknowledgements

C.M.-E. thanks J. Olmos Trigo for fruitful discussions. C.M.-E. and J.A.
further acknowledges grant no. IT 1526-22 from the Basque Government for
consolidated groups of the Basque University. R.H acknowledges support from
the Spanish Ministry of Science and Innovation under the María de Maeztu Units
of Excellence Program (CEX2020-001038-M/MCIN/AEI/10.13039/501100011033) and
Grant PID2021-123949OB-I00 funded by MCIN/AEI/10.13039/501100011033 and by
“ERDF A way of making Europe”. A.B.Y. acknowledges funding from the Swedish
Research Council (VR, under grant No. 2020-04986). T.O.S. acknowledges funding
from the Swedish Research Council (VR, Research environment grant No.
2016-06059). A.B.Y., B.M., E.O., and T.O.S. acknowledge funding from the Knut
and Alice Wallenberg Foundation (KAW, under grant No. 2019.0149). D.G.B.
acknowledges financial support from the Ministry of Science and Higher
Education of the Russian Federation (Agreement No. 075-15-2021-606), Russian
Science Foundation (grant No. 21-72-00051), and BASIS Foundation (grant No.
22-1-3-2-1). This work was performed in part at the Chalmers Material Analysis
Laboratory (CMAL).

## Author contributions

C.M.-E., D.G.B., and T.O.S. conceived the idea. B.M. fabricated the samples
under the supervision of T.O.S. A.B.Y. performed EELS measurements under the
supervision of E.O. C.M.-E. performed numerical calculations under the
supervision of R.H. and J.A. C.M.-E., D.G.B., J.A., and T.O.S. developed the
theoretical model to describe the anapole-exciton system and analyzed the
data. C.M.-E., A.B.Y., and D.G.B. wrote the manuscript with contributions from
all authors. E.O., J.A., and T.O.S. supervised the project.

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#  Qabas: An Open-Source Arabic Lexicographic Database

###### Abstract

We present Qabas, a novel open-source Arabic lexicon designed for NLP
applications. The novelty of Qabas lies in its synthesis of $110$ lexicons.
Specifically, Qabas lexical entries (lemmas) are assembled by linking lemmas
from $110$ lexicons. Furthermore, Qabas lemmas are also linked to $12$
morphologically annotated corpora (about $2M$ tokens), making it the first
Arabic lexicon to be linked to lexicons and corpora. Qabas was developed semi-
automatically, utilizing a mapping framework and a web-based tool. Compared
with other lexicons, Qabas stands as the most extensive Arabic lexicon,
encompassing about $58K$ lemmas ($45K$ nominal lemmas, $12.5K$ verbal lemmas,
and $473$ functional-word lemmas). Qabas is open-source and accessible online
at https://sina.birzeit.edu/qabas

utf8

Qabas: An Open-Source Arabic Lexicographic Database

Mustafa Jarrar, Tymaa Hammouda
---
Birzeit University, Palestine
{mjarrar<EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

As the need for lexicographic databases in modern applications continues to
grow, lexicography has evolved into a multidisciplinary field intersecting
with natural language processing (NLP), ontology engineering, e-health, and
knowledge management. Lexicons have evolved from being primarily hard-copy
resources for human use to having substantial significance in NLP applications
(Maks et al., 2009; Jarrar et al., 2019; McCrae et al., 2016).

Although Arabic is a highly resourced language in terms of traditional
lexicons, less attention is given to developing AI-oriented lexicographic
databases. Recent efforts at Birzeit University have been devoted to
digitizing traditional lexicons and publishing them online through a
lexicographic search engine Jarrar and Amayreh (2019); Alhafi et al. (2019),
but none of the lexicons are open-source due to copyright restrictions imposed
by their owners Jarrar (2020). The LDC’s SAMA database Maamouri et al. (2010),
is an Arabic lexicographic database, but it is also restricted to LDC members
only. SAMA, an extension of BAMA Buckwalter (2004), is a stem database,
designed only for morphological modeling. It contains stems and their lemmas
and compatible affixes.

