# Factors Hindering the Adoption of DevOps in the Saudi Software Industry

Mamdouh Alenezi
College of Computer and Information Sciences
Prince Sultan University
Riyadh, Saudi Arabia
<EMAIL_ADDRESS>
###### Abstract

DevOps has gained high importance in the global software industry due to the
ease of software development, testing and deployment it provides. However, the
Saudi software industry has not been able to adopt DevOps at a great pace due
to various factors. This study, thus, aimed to examine different factors that
hindered the adoption of DevOps in the Saudi software industry. Also,
recommendations are provided at the end for Saudi Arabia to enhance the
adoption of DevOps in its software industry. To accomplish the aims, this
study used a literature review and interviews to gather data and examine it to
produce the findings. The findings of the study highlight lack of support from
organizational management and lack of laws as the major factors for the
adoption of DevOps in the Saudi software industry.

_K_ eywords Software Engineering $\cdot$ DevOps $\cdot$ Adoption

##  1 Introduction

The primary aim of the study is to evaluate the factors that hinder the
adoption of DevOps in the Saudi software industry [1]. The gap has been
noticed by the software engineers that there is a lack of collaboration
between operations and development teams in Saudi Arabia’s software industry.
The idea of collaboration has been considered an important aspect, and this
creates cooperation between the two teams. The new process models called
DevOps have been considered to discuss collaboration [1]. Presently, IT
organizations are not adopting DevOps as the added value or competitive gain,
and thus, the companies are surviving a lot if they do not adopt it. The idea
of the new process model aims to attain a fast and high-quality release of the
software. DevOps is among the new software processes that help in the
extension of the agility practices within the collaborative culture to empower
the process of software delivery and development [2].

The background reveals that the approach of DevOps is much concerned with
improving the collaboration between the operation teams and development, which
illustrates a new shift in the understanding of the way to build up the
software system [3]. It has also been denoted that the operational and
development team have different goals in any project and the goal of the
developer is to release the new aspect of the software. Thus, the goal of the
operator is to keep the software stable and available. It is important to
maintain the goals, and the coordination between the operational and
development teams is considered vital in the project. The idea of DevOps helps
to change the workflow of the traditional software development to streamline
and accelerate the software delivery, which means to change the organizational
culture in the delivery of software, not only the flow of process [4].

The idea to adopt DevOps might spur the company to introduce new process
changes, technological changes and personnel changes. The idea of software
delivery has been treated as a continuous evolving procedure to obtain the
expectations of users. DevOps makes it possible by bringing the operational
and development teams together to facilitate the continuous integration,
delivery and automation in the process that would result in reducing the time
to market and would also result in enhancing the experience of customers and
making the work quality-oriented [5]. The research also depicts that there are
more than 50% of the companies across the industries, including manufacturing,
banks and healthcare, are already involved in DevOps and have made it their
digital strategy. The software DevOps has been prominent in academic and
practical fields, but still, there is a lack of literature and academic
publications regarding the empirical investigation of DevOps [6].

The main motivation to evaluate the factors hindering the adoption of DevOps
is to explore why organizations are still not able to adopt DevOps. The
implementation of DevOps could increase the competitive advantage of the
companies but go through the factors including lack of strategic direction,
lack of knowledge, resistance to change, and silo mentality could help to
understand why there is a lack of adoption of DevOps even in the large
organizations. For this, the study focuses on this research question: "What
are the factors hindering the adoption of DevOps in the Saudi Software
Industry?"

In general, the following is needed to address most of the challenges of
adopting DevOps. Software engineers need to know how to design and restructure
their systems to integrate continuous delivery. Managers should focus on
knowing DevOps and how it can be introduced and assessed as added value to the
organization. Both managers and engineers should discuss and collaborate in
choosing right level of automation toolset [7]. There are few Saudi IT
companies that have adopted DevOps, but still, there are many who are facing
hindrances to adopting it [8]. Thus, the purpose of this study is to study the
factors that are creating hindrances for Saudi IT companies in the adoption of
DevOps.

###  1.1 Google Trend (Saudi Arabia (DevOps))

The google trend depicts the growth of DevOps in Saudi Software Industry from
2021 to 2022. The graph shows tremendous growth from 2021 to 2022, but there
are fluctuations that have been making the graph unstable due to the
hindrances that are making the companies difficult to adopt DevOps, especially
in Eastern and Makkah Province.

Figure 1: Google Trends [9]

###  1.2 LinkedIn Insights (Saudi Arabia (DevOps)

The LinkedIn insight shows that the companies in Saudi Arabia have been
exploring DevOps engineers to implement it efficiently in their organization.

Figure 2: LinkedIn Insights [10]

##  2 Literature Review

###  2.1 DevOps History

Prior to the development of DevOps (Development and Operations) by Patrick
Debois and Andrew Clay in 2008, the Agile methodology and waterfall model were
used for the development of software [11]. The former deals with a linear
approach of process execution with no option for testing errors in between the
levels of processes, while the latter basis itself on rapid releases in new
technologies, the collaboration of emerging processes and the introduction of
improved customer feedback with linear process execution [12]. It releases the
final product after the development of its constituent processes through the
collaboration of stakeholders with room for continuous development in case of
negative customer feedback. Agile did not focus on continuous development and
integration of software with no room for monitoring of products (software) and
customer feedback, and neither did it intend to work for the cultural aspect
of organizations. With the introduction of DevOps and its development tools,
agile techniques get integration with the elimination of their drawbacks and
introduce a diversified culture in operations and development of software by
integrating the efforts of all the team members ranging from developers in the
deployment of the software, engineers in the testing of the software and
administrators in documenting the products [5].

###  2.2 DevOps Building Blocks

DevOps integrate the cultural philosophies of an organization by merging all
the departments in a single stream with the introduction of advanced practices
based on some building blocks. It integrates the codes of different developers
and stores them in a single repository for fellow developers to change and
review in case of error [13]. DevOps focuses on the correct metric and sets of
measurements for the processes in the development and operations in the
creation of software with continuous deliveries of tests and workings
alongside customer feedback. Its iterative approach, tested from regular
feedback in between the execution of processes, allow the formation of value-
added products while eliminating practices that compromise quality and those
rejected by the customers [1]. This eliminates the gap between the developers
and operation engineers through robust delivery and integration of service and
the discard of time-consuming development processes. There are some processes
in the system employed for the development of the software that needs regular
check and balance, so in order to investigate the performance hindrance
components, DevOps deploy a monitoring system in parallel with the development
of the software to ensure optimized system performance [14]. It also allows
robust cycle-wise deployment and multiple scaling of the resources of the
product that reduces time and cost by allowing regular change and updates in
the system.

###  2.3 DevOps Principles and Practices

DevOps uses short feedback customer-related action loops that allow a
continuous meeting of the standards proclaimed by the customers [15]. DevOps
allows better communication and understanding between the employees in order
to increase the productivity of the system as a whole. The workers are cross-
skilled that can both develop and execute the tested codes. The workers
understand the expertise, needs and functions of each and every other employee
[6]. It works in a culturally unified system where each and every member of
all the departments know the actual processes going on during the development
and operations of the products with a vertically integrated environment of
full accountability for the performance and productivity of the system [16,
17]. The developers, coders, engineers and administrators specialize in their
respective skill sets and attributes and contribute towards a balanced
environment with expertise in all domains. DevOps always allow room for
continuous development in technologies, customer demands and organizational
culture that work for cost optimization, time reduction and improved service
of products. It also advocates the automation of industrial processes and
information technologies [18].

Nowadays, users and customers assume that modern software applications should
accommodate their frequently changing requirements and needs [19]. To cope
with these frequent changes, it is crucial for software companies to make
frequents releases and deployments. TO achieve that, your environment has to
be disciplined and transparent; otherwise, it may lead to major issues and
failures including customer dissatisfaction. DevOps tries to close this gap
and its guiding principles can be summed up as follows: culture, measurement,
collaboration, and automation [7]. Gupta et al. [19] pinpointed four main
factors that affect DevOps implementation namely, source control, automation,
cohesive teams and continuous delivery.

With regards to DevOps cultural movement, there are usually four defining
characteristics: open communication, incentive and responsibility alignment,
respect, and trust. However, these cultural aspects cannot be the defining
characteristics of DevOps but rather enablers to support software engineering
process capabilities [20].

###  2.4 DevOps Practices Usage

DevOps works for the development of high-end objectives, unlike traditional
methods that cater to small-scale projects. DevOps involves continuous
development in the automation and operations of the formation of software with
the use of automation tools that allow bug detection and elimination from the
codes [21]. It works in a loop system where developers build code that is
compiled by the team for testing by the operations team, which checks for the
credibility of the code. It continuously plans and tests codes before
dispatching them to production. The components of codes ready for production
are rapidly identified and then sent for tracking of the usable parts of the
codes under continuous integration with constant feedback between development
and testing [22]. These tested codes are continuously being delivered to
production. In case a new part of code needs to be incorporated in between the
codes, DevOps uses a continuous deployment tool across different departments
before providing codes for continuous monitoring that checks the code and
system sending it. Further, the continuous monitoring system detects the
problems in the processes while the codes are being dispatched for production.
Thus, inaccuracies are removed, and efficiency and productivity are enhanced.
The software is then released with an infrastructure code that allows
configurations and changes during operations. These codes allow the automatic
configuration of the software with respect to the environment in which the
software is to be operated [22].

DevOps is primarily used to enhance integration processes and allow fast
solutions to problems resulting during production. With the advanced practices
and unique principles of DevOps in the development and operation of software,
widespread areas imply its applications [23]. DevOps shows significant results
in financial trading companies where it automates the testing, building and
development of the production processes with 45 second deployment time. It
significantly reduces the time consumption of the processes with good customer
feedback. Car production uses precise metrics and measurements of the scale of
products. DevOps allows remedies for error correction and provides increased
precision in error selection through its testing, monitoring and integration
practices [1]. Similarly, it shows a great importance in bug reduction while
dealing with codes due to its robust code deployment in between operations. In
networking industries, DevOps allows rapid installations of security patches
for the protection of firewalls by the rapid introduction of solutions for
bugs and viruses [24].

##  3 Research Methodology

This paper uses two main techniques to examine the factors hindering the
adoption of DevOps in the Saudi software industry. A literature review is
conducted in this study to examine the technological, organizational, and
environmental aspects that hinder the adoption of DevOps in the Saudi software
industry. Semi-structured interviews were chosen as the main data collection
method to get more insights about the current status of the Saudi software
industry. The findings are presented in the following section.

Interviews have been selected to gather rich information about different
experiences and perceptions of a small number of respondents [25, 26]. In
qualitative research, interviews are considered the most effective data
collection method [26]. Different questions were devised to collect the
respondents’ opinions about DevOps adoptions. The questions are Open-ended
questions to give the freedom to the respondents to express themselves.

DevOps practitioners from the operational and development teams of various
Saudi software companies that implement the DevOps practices as a prerequisite
are chosen as the participants of this research. These practitioners may
function as different roles during different phases of development as a part
of their work.

The following guidelines have been followed while conducting the interviews
[27]:

  * •

Clear interview purpose and how the data will be used.

  * •

Introductory questions about background and role.

  * •

Avoid personal/sensitive matters.

  * •

Summarize the conclusions at the end of the interview.

  * •

Record the interviews to transcribe them into text.

  * •

Pre-schedule these interviews.

The following table 1 shows the interview questions used in this study. We
tried to use a small set of questions in very clear English language to
clarify and ease the process of collecting the data.

Table 1: Questions asked during the interviews # | Interview Question
---|---
1 | Could you please state your background - your name, role, and work experience?
2 | What does DevOps mean to you and your organization?
3 | What are the challenges of adopting DevOps practices?
4 | How do you go about solving those challenges?
5 | Which of those challenges are you able to successfully solve?
6 | What kind of support is needed to solve these challenges?
7 | Any other comments you would like to add?

##  4 Results and Discussion

This section discusses the impact of social, organizational, technological and
environmental factors on the implementation of DevOps in an organization.
Also, the findings are discussed based on their impact on the Saudi software
industry.

###  4.1 Interviews Details

This section discusses the results of the interviews. A total of 12
participants working in different companies were selected.Table 2 gives a
description of these participants.

Table 2: Description of semi-structured interviewees # | Role | Experience | Company Size
---|---|---|---
1 | DevOps Engineer | 1-3 years | 200 employees
2 | DevOps Architect | 3-5 years | 300 employees
3 | DevOps Engineer | 3-5 years | 160 employees
4 | Platform Engineer | 1-3 years | 500 employees
5 | DevOps Engineer | 3-5 years | 400 employees
6 | CI/CD Engineer | 3-5 years | 120 employees
7 | Software Engineer | 1-3 years | 400 employees
8 | Platform Engineer | 3-5 years | 280 employees
9 | Software Engineer | 3-5 years | 320 employees
10 | DevOps Engineer | 1-3 years | 640 employees
11 | DevOps Architect | 3-5 years | 480 employees
12 | DevOps Engineer | 1-3 years | 240 employees

###  4.2 Technological aspect

The technological strength of an organization defines the potential for
introducing new technologies in an attempt to integrate them with the already
established technologies of an organization. Large organizations, in contrast
to smaller organizations, possess readily available technologies that account
for the adaptation of DevOps in the software industry. The implementation of
DevOps can significantly reduce costs for businesses in Saudi Arabia and has a
significant impact on implementing DevOps in the software industry [21].
Technological use of tools and processes accounts for a positive impact on
DevOps adaptation. With the implementation of new technologies and the
perceived benefits it reaps for the organization in terms of development and
operations, businesses in Saudi Arabia significantly invest in adopting DevOps
technologies due to highly anticipated positive outcomes. The integration of
new operational services and technologies with the previous ones positively
impacts the implementation of DevOps in Saudi Arabia [22].

Security complications and concerns regarding its credibility promote threats
to Saudi Arabia’s software companies. Therefore, a strong and flawless
security protocol with ample assurance from the security departments provides
great motivation for officials from software companies in Saudi Arabia to
invest in the introduction of DevOps. New technologies require severe testing,
experimentation, and trials of the new processes and operations before putting
them into real-life action. However, this factor has negligible importance for
the adaptation of DevOps operations in Saudi Arabia’s software companies [28].

###  4.3 Organizational aspect

Several organizational factors, like interest and support from top management
levels of the organization, the scale and size of the company, knowledge of
the processes and technologies implemented, and the eagerness of the
management in the implementation of new processes, contribute towards the
adaptation of DevOps in the software industry of Saudi Arabia [23]. Top
officials and management in Saudi Arabia do not believe in the credibility and
benefits of adopting DevOps technologies. The implementation of new
technologies and advanced processes requires a large domain of operations and
a considerably large size of the organization where the practices can be amply
tested, experimented with and developed prior to their execution [12]. Saudi
Arabia intends to adopt DevOps in large software organizations, and it already
shows a greater induction of DevOps in big Saudi software industries than in
smaller industries. It should not be neglected that the adaptation of new
technologies is facile in smaller organizations, but when assessing the
complexity of DevOps technologies, large organizations are preferred [24].

###  4.4 Environmental aspect

Saudi Arabia experiences tough competition from software organizations,
elevated pressures through government policies and laws, and a lack of trusted
vendors of software products [29]. The technological advancements on national
levels in Saudi Arabia are underdeveloped, with no local data centers and
software houses. The competition between the software companies significantly
defines the promotion and adaption of DevOps in Saudi Arabia, as Saudi Arabia
already has few advancements in software industries, and the already
established software companies provide tough competition in the development of
operations to a considerable extent. In the previous research, the role of
governmental legislation proved to be a hindrance in the development of the
principles of DevOps in Saudi Arabia’s industries [30]. In order to run
software companies effectively with greater productivity, companies need to
develop good relations with vendors. Saudi Arabia has a lack of vendor trust
owing to a lack of data centers and developed technologies. A good vendor
reputation accounts for the adaptation of DevOps principles in software
companies. Saudi Arabia lacks a developed infrastructure of technologies with
lower connection speeds owing to strict governmental policies and data
transfer complications. This discourages software company owners from adapting
to DevOps in their organizations as DevOps requires relatively high connection
speeds with advanced technologies in the operations and development of
software. However, research does not promote this fact as a hindrance to the
development of DevOps in Saudi Arabia’s software industry [31]. The effective
development of DevOps in the software industry requires highly established
data centers for the flow of data and information between different
departments of the software industry and also with foreign data centers and
companies. Saudi Arabia imposes strict policies regarding the transfer of data
in and out of companies from their country. This considerably hinders the
introduction of new technologies and DevOps principles. It is seen that local
data centers provide a boost for new technologies and methodologies like
DevOps [3].

DevOps is based on a strong, interlinked cultural environment in the software
industry. It focuses on establishing a rich diversity of employees. Saudi
Arabia imposes and exercises strict social values and culture. Assessing this
factor, Saudi Arabia provides a hindrance to the adaptation of DevOps in the
operations and processes of software companies. The growth of these companies
is affected as a less diverse work environment culture contributes to a lack
of communication between different departments within a company [32].

##  5 Recommendations

Some of the recommendations for promoting the adaptation of DevOps in the
Saudi software industry are as follows:

In a software company, there is significant automation in the processes of the
DevOps method, ranging from development to testing and successful
implementation of codes in the software industry [30]. Still, there is room
for introducing more automation tools for testing new frameworks for the
assessment of the correct framework for every specific industry in terms of
their types and domains of operations [31]. Countries like Saudi Arabia
sincerely need to introduce new laws and regulations regarding the
introduction of new technologies like DevOps. They need to allow for the
diversification of cultures in their software companies along with revised
legislation to develop local software houses and data centers for an efficient
flow of data. The development of DevOps needs proper documentation of its
processes and technologies for industrialists, company owners, and employees
in order to promote their interest in the development of emerging technologies
and to improve communication levels among cross-department employees [3].

In addition to this, the problems faced by Saudi Arabia regarding the
implementation of DevOps also require a collaborative environment with
enthusiasm from the upper management. There is less research that talks about
the role of leadership types [18]. Therefore, this domain needs research to
develop leadership types in accordance with the scope, size, and type of
industries. Also, most of the researchers provide analysis of a specific
target department of an industry. The domain of analysis needs to be enlarged,
incorporating different departments and levels of hierarchy. Researchers also
need to provide multiple solutions for each problem so that industrial
practitioners adopt different strategies and methods for optimizing their
business processes. Training sessions for developers, engineers, staff, and
managers provide an effective understanding of the proper implementation of
DevOps in software industry processes [22]. There is no proper management of
data in many industries that require proper protection and security of
information [33].

##  6 Conclusion

Continuous and productive development in the software industry needs
innovation and the introduction of new, improved technologies. DevOps is the
latest emerging technological method that reaps great results for the
optimization of industrial processes. This paper highlights all the challenges
modern industries face while coping with increased modernization in software
industries. This research paper provides a comprehensive analysis of the
factors that promote and degrade the adaptation of emerging technologies and
methods of industrial optimization and automation like DevOps and highlights
the key factors that specifically hinder the adaptation of DevOps in the
software industries of Saudi Arabia. This paper incorporates literature review
and interviews. It explains the technological, social, organizational, and
environmental factors that affect the implementation and adaptation of DevOps
principles in Saudi Arabia. The paper covers extensive analysis of DevOps
operations, including their processes, tools, and associated technologies. It
especially highlights the key areas and domains for the Saudi Arabian software
industry where improvement is anticipated in the future regarding the
introduction of new industrial technologies and processes. It also highlights
and recommends the key areas that require further research to come up with new
processes and experiments.

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# New $\mu$ Forces From $\nu_{\mu}$ Sources

Cari Cesarotti  0000-0001-5128-7919<EMAIL_ADDRESS>Center for Theoretical
Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Yonatan Kahn  0000-0002-9379-1838<EMAIL_ADDRESS>Illinois Center for
Advanced Study of the Universe and Department of Physics, University of
Illinois Urbana-Champaign, Urbana, IL 61801  Gordan Krnjaic
0000-0001-7420-9577<EMAIL_ADDRESS>Theoretical Physics Department, Fermi
National Accelerator Laboratory, Batavia, Illinois 60510  Department of
Astronomy and Astrophysics, University of Chicago, Chicago, IL 60637  Kavli
Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637
Duncan Rocha  0000-0001-7420-9577<EMAIL_ADDRESS>Kavli Institute for
Cosmological Physics, University of Chicago, Chicago, IL 60637  Joshua Spitz
0000-0002-6288-7028<EMAIL_ADDRESS>Department of Physics, University of
Michigan, Ann Arbor, MI 48109

###### Abstract

Accelerator-based experiments reliant on charged pion and kaon decays to
produce muon-neutrino beams also deliver an associated powerful flux of muons.
Therefore, these experiments can additionally be sensitive to light new
particles that preferentially couple to muons and decay to visible final
states on macroscopic length scales. Such particles are produced through rare
3-body meson decays in the decay pipe or via muon scattering in the beam dump,
and decay in a downstream detector. To demonstrate the potential of this
search strategy, we recast existing MiniBooNE and MicroBooNE studies of
neutral pion production in neutrino-induced neutral-current scattering
($\nu_{\mu}N\to\nu_{\mu}N\pi^{0},~{}\pi^{0}\rightarrow\gamma\gamma$) to place
new leading limits on light ($<2m_{\mu}$) muon-philic scalar particles that
decay to diphotons through loops of virtual muons. Our results exclude scalars
of mass between 10 and 60 MeV in which this scenario resolves the muon $g-2$
anomaly. We also make projections for the sensitivity of SBND to these models
and provide a road map for future neutrino experiments to perform dedicated
searches for muon-philic forces.

††preprint: FERMILAB-PUB-23-539-T††preprint: MIT-CTP/5649

##  I Introduction

Light, weakly-coupled particles arise in many well-motivated extensions of the
Standard Model (SM) and may shed light on several open questions in particle
physics, including the particle nature of dark matter [1], the hierarchy
problem [2], and the strong CP problem [3]. Motivated by these fundamental
questions, there is a global program of accelerator searches to discover these
new particles (see Ref. [4] for a review). However, most searches involve
beams of protons or electrons, which are naively limited in their sensitivity
to particles that couple preferentially to heavy flavor.

Figure 1: Schematic cartoon of our MiniBooNE and MicroBooNE signal processes.
Top: the 8 GeV proton beam impinges on a fixed Be target and produces mesons
including charged kaons, whose decays yield a flux of muons and associated
scalars $S$ through $\pi^{\pm},K^{\pm}\to\mu^{\pm}\nu_{\mu}S$ decays. Bottom:
$S$ may also be created via a spray of pions/kaons whose decays yield a
secondary muon beam in the decay pipe. The muons then interact with the beam
dump, where they produce long-lived muon-philic scalar particles $S$ through
bremsstrahlung-like processes. Note that the kaon production mode is
independent of the beam dump, while the muon bremsstrahlung mode requires
scattering in the beam dump. In both cases, for $m_{S}<2m_{\mu}$, the scalars
eventually decay to diphotons in the downstream detector. For details of the
experimental setup and detector performance, see Ref. [5].

Over the past decade there have been several proposals for dedicated muon-beam
experiments. Studying muons directly is of interest as many experimental
milestones remain unexplored or unexplained, such as muon-philic forces [6, 7,
8], dark matter [1, 9, 10], and the persistent $g-2$ anomaly [11]. If the new
muon-philic particles are invisible on accelerator length scales, the proposed
NA64$\mu$ [12, 13] and $M^{3}$ [9] fixed-target experiments can leverage
missing energy and momentum to probe key targets related to these questions.
Conversely, if the new states decay visibly as long-lived particles on
accelerator scales, they can be probed with new beam-dump experiments [14, 15,
16]. It has also been shown that a future muon collider program can
comprehensively expand the reach for a variety of decay channels and event
topologies, particularly for heavier states [17].

However, we do not have to wait for a dedicated muon beam facility to study
such interactions. Since relativistic proton scattering can efficiently
produce mesons which decay to secondary muons, existing data can be used to
probe muon-philic forces. These muons can source new particle production
directly through radiative meson decays or through secondary muon interactions
in macroscopic material. For example, kaon decays at NA62 can source new
forces as final-state radiation from muon lines [18], and the muons produced
through the Drell-Yan process at ATLAS can exhibit kinked tracks if they emit
new invisible particles by scattering off detector constituents [19].
Alternatively, secondary muons produced in fixed-target proton collisions at
SpinQuest/DarkQuest can interact with the target to yield new states that
decay visibly and can be constrained using the downstream tracker [20].

In this Letter, we show that neutrino sources are powerful probes of new muon-
philic particles. As a proof of concept, we place new limits on long-lived
muon-philic particles using existing MiniBooNE and MicroBooNE searches for
neutral pion production in neutral current neutrino scattering, $\nu N\to\nu
N\pi^{0}$ [21, 22]. Based on a conservative analysis of these data, we improve
existing constraints on light scalars that couple exclusively to the muon and
decay to diphotons at loop level. Notably, as shown in Fig. 6, our limits
already exclude almost an order of magnitude in scalar mass over which this
scenario could resolve the muon $g-2$ anomaly, parameter space which was
previously targeted by a proposed dedicated muon beam-dump experiment [14].

##  II Model Overview

We consider a muon-philic scalar $S$, a SM singlet of mass $m_{S}$ with the
Yukawa interaction

$\displaystyle\vspace{-0.25cm}\mathscr{L}_{\rm int}\supset
yS\bar{\mu}\mu~{},\vspace{-0.2cm}$ (1)

which we have written in four-component Dirac fermion notation. This
interaction can arise from a gauge-invariant dimension-5 operator

$\displaystyle\mathscr{L}_{\rm
eff}\supset\left(\frac{y}{v}\right)SH^{\dagger}L_{2}\mu^{c}+{\rm h.c.}$ (2)

where $H$ is the SM Higgs doublet, $v=246$ GeV is its vacuum expectation
value, $L_{2}$ is the second generation lepton $SU(2)_{L}$ doublet, and
$\mu^{c}$ is the $SU(2)_{L}$ singlet muon field. This non-renormalizable
interaction may be UV-completed with a heavy vector-like fourth generation of
leptons, which mixes with the muon and is integrated out in the low-energy
effective theory [23, 24, 25].

Figure 2:  Left: Feynman diagram for scalar production from $K,\pi\to\mu\nu S$
decays. Middle: Scalar production via $\mu$-$N$ scattering in the beam dump.
Right: Scalar decay through a muon loop using only the coupling in Eq. (1).
Figure 3: Heatmaps (arbitrary units) of the processes in the beam dump that
produce muon-philic scalars, for $r_{\perp}<0.9$ m, where $r_{\perp}$ is the
cylindrical radius in the $x-y$ plane. This displays the scalar production
inside the decay pipe, however the analysis considers production events that
occur outside the pipe as well. The top (middle) diagram shows the vertices
where the $\pi^{\pm}$ ($K^{\pm}$) decays, which may contain scalars in their
decay products. The lower diagram shows the spatial distribution of scalar
emission from muons scattering in the beam dump, specifically for $m_{S}=100$
MeV, although this distribution does not vary significantly over the scalar
mass. The plot has several features: the target can be seen on the far left,
with the electromagnet adjacent, and the beam dump is visible on the right.

If the operator in Eq. (1) is the scalar’s only coupling to SM fermions, then
for $m_{S}<2m_{\mu}$, $S$ will decay to diphotons through muon loops. The
width for this process is [14]

$\displaystyle\Gamma_{S}=\frac{\alpha^{2}y^{2}m_{S}^{3}}{64\pi^{3}m_{\mu}^{2}}x^{2}\left|1+(1-x)f(x)\right|^{2},$
(3)

where $x\equiv 4m_{\mu}^{2}/m_{S}^{2}$ and $f(x)=\arcsin^{2}(x^{-1/2})$ for
$x>1$. Note that for nearly all viable parameter values in this low mass
range, $S$ is a long-lived particle with a decay length

$\displaystyle\frac{c\tau_{S}}{\gamma}\approx 300\,{\rm
m}\left(\frac{10^{-4}}{y}\right)^{2}\left(\frac{40\,\rm
MeV}{m_{S}}\right)^{3},$ (4)

where $\tau_{S}=1/\Gamma_{S}$ is the $S$ lifetime and $\gamma$ is the boost
factor. This estimate uses Eq. (3) in the $x\gg 1$ limit.

In our parameter space of interest (see Fig. 6), the Yukawa coupling in Eq.
(1) always satisfies $y\gtrsim 10^{-5}$, which is sufficient to bring $S$ into
chemical equilibrium with SM particles in the early universe. Therefore, in
order to avoid cosmological limits on extra light degrees of freedom during
Big Bang nucleosynthesis, we generically require $m_{S}\gtrsim$ few MeV [7,
26].

##  III Analysis

Our search concept leverages secondary muon production at MiniBooNE and
MicroBooNE following a sequence of steps, depicted schematically in Fig. 1
with relevant Feynman diagrams in Fig. 2:

  1. 1.

The 8 GeV proton beam from the Fermilab Booster Neutrino Beamline (BNB)
strikes the Be target, producing a forward shower of pions and kaons;

  2. 2.

The charged pions and kaons are focused down the beamline via an
electromagnet, called the horn, and then typically decay in flight in the
decay pipe;

  3. 3.

New scalar singlets $S$ can be produced either directly through radiative
3-body $\pi^{\pm},K^{\pm}\to\mu^{\pm}\nu_{\mu}S$ decays (Fig. 1, top), or
through $\mu N\to\mu NS$ scattering from the secondary interactions in the
beam dump (Fig. 1, bottom);

  4. 4.

The $S$ particles propagate on-shell and decay visibly to $\gamma\gamma$ in
the downstream detector.

To perform our numerical analysis, we utilize samples of pions, kaons, and
muons from $10^{7}$ protons-on-target (POT) created from a custom GEANT4 [27]
simulation of the BNB in neutrino mode. The detailed simulation includes all
relevant beamline elements – the target, horn electromagnet and magnetic
field, collimator, decay pipe, shielding, and beam dump – and is based on the
description in Refs. [5, 28]. The $10^{7}$ POT produce $\sim 10^{6}$ charged
kaons and $\sim 2\times 10^{7}$ muons (primarily via decays of pions produced
at the target).

Figure 4: Energy distribution of charged pions (dark green), charged kaons
(dark blue), and secondary muons (dark red) produced from proton-Be collisions
at 8 GeV. Also shown are energy distributions for scalars produced from pion
decays (light green), kaon decays (light blue) and from secondary muon
scattering in the beam dump (orange). The scalar distributions are normalized
to $y=1$ to enhance visibility on the plot, but in our analysis we explore the
region $y\in[10^{-5},10^{-2}]$. These curves were generated with a GEANT
simulation utilizing the setup described in Refs. [5, 28].  Figure 5: Example
signal distributions generated by scalar decays in the MiniBooNE and
MicroBooNE detectors. The data points are measured $\gamma\gamma$-like events,
and the background prediction arises primarily from neutrino-induced
$\pi^{0}\to\gamma\gamma$ events, and digitized from [21, 22]. The MiniBooNE
error bars include statistical and systematic uncertainties. The MicroBooNE
error bars are statistical only. These particular signal distributions
correspond to 20$\sigma$ (top panel) and 6$\sigma$ (bottom panel)
discrepancies with the data.

For the decay production channel, we generate a Monte Carlo (MC) sample of the
scalars produced in $K/\pi$ decays by sampling the available phase space of
the decays, and weighting each event by the squared matrix element. The
amplitude and branching ratio formulas are given in Ref. [18], and our
sampling method agrees with their reported $K\to\mu\nu S$ branching ratios.
The pion MC is generated using the same amplitude, with the general
substitution $K\to\pi$. The kinetic energy distribution of scalars produced
via these modes, for $m_{S}=24$ MeV, is shown in Fig. 4. The locations of the
decays are shown in Fig. 3 (top and middle panels).

For the scalars produced by muons scattering in the beam dump, we use the
FeynRules [29] Mathematica package to construct the Feynman rules for muon-
philic interactions in Eq. (1). This model is then used as input to the
CalcHEP [30] event generator to generate scalar emission $\mu N\to\mu NS$
cross sections (Fig. 2, center) and MC events. These events are then re-
weighted according to the electromagnetic form factor of the iron nucleus (see
Ref. [20] for a more detailed treatment). The probability of emitting a scalar
in a muon-nucleus scattering event, as a function of muon energy incident on
the beam dump, is

$\displaystyle P_{\rm emit}(E_{\mu})\simeq\frac{n_{N}}{\langle
dE/dx\rangle}\int_{0}^{E_{\mu}}\sigma(E)dE,$ (5)

where $n_{N}=8.6\times 10^{22}/{\rm cm}^{3}$ is the number density of nuclei
in the iron beam dump, $\sigma(E)$ is the energy-dependent $\ \mu N\to\mu NS$
cross section, and $\langle dE/dx\rangle$ is the average energy loss of the
muon in the medium, conservatively taken to be 16 MeV/cm [31]. The typical
path length in the beam dump is thus $l\sim 50$ cm [32]. For each muon
produced by the GEANT4 simulation, the differential scalar emission
probability in Eq. (5) is used to generate a random scattering event. A
CalcHEP MC event of matching incident muon energy is randomly selected to
generate the scalar 4-momentum. The production locations for scalars with
$m_{S}=100\ {\rm MeV}$ are shown in Fig. 3 (bottom panel).

Example energy distributions of the mesons and scalars for $m_{S}=24\ {\rm
MeV}$ are shown in Fig. 4. Using the 4-momenta of the scalars generated via
the meson decay and scattering channels, we then evaluate the probability of
$S$ decay within the fiducial volume of MiniBooNE/MicroBooNE, via the loop
diagram in Fig. 2, right. This is computed using the distance from the
emission event to the detector, its line-of-sight width along the direction of
the scalar momentum, and the decay length. The approximate decay length is
given in Eq. 4, but in our analysis we use the full expression (3) for each
value of $m_{S}$. Diphoton invariant mass distributions for two representative
scalar masses are shown alongside data and background expectations in Fig. 5.
We find that the largest signal rate given the MiniBooNE and MicroBooNE target
and detector geometry comes from boosted $K^{\pm}\to\mu^{\pm}\nu_{\mu}S$
decays. Pion decays $\pi^{\pm}\to\mu^{\pm}\nu_{\mu}S$ are only kinematically
allowed for $m_{S}<m_{\pi}-m_{\mu}=34\ {\rm MeV}$, but even at $m_{S}=24\ {\rm
MeV}$ (Fig. 5, bottom) the kaon decays still dominate. The contribution to the
total $\gamma\gamma$ rate from muon scattering is largest at $m_{S}\sim 30\
{\rm MeV}$, but is generally subdominant over the whole relevant mass range;
unlike the meson decay channels, the scattering rate depends on the beam dump
thickness and density, and thus this contribution may be more important in
other experimental setups.

To evaluate our sensitivity to the $S$ decay diphoton signal, we use the fact
that the same final state was used in MiniBooNE and MicroBooNE’s measurements
of neutrino-induced neutral current (NC) $\pi^{0}$ production,
$\nu_{\mu}N\to\nu_{\mu}N\pi^{0}\,(\pi^{0}\to\gamma\gamma)$. In both analyses,
the diphoton invariant mass $m_{\gamma\gamma}$ is reported, and we recast
these analyses as searches for resonances with $m_{\gamma\gamma}=m_{S}$.
Notably, the NC$\pi^{0}$ signal definition was slightly different for the two
experiments. In MiniBooNE, the measurement included events with $\geq 0$
visible protons since MiniBooNE was insensitive to proton(s) at the
interaction vertex [21]. MicroBooNE was able to separate their measurement
into NC$\pi^{0}$ events with either 0 or 1 associated visible protons [22]. We
consider the 0 proton case in MicroBooNE here since no protons are expected in
an $S$ decay.

The MiniBooNE (MicroBooNE) measurement was performed in neutrino mode with
$6.46\times 10^{20}$ ($5.89\times 10^{20}$) POT and utilized a fiducual mass
of 450 tons (77 tons). MiniBooNE’s measurement in antineutrino mode is not
considered here for simplicity. For MiniBooNE, we impose a “track mass” cut,
which is used to separate diphoton and single-electron events, providing a
natural lower bound on sensitivity,

$\displaystyle
m_{\gamma\gamma}\equiv\sqrt{2E_{1}E_{2}(1-\cos\theta_{12})}>f(E_{1}+E_{2}),$
(6)

where $E_{1,2}$ are the energies of the two photons, $\theta_{12}$ is their
separation angle in the lab frame, and the specific function
$f(E_{1}+E_{2})\approx 32\,$MeV is given in Ref. [33]. For MicroBooNE, we
employ the minimum photon energies used in their analysis ($E_{\rm high}>30$
MeV and $E_{\rm low}>20$ MeV), but allow arbitrary separation angles. The
smeared signal distribution of $m_{\gamma\gamma}$ is approximated as a
Gaussian centered at the scalar mass with $15\%$ (33%) resolution, consistent
with the measured MiniBooNE (MicroBooNE) $\pi^{0}$ invariant mass in this
region [34, 21]. We assume that the 2$\gamma$ detection efficiency is a flat
40% (6%) across the invariant mass range used in this analysis, 32–128 MeV
(10–120 MeV) in MiniBooNE (MicroBooNE), which is reasonably consistent with
Refs. [21, 22]. There is minimal sensitivity above these mass ranges primarily
because the scalar decays before reaching the detectors.

The lower threshold at MicroBooNE is noteworthy. Since MicroBooNE does not
expect any true neutrino-induced $\pi^{0}$ (2$\gamma$, 0p) events in the 0–10
MeV bin [22] and it is difficult to estimate the detection efficiency behavior
within this region, we have conservatively set the lower threshold to be 10
MeV. However, in principle, LArTPCs are sensitive to invariant masses below
this value and we therefore encourage these experiments to explore sensitivity
to $m_{\rm\gamma\gamma}<10\,{\rm MeV}$, where pion decay could dominate and
for which there is a large swath of allowed parameter space that could be used
to explain the $g-2$ anomaly.

The primary background for our analysis is $\pi^{0}$ production in neutrino-
induced NC$\pi^{0}$ scattering, and in setting our limits we compare our
predicted signal yield against the observed diphoton distributions from Refs.
[21, 22], noting that no significant excess is apparent in the datasets. For
MiniBooNE, we calculate the significance of an injected signal ($s_{i}$) with
a standard $\chi^{2}$ test,

$\displaystyle\chi^{2}=\sum_{i,j={\rm
bins}}(d_{i}-s_{i}-b_{i})M_{ij}^{-1}(d_{j}-s_{j}-b_{j})~{},$ (7)

where $d_{i}$ is the observed data, $b_{i}$ is the background prediction, and
$M_{ij}$ is the uncertainty matrix. We construct $M_{ij}$ using the
statistical uncertainties on the data and assume fully correlated bin-to-bin
systematics associated with flux (12.4%), cross section (8.4%), and the
detector (5.1%), consistent with Ref. [21]. We note that these systematics are
nominally applicable to MiniBooNE’s NC$\pi^{0}$ analysis, rather than a
generic 2$\gamma$ search, and that the detailed correlations between bins may
be important. For MicroBooNE, we use a Poisson extended maximum likelihood
$\chi^{2}$ definition [31, 35] since the number of reported events is $<20$
across many of the relevant bins:

$\displaystyle\chi^{2}_{\rm poiss}=2\sum_{i=\rm
bins}\Big{[}N_{\text{pred},i}-d_{i}+d_{i}\ln(d_{i}/N_{\text{pred},i})\Big{]},$
(8)

where $N_{\text{pred},i}=s_{i}+b_{i}$. This MicroBooNE estimate is a
“statistical uncertainty only” approximation, which ignores systematic
uncertainties. However, the relevant reported invariant mass bins (10–120 MeV)
are dominated by statistical errors and a more complete treatment is therefore
not expected to markedly change our reported limit. A more detailed study by
the collaboration, in particular to search for generic 2$\gamma$ (rather than
NC$\pi^{0}$) events, validate the $\chi^{2}$ thresholds with fake data studies
(given the low statistics), and include systematics, would be valuable. We
define a $5\sigma$ exclusion limit in the region where the $p$-value
associated with the $\chi^{2}$ falls below $2.8\times 10^{-7}$.

##  IV Results

In Fig. 6 we show our sensitivity in the coupling $y$ versus mass $m_{S}$
parameter space. Our main results are the red shaded region which represents
the MiniBooNE exclusion at $5\sigma$ confidence, and the purple shaded region
with the analogous interpretation for MicroBooNE. We also include a projection
for the SBND LArTPC-based experiment at Fermilab [36], set to take first data
in 2024 111This projection is not to be considered as coming from the SBND
collaboration.. We consider a realistic detector geometry (77 ton fiducial
mass) at a distance of 60 m from the beam dump, $10^{21}$ POT, and use the
same invariant mass resolution and efficiency assumptions as MicroBooNE. The
excluded regions all have similar characteristic shapes. At large coupling and
high mass, the decay length is much shorter than the detector baseline, and
the signal flux is exponentially suppressed. In the low-coupling region,
scalar production becomes increasingly unlikely. In the low-mass limit, the
analyses are no longer suited to detect the diphoton signal. It is noticeable
that SBND has a much shorter baseline - this allows it to exclude further into
the shorter lifetime region. It also has a higher geometric acceptance, which
allows it to extend further into the small coupling regime. The SBND
NC$\pi^{0}$ background estimate comes from scaling MicroBooNE to the SBND
location using the ray tracing simulation, which estimates an increase in
background event rates of a factor of $N_{\rm bkg,SBND}\approx 90N_{\rm
bkg,MicroB}$. This reasonably agrees with the simple estimate $N_{\rm
bkg}\propto N_{\rm POT}V/r^{2}$, with $V$ the detector volume and $r$ the
baseline.

The green band in Fig. 6 represents the favored region for reconciling the
anomalous observed experimental value of $g-2$ to within $2\sigma$ agreement
[11]. The combination of MiniBooNE and MicroBooNE constraints exclude scalars
of mass between 10 and 60 MeV in this band. The gray shaded region directly
above the green band is excluded by muon $g-2$ measurements, as loop
contributions from $S$ would contribute beyond the observed value and
reintroduce a discrepancy between theory and experiment at the $>5\sigma$
level. For $m_{S}>2m_{\mu}$, Fig. 6 also shows constraints from
$S\to\mu^{+}\mu^{-}$ decays assuming a $100\%$ branching fraction into this
channel. We show limits from the BaBar $e^{+}e^{-}\to 4\mu$ search dashed
projections for improving $B$-factory limits with future Belle-II analyses
[7]. For $m_{S}>$ few GeV, there is also a CMS constraint based on
reinterpreting a $Z\to 4\mu$ decay search [7].

Figure 6: Parameter space for the singlet scalar in Eq. (1), decaying to
diphotons via Eq. (3). The red and purple shaded regions are excluded at
$5\sigma$ by existing MiniBooNE and MicroBooNE data, respectively, based on
the analysis in this paper and the magenta dashed curve represents a future
$2\sigma$ projection for SBND sensitivity. The green band represents the
parameter space where this scenario resolves the muon $g-2$ anomaly. For
$S>2m_{\mu}$ we show constraints from BaBar and CMS based on the
$S\to\mu^{+}\mu^{-}$ decay channel along with future projections for Belle-II
[7]. For $S<2m_{\mu}$ we also show projections for a dedicated muon beam-dump
experiment [14] and for the $M^{3}$ muon missing momentum proposal [9]. Also
shown are cosmological bounds for $m_{S}<1$ MeV where $S$ particles thermalize
with the SM as a relativistic species during Big Bang nucleosynthesis [38].

Below the dimuon mass threshold, Fig. 6 also shows several projections for
future searches. The blue dashed region is the projection for a dedicated muon
beam-dump experiment proposed in Ref. [14], which could cover much of the
remaining $g-2$ band. The orange dashed curve is based on a proposed muon
missing momentum ($M^{3}$) search strategy [9]. Although $M^{3}$ is nominally
sensitive to invisibly-decaying particles produced in muon interactions, the
scalar $S$ can be sufficiently long-lived on the length scales of the proposed
experiment such that it is effectively invisible, and $M^{3}$ would probe the
same parameter space as the model considered here. As mentioned earlier,
access to the $0-10\ {\rm MeV}$ bin in $m_{\gamma\gamma}$ at MicroBooNE/SBND
would allow us to place strong limits on $m_{S}<10\ {\rm MeV}$ from $S$
production in charged pion decays, which would likely be competitive with the
dedicated muon beam dump projections.

##  V Conclusions and Outlook

The results of this work should be taken as a proof-of-concept validation of
the potential of reinterpreting data collected at neutrino short-baseline
experiments in the context of muon interactions beyond the SM. There are some
experimental subtleties that were not taken into account in this analysis, and
thus we expect the results to be correct to within an $\mathscr{O}$(1) factor.
Nonetheless, given the amount of parameter space which is accessible given
current data, espeically the highly-motivated $g-2$ region, we strongly urge
the MiniBooNE and MicroBooNE collaborations to undertake a generic 2$\gamma$
search (including systematics and detailed bin-to-bin correlations not present
in publicly-available data) in order to achieve more accurate results.
Futhermore, we encourage other neutrino experiments producing copious
auxiliary muons—such as NOvA [39], T2K [40], DUNE [41], and ESS [42]—to
undertake similar muon studies to maximize the physics potential of the
experimental infrastructure.

More generally, in this Letter we have illustrated the potential of neutrino
experiments to also function as probes of weakly-coupled new physics produced
via muon interactions. The production of muons associated with neutrinos is
completely generic with a primary proton beam, and thus the secondary muon
source is a byproduct of the neutrino production and is generated at no
additional cost to the experiment. Not only is a muon program at neutrino
sources economical, but it is also uniquely sensitive to muon-philic new
physics scenarios, which is an under-explored region of parameter space due to
the lack of dedicated muon sources.

Finally, we emphasize the practical importance of these secondary muon
programs: the costs are small and the required timescales are short. An
investment in exploring the implications from muon physics at these
experiments can not only inform and shape the future construction of other
large-scale experiments, but also could provide the first hints towards
understanding the persistent puzzles of the SM.

## Acknowledgments

We would first like to thank the organizers and participants of the 2023 ACE
Science Workshop at Fermilab, where the idea for this work was conceived, for
stimulating discussions and feedback. C.C. is supported by the U.S. Department
of Energy (DOE) Office of High Energy Physics under Grant Contract No. DE-
SC0012567. The work of Y.K. was supported in part by DOE grant DE-SC0015655.
J.S. is supported by the Department of Energy, Office of Science, under Award
No. DE-SC0007859.

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# Near-Perfect Absorption of Light by Plasmene Sheets

Qianqian Shi  Department of Chemical Engineering, Faculty of Engineering,
Monash University, Clayton, VIC 3800, Australia  Timothy U. Connell  RMIT
University, Melbourne, VIC, 3000, Australia  Qi Xiao  CSIRO Manufacturing,
Clayton, VIC, 3169, Australia  Anthony S. R. Chesman  CSIRO Manufacturing,
Clayton, VIC, 3169, Australia  Melbourne Centre for Nanofabrication, Clayton,
VIC, 3169, Australia  Wenlong Cheng  Department of Chemical Engineering,
Faculty of Engineering, Monash University, Clayton, VIC 3800, Australia  Ann
Roberts  Timothy J. