# Does Melania Trump have a body double from the perspective of automatic face
recognition?

Khawla Mallat1, Fabiola Becerra-Riera2, Annette Morales-González2, Heydi
Méndez-Vázquez2 and Jean-Luc Dugelay1
1 Digital Security Department, EURECOM Campus Sophia Tech, 450 route des
Chappes F-06410 Biot Sophia Antipolis, France. Email: {mallat,
<EMAIL_ADDRESS>2Advanced Technologies Application Center (CENATAV) 7A
#21406 Siboney, Playa, P.C.12200, Havana, Cuba. Email:
<EMAIL_ADDRESS>
###### Abstract

In this paper, we explore whether automatic face recognition can help in
verifying widespread misinformation on social media, particularly conspiracy
theories that are based on the existence of body doubles. The conspiracy
theory addressed in this paper is the case of the Melania Trump body double.
We employed four different state-of-the-art descriptors for face recognition
to verify the integrity of the claim of the studied conspiracy theory. In
addition, we assessed the impact of different image quality metrics on the
variation of face recognition results. Two sets of image quality metrics were
considered: acquisition-related metrics and subject-related metrics.

##  I Introduction

This is not Melania! In October 2017, the hypothesis of the existence of a
body double of Melania TRUMP appeared for the first time on social networks.
Then regularly, what is now referred to as _‘The Melania Trump replacement
conspiracy theory’_ 111
https://en.wikipedia.org/wiki/Melania_Trump_replacement_conspiracy_theory by
mass media, reappears in the front of the stage, at least once a year, with a
peak during the last presidential election campaign. Face is used by all of us
as the main human trait to recognize each other in daily life. This is why,
even if some other criteria have been used to demonstrate that Melania is not
Melania, like her attitude and behavior or her body height, most arguments
advanced by people are related to her facial appearance.

Algorithms based on artificial intelligence, image/video processing and
computer vision are designed and used to fight against fake news that include
doctored images [10] and/or AI-based generated videos (i.e. deepfakes) [7].
The issue addressed in this article is different in the sense that the open
question is not about the integrity of the picture but about the physical
presence of the real Melania or of a body double in the scene recorded by the
camera. So Biometrics (and more particularly Automatic Face Recognition), more
than image forensic tools, is the appropriate technology to address the
problem.

There are two possibilities in case of the non-existence of a body double of
Melania: either people are complotists in the sense that they are aware that
Melania has no double body but claim the contrary or, people are of good faith
and consider by visual inspection that there are two different people on
photographs: Melania and a body double based on some possible visual
differences among faces. Visual inspection by human is subjective and today
less accurate than a digital and objective inspection by machines for many
tasks related to face analysis [14]. This is why automatic face recognition
may significantly help in the process for forming a robust opinion concerning
this supposed conspiracy theory.

In this work, we use automatic face recognition to conduct an analysis of a
group of images of Melania Trump, in order to try to determine if she has a
body double or not.

##  II Automatic face recognition

In this section, we present primarily the image samples of Melania Trump on
which our study has been based. Then, we introduce the state-of-the-art
descriptors of face recognition employed in this study followed by the
experimental protocol and results that will help answering the question _‘Does
Melania Trump has a body double?’_.

###  II-A Face samples

The presented study was driven by the interest of W9, a French TV channel, in
the conspiracy theory case related to Melania Trump
222https://www.youtube.com/watch?v=9HJKKYeJdTk&t=1239s. The TV channel
provided us with a set of images of Melania Trump collected from social media,
mainly Twitter, collected by journalists. These images were labeled by the
social media users as the _‘real’_ Melania Trump or as the _‘body double’_.
Faces were detected using RetinaFace [5] and only faces of Melania Trump were
selected and then aligned. Figure 1 shows the preprocessed face images. At
first glance, one could see that there is an important discrepancy between the
two sets of images. First, the set of the alleged _‘body double’_ contains 6
out of 14 images in which Melania is wearing large dark glasses which covers
up the ocular area, while it is the case for only 1 out of 16 images for the
_‘real’_ Melania. In addition, one could see that the set of images of the
_‘real’_ Melania contains images where Melania is captured with a smiling
face, open eyes and proper illumination conditions, while the images contained
in the set of the alleged _‘body double’_ of Melania seem to be taken from
video recordings, where Melania appears with blinking eyes, head down and low
illumination conditions.

Figure 1: Preprocessed face images of the _‘real’_ Melania and the alleged
_‘body double’_.

###  II-B Automatic face recognition models

In this study, we employ four state-of-the-art face recognition descriptors
that achieved more than 99.3% of accuracy when evaluated on LFW dataset. For
each face descriptor, feature embeddings are extracted from Melania’s face
images and compared against each other using cosine similarity.

LightCNN [15] is an implementation of CNN for face recognition designed to
have fewer trainable parameters than a vanilla CNN and to handle noisy labels.
This network introduces a new concept of max-out activation in each
convolutional layer for feature filter selection. We use the pretrained
network with 29-layers to obtain embeddings of 256-dimension from face images.

MobileSqueezeNet [1] is a lightweight CNN released with Intel’s OpenVino
framework and model zoo, for face recognition in re-identification scenarios.
It is based on MobileNet V2 [8] backbone, which consists of 3x3 inverted
residual blocks with squeeze-excitation attention modules. After the backbone,
the network applies global depthwise pooling and then uses 1x1 convolution to
create the final 256-dimensional embedding vector.

SphereFace [9] refers to angularly distributed feature embeddings designed for
face recognition. In contrast to employing Euclidean margin to the CNN’s
learned features, SphereFace proposes to use an angular softmax (named
A-Softmax) to learn discriminative face features with a novel geometric
interpretation. A-Softmax loss can be interpreted as constraining learned
features to be discriminative on a hypersphere manifold, which intrinsically
matches the prior that face images lie on a manifold. We use the
512-dimensional SphereFace embeddings.

ArcFace [6] is Additive Angular Margin loss function, a new loss function for
face recognition designed to improve the discriminative power of the learnt
feature embeddings. The proposed loss function aims to optimise the geodesic
distance margin by considering the correspondence between the angle and arc in
the normalised hypersphere. We used a model pretrained on LFW dataset to
extract embeddings of 512-dimension from face images.

###  II-C Experimental protocol and results

Assuming we have 2 identities for Melania Trump, the first consists of the
_‘real’_ Melania and the second consists of the alleged _‘body double’_ , we
performed a face verification experiment using an All-vs-All comparison
scheme. _Genuine_ pairs belong to the same identity, while _Impostors_ pairs
correspond to the comparison of one identity vs. the other, meaning the
_‘real’_ Melania against the alleged _‘body double’_. We illustrate in Figure
2(d) the score distributions of Genuines in green and of Impostors in red
using the four selected face descriptors. We also introduced the score
distributions of imposters and genuines deduced from a dataset, collected from
the web by the authors, of female celebrities in their 50s similar in profile
to Melania Trump. This dataset contains 50 identities, with 30 images per
identity.

(a)

(b)

(c)

(d) Figure 2: Similarity score distribution of _‘real’_ against _‘body
double’_ Melania Trump (a) Arcface (b) LightCNN (c) MobileSqueezeNet (d)
SphereFace.

Genuines (Melania)  Imposters (Melania)  Genuines (Celebrities)  Imposters(
Celebrities)

It can be seen that the genuine (in green) and the imposter (in red) score
distributions overlap substantially, although, there is a slight difference
between the two score distributions. This difference might be due to the
discrepancy in image samples between the set of _‘real’_ Melania and the
alleged _‘body double’_ as depicted in section II-A. In section III, we
evaluate the impact of different factors that might affect the automatic face
recognition score as an attempt to justify the slight difference between the
green and the red score distribution. In addition, one could see that the
distributions of genuine and imposter scores deduced from the Melania data
generally fall into the genuine score distribution deduced from the
celebrities dataset, with a minor overlap with the imposters score
distribution, meaning that the images of the real Melania and the images of
the alleged body double belong to the same person.

##  III Factors affecting automatic face recognition

In this section, we suppose that Melania Trump does not have a body double
according to the significant overlap between genuine and imposter score
distributions deduced from Melania image set, illustrated in section II-C.
However, in this section, we attempt to justify the difference between these
two distributions highlighted hereabove. There are several factors that could
affect the utility of a face image for a specific task. In this section, since
we are particularly interested in face recognition, we explored the impact of
key quality metrics [13, 3, 11] which were considered according to the
particular conditions of our case of study and that are subject and
environmental/sensor-related.

To highlight the impact of a given quality metric on the face recognition
performance, we sorted all the 30 image samples of Melania Trump according to
their corresponding quality measure in an ascending order. Feature embeddings
were extracted from all the images. Then, the affinity matrix of the cosine
similarity scores is computed between feature embeddings of Melania Trump’s
images in an All-vs-All comparison scheme. Hereafter, only results obtained
using ArcFace feature embeddings will be reported as all the four face
descriptors depict the same behaviour.

###  III-A Acquisition-related image quality metrics

From simply looking at the image samples of Melania Trump, one could see a
prominent difference between the _‘real’_ and the alleged _‘body double’_ sets
mainly in the image acquisition quality.

Brightness [11] Depending on the acquisition conditions and the camera
devices, images could often be affected by variations in terms of illumination
and color leveling (the degree of lightness or darkness of a color) which
result in brightness variations. Brightness is the perception caused by the
luminance of an object, a face in our case. Major fluctuations of these
measures could drastically change the appearance of subjects causing different
skin color and shaded or extremely brighten zones that could even partially
occlude discriminative face parts. Since brightness does not visually appear
to be homogeneous across the Melania Trump image set, we decided to analyse
how much it really affects the recognition.

Face luminance [13] Face luminance deals with the distribution of light across
the face and it is measured in specific face regions that are prominent for
the face recognition process. The face image quality based on luminance, was
measured by averaging the normalized mean luminance values for a set of
triangles, representing key face regions, that are more likely to be affected
by changes in illumination. Since illumination does not appear to be
homogeneously distributed across the face, an assessment of the variation of
face luminance on the face recognition score is conducted.

Exposure [11] is the amount of light that reaches the acquisition sensor and
it can be controlled using aperture and shutter settings. When the face image
is correctly exposed, the image provides rich details in both dark shadow
regions as well as bright regions. The Melania Trump set of images contain
mainly underexposed images in which the dark shadow regions lose fine details
and appear as pure block regions because of receiving too little light.

Contrast [11] Low contrast images are commonly due to poor illumination
conditions during the image acquisition, wrong setting of the aperture and
shutter speed. Low contrast face images contain underexposed and overexposed
regions that result in loss of geometrical and color information of facial
attributes. Image contrast is defined as the separation between the darkest
and brightest areas of the image, and it can be computed as the difference in
color intensities.

Sharpness [13] In blurred images, the face regions (eyes, nose, mouth, etc.)
are usually not sufficiently clear or well delimited due to the loss of visual
information by confusing and mixing shapes, textures and colors. To decide to
which extent more or less defined/sharp edges are influencing the face
recognition process, we applied an unsharp masking process to sharpen the
original face image and average the resulting pixel intensities to obtain a
sharpness quality score.

###  III-B Subject-related image quality metrics

The second main difference between the set of the _‘real’_ and the alleged
_‘body double’_ is related to the physical appearance of Melania herself. One
could see that the set of the _‘real’_ Melania shows images of her with the
head straight and a glowy face, whilst for the set of the alleged _‘body
double’_ , Melania appears either wearing sunglasses or with the eyes closed
with a varying head pose. Accordingly, 3 quality metrics that are subject-
related were selected to evaluate their impact on face recognition similarity
score.

Occlusion by sunglasses [13] Since several samples of the alleged _‘body
double’_ set show Melania wearing sunglasses, our focus was drawn on the
occlusion of the periocular region, which has been shown to be a very
discriminative region in face recognition, and its impact on face recognition
performance. Therefore, to measure the quality of a face image based on the
use of sunglasses, we first used a CNN classifier as sunglasses detector, and
then we employed the output probability of the class representing “non
sunglasses” as final quality score: face images with higher ‘non sunglasses’
probability are more likely to be good quality images and vice versa.

Femininity [12] A main factor that might have affected the face recognition
performance can clearly observed in the Melania Trump images is her physical
appearance. In the set of the _‘real’_ Melania, she appears with radiant face
and make up on, whilst in the alleged _‘body double’_ set, Melania seems to be
wearing too little make up or no make up at all, with a wearied face.
Consequently, we propose to quantify the femininity appearance of Melania
Trump on all the image samples and evaluate their impact on face recognition
performance. For this purpose, a gender estimation model [2] was employed to
deliver a score representing the probability of being a male or a female. We
consider the femininity score as the probability of being a female. Mallat et
al. [12] proved that the more makeup is applied (up to a certain level), the
higher the femininity score is.

Head pose [13] The complexity of dealing with multiple head rotations under
uncontrolled conditions has long been a bottleneck in face recognition.
Different head poses usually imply the occlusion or deformation of some face
regions, which can lead to the mismatch of two samples of the same person just
because they were captured from different angles. It is worth noting that
general Melania postures are basically frontal and just a few samples present
some yaw or pitch variation, in particular for the alleged _“body double”_
set.

###  III-C Discussion

Figure 3 reports the affinity matrices of the cosine similarity scores that
highlight the impact of image quality metrics that are related to the image
acquisition: brightness, face luminance, sharpness, exposure and contrast.
Blue cells reflect a low similarity score (closer to 0) whereas green cells
correspond to high similarity score (close to 1).

(a)

(b)

(c)

(d)

(e)

image labeled as _‘real’_ Melania  image labeled as _‘body double’_

Figure 3: Affinity matrix of cosine similarity between ArcFace embeddings of
Melania Trump’s images, sorted according to: (a) Brightness (b) Face luminance
(c) Contrast (d) Exposure (e) Sharpness.

In Figures 3(a), 3(b), 3(c) and 3(d), one could see that images with low
quality yield low similarity scores and they correspond to image samples from
the alleged _‘body double’_ , whilst high quality images deliver high
similarity score and they are mostly associated to image samples of _‘real’_
Melania. For the exposure quality metric, the lines of the affinity matrix, in
Figure 3(c), that depict low similarity scores for images with higher exposure
correspond to specific image samples in which Melania Trump appears either
with sunglasses or with the head down. Figure 3(e) shows a small correlation
between sharper images and high similarity scores. However, we can deduce from
the matrix that there are different and more relevant factors that are
influencing the face recognition performance. The cross-shaped blue area that
depict low similarity scores from Figure 3(e) corresponds to the comparison of
four images of average sharpness but considerably affected by illumination and
using sunglasses; this is also the case of the two isolated sharp images
producing the blue lines that converge in the bottom right corner of the
matrix.

Figure 4 portrays the affinity matrices of the cosine similarity scores by
sorting the image samples in an ascending order according to occlusion by
sunglasses, femininity and head pose quality metrics, in order to highlight
their impact on face recognition performance.

(a)

(b)

(c)

image labeled as _‘real’_ Melania  image labeled as _‘body double’_

Figure 4: Affinity matrix of cosine similarity between ArcFace embeddings of
Melania Trump’s images, sorted according to: (a) Occlusion by sunglasses (b)
Femininity (c) Head pose.

In Figures 4(a) and 4(b), one could perceive that the images with low quality
scores yield low similarity scores and correspond to the image samples of the
_‘body double’_ , whereas the images with the highest quality coincide with
samples of the _‘real’_ Melania and they deliver relatively higher similarity
scores. The linear behaviour observed in Figure 4(a) is a confirmation that
sunglasses have high impact on the variation of face recognition scores when
comparing the set of _‘real’_ Melania with the alleged _‘body double’_. The
two crossed shaped blue areas, in Figure 4(b), depicting low similarity scores
for higher femininity values correspond to two samples of Melania wearing
sunglasses. However, Figure 4(c) shows the pose variation is barely
influencing the recognition: comparisons between good and bad quality samples
output higher or lower similarity scores alike. This behaviour is an indicator
that the used face descriptors are robust enough to the slight head pose
variation across Melania’s image samples.

Among the selected quality metrics, one could affirm that brightness, face
luminance and occlusion by sunglasses are the most relevant quality metrics
affecting the face recognition performance, and to a lesser degree with
exposure, contrast and femininity. Brightness, face luminance, exposure and
contrast being all related to the illumination conditions during the image
acquisition depict the same behaviour of the affinity matrix that could be
seen in figures 3(a), 3(b), 3(c) and 3(d). The slight shift between the
genuine and imposter score distributions deduced from Melania Trump image
samples, observed in subsection II-C, is certainly due to the fact that the
set of the _‘real’_ Melania contains overall images of better quality compared
to the set of the alleged _‘body double’_ , and obviously not because of the
existence of a Melania Trump _‘body double’_.

##  IV Conclusion

In this paper, different state-of-the-art descriptors of face recognition were
used to compare the _‘real’_ Melania image set to the the images of the
alleged _‘body double’_. According to the proposed study, the answer to the
question _‘Does Melania Trump have a body double?’_ is definitely a _No_.
Automatic face recognition invalidates the polemical conspiracy theory
claiming the existence of a replacement of Melania Trump during the presidency
term of Donald Trump. This disclaimer could only be reliable if we presume
that the provided face image samples were not priorly manipulated. Recently, a
new type of image manipulation intended to trick the deep leaning based models
into delivering an erroneous output. This type of image manipulation, called
adversarial attacks, is performed by adding an adversarial perturbation that
can be imperceptible to the human eye [4]. It could be imagined, for instance,
that a replacement of Melania Trump exists indeed and that the associated
image samples were manipulated in a way that the replacement will be
recognized as Melania Trump.

## References

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# High Conversion Efficiency in Multi-mode Gas-filled Hollow-core Fiber

Md. Selim Habib, Christos Markos, and Rodrigo Amezcua-Correa, Manuscript
received August XX, 2021.M. Selim Habib is with the Department of Electrical
and Computer Engineering, Florida Polytechnic University, FL-33805, USA
(e-mail: mhabib@floridapoly.edu).C. Markos is with the Department of Photonics
Engineering, Technical University of Denmark, DK-2800, Denmark (e-mail:
chmar@fotonik.dtu.dk).R. Amezcua-Correa is with CREOL, University of Central
Florida, FL-32826, USA (e-mail: r.amezcua@creol.ucf.edu).

###### Abstract

In this letter, an energetic and highly efficient dispersive wave (DW)
generation at 200 nm has been numerically demonstrated by selectively exciting
LP02-like mode in a 10 bar Ar-filled hollow-core anti-resonant fiber pumping
in the anomalous dispersion regime at 1030 nm with pulses of 30 fs duration
and 7 $\mu$J energy. Our calculations indicate high conversion efficiency of
$>$35% (2.5 $\mu$J) after propagating 3.6 cm fiber length which is due to the
strong shock effect and plasma induced blue-shifted soliton. It is observed
that the efficiency of fundamental LP01-mode is about 15% which is much
smaller than LP02-like mode and also emitted at longer wavelength of 270 nm.

###### Index Terms:

Hollow-core anti-resonant fiber, ultrafast nonlinear dynamics, higher-order
mode, dispersive wave.

##  I Introduction

The ultraviolet (UV) spectral range (100-400 nm) is of great interest in the
scientific community because of wide range of applications such as
spectroscopy [1], control of chemical reactions [2], biomedicine [3], and
femtosecond (fs) pump–probe measurements [4]. Despite of numerous
applications, the availability of such UV sources in this spectral regime are
limited and a very few laser sources directly emit UV light and some require
complex set-up [5]. These UV laser sources include excimer lasers [6], cerium
fluoride lasers [7], harmonic generation [8], and diode lasers [9]. Recently,
hollow-core anti-resonant fibers (HC-ARFs) offer many appealing features
including broadband guidance, low-light glass overlap, low propagation loss,
and weak anomalous dispersion to study ultrafast nonlinear dynamics when
filled with noble gases [10, 11, 12, 13, 14, 15]. One of the remarkable
features of adding gas in HC-ARF is that both the dispersion landscape and
nonlinearity can be tuned by simply changing the pressure of the gas. Based on
these properties, several impressive results have been reported to generate
light in the UV [12, 13, 11, 5]. However most of the works on the UV light
generation have been performed considering the excitation of a pure LP01-like
mode and it is relied on a well-known process called soliton self-compression
to the sub single-cycle regime, followed by resonant DW radiation [10]. For
example, bright emission of UV light was first theoretically predicted in an
Ar-filled HC-ARF with efficiency of 20% [16] and later experimentally reported
with efficiency of 6% [11]. Recently, an energetic DW generation at 275 nm is
experimentally demonstrated by pumping in the mid-IR regime of 2460 nm [12].

In this work, blue-shifted DW generation with high conversion efficiency at
around 200 nm has been demonstrated by exciting LP02-like mode in an uniform
Ar-filled HC-ARF with experimentally feasible fiber and pulse parameters. The
generated DW has an efficiency of $>$35% when the fiber is filled under 10 bar
Ar, pumped in the anomalous dispersion regime of 1030 nm, 30 fs pulse
duration, and 7 $\mu$J pulse energy. The high efficiency of the generated DW
wave is due to the combination of self-phase modulation and anomalous
dispersion, extreme shock effect and plasma-induced blue-shifted soliton. The
temporal pulse is compressed down to less than single cycle of $\sim$1.5 fs.
In comparison, the the nonlinear dynamics of LP01-like mode is also
investigated. When a LP01-like mode is excited, the DW emits at a longer
wavelength of $\sim$270 nm with efficiency of 15%. However, the compressed
pulse is not sufficient to ionize the gas due to the lack of sufficient free
electron generation.

##  II Fiber modeling and Modal dispersion

The HC-ARF considered in this work consists of 10-nested tubes with a core
diameter of 40 $\mu$m, wall thickness of 300 nm, gap separation of 2 $\mu$m,
and nested tube tube ratio, $d/D$ = 0.5. The wall thickness of 300 nm provides
the center of first-order resonance at 630 nm calculated using [17]:
$\lambda_{r}=\frac{2t}{m}\sqrt{(n_{\text{g}}^{2}-1)}$, where $t$ is the wall
thickness, $n_{\text{g}}$ is the refractive index of silica glass, and $m$ is
the resonance order. The wall thickness is chosen 300 nm such that the
resonance is far away from the laser pump wavelength of 1030 nm. The modal
properties of the fiber was calculated using finite-element (FE) modeling
based on Comsol® software according to [17, 18, 19]. The HC-ARF can be
designed multi-mode by carefully engineering the cladding parameters and
number of tubes [18]. The fiber is shown in Fig. 1(a) which can support more
than 20 spatial modes and has maximum threshold loss of $<$100 dB/km. Fig.
1(a) shows the mode-field profiles of LP01 and LP02-like modes which are well
confined in the core and the loss of these modes are $<$10 dB/km at the pump
wavelength of 1030 nm.

Figure 1: Numerically calculated (a) GVD of LP01 (blue) and LP02 (red)-like
mode using modified capillary model [20] and FM modeling. solid: modified
capillary model; dotted: FM modeling. The fiber has a core diameter of 40
$\mu$m, wall thickness of 300 nm, gap separation of 2 $\mu$m, and nested tube
ratio of 0.5. The definition of fiber geometrical parameters can be found in
[19]. Inset of (a): mode-field profile of LP01 and LP02-like mode. (b)
propagation constant mismatch $\Delta\beta$ between soliton and DW according
to [10]. The contribution of ionization is not included. N: normal and A:
anomalous dispersion. The light green shaded area presents the anomalous
dispersion regime.

The propagation constant of LPmn-like mode of HC-ARF can be represented using
a capillary model [21]:

$\begin{split}\beta_{mn}(\omega)=\sqrt{\frac{\omega^{2}n_{\text{gas}}^{2}(\omega,p)}{c^{2}}-\frac{U_{mn}^{2}}{R_{\text{eff}}^{2}}},\end{split}$
(1)

where $\omega$ is the angular frequency, $c$ is the velocity of light in
vacuum, $n_{\text{gas}}(\omega,p)$ is the frequency and pressure dependent
refractive index of the filling gas calculated using [22], $U_{mn}$ is the
$n$th zero of the $m$th-order Bessel function of the first kind (LP01-like
mode: $U_{01}=2.450$ and LP02-like mode: $U_{02}=5.520$), $R_{\text{eff}}$ is
the effective core radius according to [20]. The group velocity dispersion
(GVD) of a 40 $\mu$m HC-ARF under 10 bar Ar was calculated using the capillary
model which has been extensively used to study the ultrafast nonlinear
dynamics in gas-filled fiber systems [23, 24, 25, 26]. In comparison, the GVD
was also calculated using FE modeling and it is seen from Fig. 1(a) that both
models agrees very well. The only difference between the two models is that FE
modeling can track the resonance bands which are determined by the fiber wall
thickness. The zero-dispersion wavelength of LP01 and LP02-like modes are 712
nm and 481 nm respectively. At the pump wavelength, the calculated GVD of LP01
and LP02-like modes are –4.95 fs2/cm and –32.91 fs2/cm respectively. The phase
mismatch ($\Delta\beta$) between the soliton and dispersive wave (DW) of LP01
and LP02-like modes are shown in Fig. 1(b). The phase mismatch was calculated
according to [10] neglecting the ionization effect. It can be seen from Fig.
1(b) that the DW of a pure LP02-like mode is blue shifted compared to the
LP01-like mode since the zero-dispersion wavelength of LP02-like mode resides
in the blue side.

##  III Pulse propagation equation

The optical pulse propagation was studied using a unidirectional pulse
propagation equation which includes free-electron effects but without
considering polarization and coupling between the different modes can be
expressed as [23, 24, 25]:

$\begin{split}\partial_{z}E(z,\omega)=i\beta_{mn}(\omega-\frac{\omega}{v_{g}})E(z,\omega)+i\frac{\omega^{2}}{\mu_{0}}\mathcal{F}\bigg{\\{}{\epsilon_{0}\chi^{(3)}E(z,t)^{3}}\bigg{\\}}\\\
-\frac{\omega\epsilon_{0}}{2\beta(\omega)}\mathcal{F}\bigg{\\{}\partial_{t}\rho(z,t)\frac{I_{\text{p}}}{E(z,t)}+\frac{e^{2}}{m_{e}}\int_{-\infty}^{t}\rho(z,t^{\prime})E(z,t^{\prime})\bigg{\\}},\end{split}$
(2)

where $z$ is the propagation direction, $t$ is the time in the reference frame
moving with the pump group velocity $v_{g}$, $E(z,\omega)$ is the electric
field in the frequency domain, $\beta_{mn}(\omega)$ is the propagation
constant, $\epsilon_{0}$ and $\mu_{0}$ are the permitivity and permeability of
free space respectively, $\chi^{(3)}$ is the third order susceptibility,
$\rho$ is the time varying free electron (plasma) density, $I_{\text{p}}$ is
the first ionization energy, $e$ and $m_{e}$ are the charge and mass of
electron respectively, and $\mathcal{F}$ denotes the Fourier transform. The
Raman contribution of silica was neglected due to the very low light–glass
overlap ($<<$1%) and we assume nonradial dependence of plasma. A quasi-static
tunneling based on Ammosov, Delone, and Krainov (ADK) model was used to
calculate the plasma density [27].

Figure 2: Numerically simulated spectral (left) and temporal (right) evolution
for a 40 $\mu$m core HC-ARF under 10 bar of Ar, pule energy of 7 $\mu$J, pulse
duration of 30 fs, and 1030 nm pump wavelength. Spectral and temporal
evolution of LP01-like mode with ionization (top row), LP02-like mode with
ionization (middle row), LP02-like mode without ionization (bottom row). The
fiber has a wall thickness of 300 nm, gap separation of 2 $\mu$m, and nested
tube ratio of 0.5. BSF: blue-shifted soliton, THG: third-harmonic generation.
The simulations were performed using modified capillary model [20]. The PSD
was calculated using:
$\text{PSD}=\frac{c}{\lambda^{2}}|E(z,\lambda)|^{2}f_{\text{rep}}$, where
$f_{\text{rep}}$ is the laser repetition rate.

##  IV Numerical results and discussions

The spectral and temporal evolution of LP01 and LP02-like mode in a 10 cm long
fiber filled with 10 bar Ar, pumped at 1030 nm with 30 fs pulse and pulse
energy of 7 $\mu$J is shown in Fig. 2. We begin our analyses by considering
the excitation of LP01-like mode. For fundamental LP01-like mode, the pulse
undergoes soliton self-compression down to $\sim$3.5 fs with peak intensity
$>$65 TW/cm2 after propagating $\sim$5.5 cm due to the interplay between self-
phase modulation and anomalous dispersion. At the maximum compression point, a
DW is emitted at $\sim$270 nm in the normal dispersion regime and a
supercontinuum generation (SC) spanning 270–1800 nm. However, the peak
intensity of the compressed pulse was not enough to ionize the gas since the
plasma density at the maximum temporal compression point was found around 1014
cm-3 (see Fig. 4(b)). Therefore, a similar spectral and temporal evolution can
be seen when the ionization effect is turned-off which is not shown in Fig. 2.

For LP02-like mode, the pulse undergoes a strong soliton self-compression down
to $\sim$1.5 fs (less than a single cycle) with peak intensity $>$220 TW/cm2
at an early stage of $\sim$3.6 cm, and a strong DW is emitted at 200 nm. Such
a high intense pulse is enough to ionize the gas and form a plasma and a blue-
shifted soliton (BSF) appears in the spectral profile. Unlike the SC of
LP01-like mode, the SC of LP02-like mode is narrower at the longer wavelengths
that can be seen after the temporal compression which is due to the high
ionization loss [28]. The spectral and temporal evolution of LP02-like mode
without ionization is shown in Fig. 2 (bottom row). When the ionization effect
was not considered, DW is not generated in the UV regime since the energy of
the compressed pulse is not sufficient to phase match to the DW. It turns out
that the ionization effect is responsible for the generation of DW for
LP02-like mode and plays an important role of DW generation.

To confirm the DW emission of LP02-like mode at 200 nm, the phase mismatch
curve ($\Delta\beta$) between the soliton and the DW including the ionization
effect is shown in Fig. 3(a). The phase mismatch can be expressed as [26]:

$\begin{split}\Delta\beta=\beta(\omega)-\bigg{(}\beta_{0}+\frac{1}{v_{g}}[\omega-\omega_{0}]+\gamma
P_{p}\frac{\omega}{\omega_{0}}-\frac{\omega_{0}}{2n_{0}c}\frac{\rho}{\rho_{cr}}\frac{\omega_{0}}{\omega}\bigg{)},\end{split}$
(3)

where $\beta_{0}$ is the propagation constant at the soliton centre frequency
$\omega_{0}$, $\gamma$ is the nonlinear fiber parameter at the pump wavelength
[10], $P_{p}$ is the soliton peak power of the compressed pulse, $n_{0}$ is
the linear refractive index of the medium,
$\rho_{cr}\equiv\epsilon_{0}m_{e}\frac{\omega_{0}^{2}}{e^{2}}$ is the critical
plasma density [29]. It can be seen from Fig. 3(a) that the phase matching
occurs at 200 nm which agrees well with the DW wave emission seen from the
power spectral density (PSD) curve of Fig. 3(b). It should be noted that when
the ionization effect is considered the phase matching condition occurred at
longer wavelengths since the pump soliton shifts toward the blue side [28]
(see Fig. 2 (middle row)).

Figure 3: (a) Phase mismatch ($\Delta\beta$) between a soliton and DW for
LP02-like mode according to [26]. The 40 $\mu$m HC-ARF was filled with 10 bar
Ar, pumped at 1030 nm with a pulse energy of 7 $\mu$J and 30 fs pulse
duration. The ionization was included to calculate the phase mismatch. The
plasma density of $>$ 1018 cm-3 is calculated at maximum temporal compression.
(b) The normalized PSD with UV dispersive wave emission. Figure 4: Efficiency
(a) and average plasma density along the fiber propagation distance for LP01
(blue) and LP02 (red)-like mode. The maximum efficiency of LP01 is $>$35%
whereas for LP02-like mode is $\sim$15 %. The plasma density was calculated
using [24, 27].

The DW efficiency and plasma density of LP01 and LP02-like modes are shown in
Fig. 4(a-b). The DW efficiency of LP02-like mode is $>$35% whereas the
efficiency of LP01-like mode is around 15%. The dramatic enhancement of the DW
emission for LP02-like mode is due to the strong shock effect and ionization-
induced blue-shift[28]. The plasma density of LP02-like mode is above $>$1018
cm-3 at the maximum temporal compression point which is enough to ionize the
gas. The free electron generation decays drastically after the temporal
compression as it propagates through the fiber due to the high ionization
loss. However, at the temporal compression point, the plasma density of
LP01-like mode is only 1014 cm-3.

Figure 5:  Calculated spectrogram of LP02-like mode for a 40 $\mu$m core HC-
ARF under 10 bar of Ar, pule energy 7 $\mu$J, pulse duration 30 fs, and 1030
nm pump wavelength at selected distances. The ionization is included in the
simulation. The spectrogram was calculated using a 10 fs Gaussian gate pulse.
The third harmonic of the pump pulse is evident at 343.33 nm.

To get more physical insights on the underlying mechanism of DW emission for
the LP02-like mode, the spectrograms are plotted in Fig. 5 using the cross
correlation frequency-resolved optical gating for different selected fiber
lengths. A 10 fs Gaussian pulse were used to plot these spectrograms. The
location of DW, blue-shifted soliton (BSF), third-harmonic generation (THG)
are shown. At the propagation distance of $z=3.6$ cm, the pulse undergoes a
maximum temporal compression and the spectrum extends towards the blue due to
the plasma formation and a DW is emitted in the normal dispersion regime at
around 200 nm. During the propagation, the DWs broadens linearly in time which
can be seen for $z=$ 5 cm and $z=$10 cm.

##  V Conclusion

In conclusion, a new approach to enhance the efficiency of a DW generated in
the UV regime by exciting LP02-like mode in Ar-filled HC-ARF has been
demonstrated. The numerical modelings are based on the experimentally feasible
fiber and pulse parameters that can predict DW generation at 200 nm followed
by SC spanning 200–1500 nm. The formation of extreme shock effect and plasma
induced blue-shifted soliton leads to an efficiency of $>$35%. The numerical
modeling predicts that it requires only 3.6 cm of fiber to generate the DW.
The DW can be further blue-shifted if higher LP0n are excited but requires
more pump energy to phase match the soliton and DW. The results presented in
this work may be valuable towards the development of compact, bright, and
highly efficient UV light source.

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