This article proposes Qabas, a novel open-source Arabic lexicon designed for
NLP applications. The novelty of Qabas lies in its synthesis of many lexical
resources. Each lexical entry (i.e., lemma) in Qabas is linked with equivalent
lemmas in $110$ lexicons, and with $12$ morphologically-annotated corpora
(about $2M$ tokens). This linking was done through $256K$ mappings
correspondences (as shown in Table 3). That is, the philosophy of Qabas is to
construct a large lexicographic data graph by linking existing Arabic lexicons
and annotated corpora. This enables the integration and reuse of these
resources for NLP tasks. For example, by linking the lemma (كَرِيم2>/كَرِيم2)
in SAMA with (كَرِيم>/كَرِيم) in the Modern lexicon, one would integrate the
morph features (stems and affixes) found in SAMA with the $4$ senses (i.e.,
glosses) of this lemma found in the Modern. Assuming this lemma is also linked
with its $41$ word forms in the Arabic Treebank corpus Maamouri et al. , then
one would compute the corpus statistics for this lemma.

Qabas was developed semi-automatically over two years, utilizing an automatic
mapping framework and a web-based tool. Compared with other lexicons, Qabas is
the most extensive Arabic lexicon and the first to be linked with such
lexicons and corpora. The main contributions of this paper are:

  * •

Novel and open-source Arabic Lexicon ($58K$ lemmas) linked with many NLP
resources.

  * •

Mappings: $256$ mapping correspondences between $110$ lexicons ($255.5K$
lemmas) and $12$ corpora ($2M$ tokens). As such, Qabas is an Arabic
lexicographic graph, interlinking Arabic lexicons and corpora at the lemmas
level.

The paper is structured as follows: Section 2 overviews the related work,
Section 3 presents the methodology, and Section 4 presents lemma mapping. In
Section 5 we evaluate the coverage; and in Section 6 we summarize our
conclusions.

## 2\. Related Work

In recent years, many standardization efforts have been proposed for
representing, publishing, and linking linguistic resources. For example, the
W3C’s Lemon RDF model (Philipp Cimiano, 2016) enables employing lexicons in
ontologies and various NLP applications. Moreover, the Linguistic Linked Open
Data Cloud (LLOD) (McCrae et al., 2016) used Lemon to interlink the lexical
entries of several linguistic resources. The ISO’s Lexical Markup Framework
(LMF) standard aims at representing lexicons in a machine-readable format
(Francopoulo et al., 2006).

Different encyclopedic dictionaries integrated WordNets with other resources,
such as BabelNet (Navigli et al., 2012) and ConceptNet 5.5 (Speer et al.,
2017). Compared with our work, we provide an interlinking of many lexicons and
corpora, forming a lexicographic, rather than an encyclopedic graph.

Given that digitized and available Arabic lexicons are limited, there are
several attempts to digitize and represent them in the standard formats. The
first attempt to represent Arabic lexicons in ISO LMF standard can be found in
(Salmon-Alt et al., 2005; Maks et al., 2009; Khemakhem et al., 2016). Other
attempts suggested using the W3C Lemon RDF model Khalfi et al. (2016); Jarrar
et al. (2019). While several online portals for Arabic lexicographic search
exist (e.g., lisaan.net, almaany.com, almougem.com), each portal contains a
limited number of lexicons, and their content is partially structured (i.e.,
available in flat text). Qabas is developed as a synthesis of $110$ lexicons
that we digitized earlier (Jarrar and Amayreh, 2019).

## 3\. Methodology

### 3.1. Scope and Objectives

The objective of Qabas is to link existing Arabic lexicons and corpora and
enable them to be integrated and re-used in NLP tasks (Darwish et al., 2021).
In other words, Qabas lemmas are used as a proxy to link between different
resources, forming a large Arabic lexicographic data graph. Thus, all Qabas
lemmas are collected mainly from these resources (Section 3.2). As such, Qabas
is designed to be an open-source and open-ended project, targeting all forms
of Arabic: Classical Arabic, Modern Standard Arabic, Arabic dialects, and
foreign words that are transliterated and commonly used in Arabic.

In this paper, we focus on including the morphological features for each
lemma, such as the spelling(s) of the lemma, its root(s), POS, gender, number,
person, and voice. Including semantic information (e.g., glosses, synonyms,
relations, and translations) is not discussed in this article due to space
limitations. Nevertheless, it is worth noting that based on Qabas mappings,
(i) we developed a synonym extraction
tool111https://sina.birzeit.edu/synonyms. It can be also used to evaluate
synonyms (Khallaf et al., 2023). (Ghanem et al., 2023); (ii) we extracted
glosses and contexts from these mapped lexicons to build a large set of
context-gloss pairs for Word-Sense Disambiguation (Al-Hajj and Jarrar, 2021;
Malaysha et al., 2023); and (iii) a graph representing morpho-semantic
relationships in Arabic was extracted based on Arabic derivational morphology,
see Figure 4 in (Jarrar, 2021).

### 3.2. Data Sources

Among the $150$ lexicons that we previously digitized Jarrar and Amayreh
(2019), $110$ lexicons and $12$ morphologically annotated corpora were
prepared to be linked and to construct Qabas. See our copyright notice in
section 6.2 regarding the collected resources and the sharing of Qabas.

Table 1 categorizes the $110$ lexicons into: the LDC’s SAMA Maamouri et al.
(2010), Modern lexicon (Omar, 2008), Ghani lexicon (Abul-Azm, 2014), the Al-
Waseet lexicon (Cairo, 2004), the Al-Waseet Madrasi lexicon, the Arabic
Ontology and two lexicons Jarrar (2021, 2011), the Arabic WordNet Black et al.
(2006), $40$ of the ALECSO ’s Unified dictionaries. We also collected $16$
lexicons produced by the Arabic Language Academies in Cairo and in Damascus
Cairo ; Damascus , the Arabic Wikdata, in addition to $7$ thesauri and $37$
Other lexicons.

As we are concerned with linking the lexical entries (i.e., lemmas) in these
resources, each distinct lemma is given a unique identifier. In addition, we
are only concerned with linking single-word lemmas, thus multi-word lemmas are
ignored at this phase, such as (ثاني أكسيد الكربون، سرعة الضوء>). The total
number of single-word lemmas in the $110$ lexicons is about $297K$ lemmas,
about $255K$ ($84\%$) of which are mapped (See Table 1).

As shown in Table 2, we collected $12$ Arabic corpora, especially those that
are annotated with morphological features: the MSA LDC’s Arabic Treebank
Maamouri et al. , the MSA SALMA corpus Jarrar et al. (2023a), the Quran corpus
Dukes and Habash (2010), the Palestinian Curras and the Lebanese Baladi
corpora Haff et al. (2022), the Lisan (Iraqi, Lybian, Sudanese, and Yemeni)
corpora Jarrar et al. (2023b), The Emirati Gummar corpus Khalifa et al.
(2018), the Syrian Nabra corpusNayouf et al. (2023), and the LDC’s Egyptian
Treebank Maamouri et al. (2021). These corpora compass $2.4M$ tokens annotated
with about $144.5K$ lemmas, $84\%$ of which are mapped with Qabas; i.e., Qabas
is linked with about $2M$ tokens.

Lexicon |  Unique Lemmas |  Lemmas mapped
---|---|---
SAMA | $40,639$ | $40,330^{99\%}$
MODERN | $32,300$ | $32,276^{100\%}$
Ghani | $29,854$ | $24,452^{82\%}$
Al-Waseet | $36,632$ | $17,829^{49\%}$
Al-Waseet Madrasi | $7,649$ | $7,384^{97\%}$
Thesuri(7) | $15,236$ | $12,892^{85\%}$
ArabicOntology&Lexicons | $28,435$ | $24,864^{87\%}$
ArabicWordNet | $10,929$ | $9,578^{88\%}$
ALCSO Unified(40) | $40,861$ | $38,876^{95\%}$
Arab Academies(16) | $9,675$ | $7,597^{79\%}$
Others(37) | $45,398$ | $34,785^{77\%}$
Wikidata | $-$ | $4665^{--}$
Total110 | 297,608 | $\textbf{255,528}^{84\%}$
Table 1: List of lexicons mapped with Qabas so far. Corpus | Tokens |  Tokens mapped |  Unique lemmas |  Lemmas mapped
---|---|---|---|---
Arabic Treebank (MSA) | $339,710$ | $282,155^{83\%}$ | $13,078$ | $12,948^{99\%}$
SALMA (MSA) | $34,253$ | $34,253^{100\%}$ | $3,875$ | $3,875^{100\%}$
Quran (Classical) | $77,469$ | $62,123^{80\%}$ | $4,830$ | $4,100^{84\%}$
Curras (Palestinian) | $56,169$ | $56,010^{100\%}$ | $6,033$ | $5,966^{99\%}$
Baladi(Lebanese) | $9,561$ | $9,493^{99\%}$ | $2,406$ | $2,365^{98\%}$
Lisan (Iraqi) | $45,881$ | $40,615^{89\%}$ | $9,306$ | $7,520^{81\%}$
Lisan (Lybian) | $51,686$ | $39,508^{76\%}$ | $10,174$ | $7,550^{74\%}$
Lisan (Sudanese) | $52,616$ | $44,136^{84\%}$ | $10,455$ | $8,709^{83\%}$
Lisan (Yemeni) | $1,098,222$ | $901,335^{82\%}$ | $44,331$ | $33,244^{75\%}$
Gummar (Emirati) | $202,329$ | $182,155^{90\%}$ | $7,590$ | $6,800^{90\%}$
Nabra (Syrian) | $60,021$ | $60,021^{100\%}$ | $10,191$ | $10,191^{100\%}$
Egyptian Treebank | $400,448$ | $297,188^{74\%}$ | $22,258$ | $18,626^{83\%}$
Total | 2,428,365 | $\textbf{2,008,992}^{\textbf{83\%}}$ | 144,527 | $\textbf{121,894}^{\textbf{84\%}}$
Table 2: List of corpora linked with Qabas so far.

### 3.3. Lexicon Construction Phases

Qabas was constructed semi-automatically over different phases, and using a
web-based tool (illustrated in Figure 1).

To bootstrap Qabas, we first adopted all lemmas from the Modern lexicon and
uploaded them to the tool. Three lexicographers then reviewed and manually
revised and enriched these lemmas with morphological features (described in
Section 3.4) and linked them with lemmas in other lexicons. This methodology
allowed the lexicographers to construct Qabas based on the information in
other lexicons while linking Qabas to those lexicons at the same time (see
guidelines in Section 3.4). To accelerate the linking process, we used
heuristic rules to automatically discover candidate mappings for the
lexicographers to verify (see Section 4.2).

To cover the remaining lemmas in lexicons other than Modern (i.e., that are
not linked in the previous phase), we collected these lemmas and prioritized
them. Higher priority is given to those lemmas that are more frequent across
the $110$ lexicons and $12$ corpora. This prioritized list of candidate lemmas
was uploaded to the tool, for the lexicographers to review and make the
necessary edits. This approach allowed us to efficiently expand the lemma
coverage of Qabas. The expansion is an ongoing and open-ended endeavor, as
there is no limit to the number of lemmas that could potentially be added to
Qabas. As will be discussed in section 5, our progress indicates that we have
covered most of the lemmas in the $110$ lexicons and $12$ corpora.

Mapping Qabas with the $12$ corpora (in table 2) was straightforward. As most
of the lemmas in these corpora are SAMA lemmas, which we manually linked with
Qabas, we only replaced SAMA lemmaIDs with Qabas lemmaIDs. For the non-SAMA
lemmas, we selected the most frequent lemmas in the $12$ corpora and added
them to Qabas manually.

Figure 1: Screenshot of our web-based tool, which we developed for
constructing Qabas

### 3.4. Guidelines

Each lemma in Qabas is tagged with the following eight morphological features:
(1) the $41$ POS tagset shown in Table 4, (2) the gender tags {$Masculine$,
$Feminine$, $N/A$}, (3) Number tags {$Singulare$, $Dual$, $Plural$}, (4) the
Aspect tags {$PV$, $IV$, $CV$, $PV\\_PASS$, $IV\\_PASS$}, (5) and Person tags
{$1^{st}$, $2^{nd}$, $3^{rd}$}. We additionally tag each lemma with its (6)
root(s), (7) augmentation {$Augmented$, $Unaugmented$}, and (8) transitivity
{$Transitive$, $Intransitive$}.

Lemma selection and spelling, our full list of guidelines not included in this
article for space limitation but can be found online222Guidelines
https://sina.birzeit.edu/qabas/about. Our guidelines are similar to those
described in the introduction of the Modern Omar (2008). However, we
introduced additional guidelines, such as: the lemma should be fully
diacritized including the last letter; the POS of a lemma can be $Noun\\_Prop$
only if all of its meanings refer to proper nouns; additional spellings of the
same lemma are separated by "|" and ordered by frequency, such as
(تِلِيفُونٌ>|تِلِفُونٌ>); dialectal lemmas are spelled according to the CODA
rules used in Curras Jarrar et al. (2017, 2014), hence we write (قَزاز>/قَزاز)
rather than (أزاز>/أزاز); each dialect lemma is mapped with an MSA lemma, e.g.
(قَزاز>/قَزاز) and its MSA (زُجاج>/زُجاج); a lemma is considered $adjective$
if all of its meanings are either $ActiveParticiple$ اسم فاعل>,
$PassiveParticiple$ اسم مفعول>, $Relative$ نسبة>, $AdjectivalPropriety$ صفه
مشبهة>, $Exaggeration$ صيغة مبالغة>, or $Diminutive$ تصغير> ; among other
guidelines.

## 4\. Lemma Linking

This section presents the framework and methods we used to map between lemmas
across lexicons.

### 4.1. Mapping Framework

This framework aims to enable lemmas to be interlinked through a mapping
correspondence.

Definition $1$: Given two lemmas $l_{1}$ and $l_{2}$, a mapping correspondence
between them is defined as:

<$l_{1}$, $l_{2}$, $R_{i}$>

Where:

  * •

$l_{1}$, $l_{2}$ are lemmas to be mapped.

  * •

$R_{i}$ is the mapping relation between $l_{1}$ and $l_{2}$, $R_{i}$ $\in$
{$R_{1}$…$R_{6}$} shown in Table 3.

This mapping framework was implemented in our tool (See Figure 1) and used by
our lexicographers. Table 3 presents the count of the mapping correspondences
for each relation, which are about $256K$ correspondences in total.

Relations | count
---|---
$R_{1}$ |  نفسها بالضبط> |  Same Exactly | 248,882
$R_{2}$ |  نفسها، اختلاف مفرد جمع> |  Same, Singular-Plural difference | 3,010
$R_{3}$ |  نفسها، اختلاف مفرد مثنى> |  Same, Singular-Dual difference | 74
$R_{4}$ |  نفسها، اختلاف مذكر مؤنث> |  Same, Male-Female difference | 1,784
$R_{5}$ |  نفسها، اختلاف حالة إعرابية> |  Same, Case difference | 372
$R_{6}$ |  نفسها، بمعنى اسم العلم> |  Same, but Proper Noun | 1,918
Total (mapping correspondences) | 256,040
Table 3: The six mapping relations and their counts

### 4.2. Automatic Mapping

To speed up the mapping process, this section proposes a set of heuristic
rules to discover candidate mappings. Before presenting these rules, we
discuss how Arabic word forms can be compared.

Comparing words in Arabic is not trivial. First, Arabic is diacritic-
sensitive, thus we cannot compare words using equality. For example, the same
lemma in one lexicon might be spelled as كَلمَة>/كَلمَةand in another as
كلَمةٌ>/كلَمةٌ. Second, lexicons are not always self-consistent or follow the
same guidelines in structuring or writing word forms Amayreh et al. (2019).
For example, some lexicons provide the feminine and masculine forms of a
perfect verb {يَكتب>/يَكتب, تَكتُب>/تَكتُب}, while others provide one
{يكتُب>/يكتُب} or none {}. To overcome these challenges, when comparing word
forms, we implemented the following definitions of compatibility \- as
explained in Jarrar et al. (2018).

Definition $2$: Given two words $w_{1}$ and $w_{2}$, we consider them
diacritic-compatible, iff: (1) both words have the same letters, and (2) no
contradictions between the diacritics of the same, pair-wise, letters of these
words.

Definition $3$: Given two sets of words $W_{1}$ and $W_{2}$, we consider these
sets compatible, iff there exists a diacritic-compatible word $w$ in both
sets, $w$ $\in$ $W_{1}$ and $w$ $\in$ $W_{2}$, i.e., their intersection is not
empty.

The mapping heuristic rules are:

  * •

$h_{1}$: A mapping correspondence is established between two verb lemmas if
the following two conditions are true: ($i$) each lemma has a perfective
form(s) $PV$ and these forms are compatible, and ($ii$) if each lemma has
root(s), imperfect form(s) $IV$ and command form(s) $CV$, and these roots,
$IV$s, and $CV$s are compatible.

Example: ($i$) $PV_{1}$={كَتَبَ>} and $PV_{2}$={كَتبَ>} which are compatible,
and ($ii$) $IV_{1}$={يكتب>, أكتب>} and $IV_{2}$={يَكْتُبُ>}, $CV_{1}$={} and
$CV_{2}$={أكتب>}, and $root_{1}$={ك ت ب>} and $root_{2}$={}, which are all
compatible.

  * •

$h_{2}$: A mapping correspondence is established between two noun lemmas if
the following two conditions are true: ($i$) each lemma has a singular form(s)
and these forms are compatible, and ($ii$) if each lemma has root(s), dual(s)
and plural(s), and these root(s), dual(s), and plural(s) are compatible.

With these heuristics, we were able to discover $179K$ candidate mapping
correspondences. We then uploaded these mapping relations to the tool and
labeled them with "Auto-mapped". Lexicographers were given these mappings to
confirm and assign them one of the six relations (See the relations division
at the bottom of Figure 1). Lexicographers can edit these relations and search
the lexicons to include more mappings if needed.

## 5\. Evaluation and Discussion

We evaluate the coverage of Qabas by comparing it with two resources: SAMA and
Modern, which are well-developed resources for Arabic. SAMA is designed for
morphological modeling, while Modern is a typical MSA lexicon focusing on
semantics. Table 4 shows that Qabas’s coverage is almost double of Modern and
is $40\%$ larger than SAMA. Table 1 also shows that Qabas contains all Modern
lemmas and $99\%$ of SAMA lemmas. We did not add the $1\%$ as we found them to
be typos or with redundant spellings. Another critical issue in SAMA is that
it treats each proper noun as a separate lemma (e.g., كَرِيم1>/كَرِيم1as a
proper noun and كَرِيم2>/كَرِيم2as adjective). We believe that this is
problematic because most Arabic words can be used as proper nouns Jarrar et
al. (2022). Proper nouns in Qabas are considered as such only if all meanings
denote proper nouns. Thus, the lemma كَرِيم>/كَرِيمwould be tagged with an
adjective, and one of its meanings is a proper noun. Hence, most of the
$5,540$ proper nouns in SAMA are merged and mapped with Qabas lemmas through
the $R_{6}$ relations.

An Inter-Annotator Agreement (IAA) evaluation was conducted to evaluate the
lemma mappings. We randomly selected $2850$ lemmas ($5\%$ of Qabas) and asked
each of the three lexicographers ($A_{1}$, $A_{2}$, $A_{3}$) to map them. The
IAAs using the Kappa coefficient $\kappa$ are: $A_{1}$-$A_{2}$ is $85\%$,
$A_{2}$-$A_{3}$ is $88\%$, and $A_{1}$-$A_{3}$ is $86\%$, which are "almost
perfect" (Viera and Garrett, 2005).

POS category | POS | Modern | SAMA | Qabas
---|---|---|---|---
Nominal |  NOUN اسم> | 21,456 | 19,705 | 29,053
NOUN_PROP اسم علم> |  | 5,540 | 4,319
ADJ صفة> |  | 5,500 | 11,067
ADJ_COMP صفة مقارنة> |  | 204 | 295
ADJ_NUM صفة عدد> |  | 12 | 12
NOUN_NUM اسم عدد> |  | 33 | 44
NOUN_QUANT اسم كم> |  | 23 | 19
DIGIT عدد> |  |  | 10
NOUN_VOICE صوت> |  |  | 16
ABBREV حرف اختصار> |  | 60 | 106
Total | 21,456 | 31,077 | 44,941
Verb |  PV ماضي> | 10,475 | 8,133 | 12,679
IV مضارع> |  | 990 | 9
CV أمر> |  | 16 | 6
PV_PASS ماضي مجهول> |  | 32 | 63
IV_PASS مضارع مجهول> |  | 78 |
Total | 10,475 | 9,249 | 12,757
Functional words |  PRON, DEM_PRON, EMOJI REL_PRON, REL_ADV, ADV, INTERROG_PART, INTERROG_ADV,PREP,CONJ, INTERROG_PRON, PART RESTRIC_PART,PUNC,INTERJ, FOCUS_PART, DET, VERB VOC_PART, PROG_PART, SUB_CONJ, VERB_PART, FUT_PART,EXCLAM_PRON PSEUDO_VERB,NEG_PART | 369 | 313 | 473
| Total | 32,300 | 40,639 | 58,171
Table 4: Coverage Evaluation of Qabas, per POS

## 6\. Conclusion

We presented Qabas, a novel and open-source Arabic lexicon linked with $110$
lexicons and $12$ morphologically annotated corpora. Additionally, the $256k$
mappings correspondences between Qabas and each of the $110$ lexicons can be
also downloaded from Qabas Page. As such, Qabas is a large lexicographic data
graph, linking existing Arabic lexicons and annotated corpora.

### 6.1. Limitations and Future Work

One of the major challenges faced during the construction of Qabas was
convincing the owners of the lexicons to publish their lexicons as open-
source. While we agreed with the owners of the lexicons to only publish the
mapping links between Qabas and their lexicons, we hope that our work will
encourage others to publish their lexicons as open-source in the future.
Adding dialect lemmas to Qabas is another challenge. Since our three
lexicographers are familiar with Levantine dialects, adding lemmas from other
dialects requires knowledge of these dialects. Qabas is currently limited to
the frequently used dialect lemmas or those that are known to most Arabs. We
plan to recruit more lexicographers from other dialects to extend Qabas. Last
but not least, we plan to represent Qabas and publish the mapping
correspondences using the W3C RDF Lemon model.

### 6.2. Ethical and copyright Considerations

We obtained permission to use the lexicons and corpora listed in this article,
and since our lexicon will be open-source, we will not share any copyrighted
data. We will share: (1) Qabas itself (all lemmas and their full morphological
features), and (2) the mapping links (i.e., correspondences) between Qabas and
the other external resources. Obtaining licenses for these external resources
is the responsibility of the users.

## Acknowledgment

We would like to thank the main lexicographers who contributed to this
project, especially Shimaa Hamayel, Hiba Zayed, and Rwaa Assi; as well as
Diyam Akra, Sanad Malaysha, Sondus Hamad, Asmaa Motan, Yaqout Abu Allia, Nour
Dana, who also contributed to various lexicographic and technical aspects.

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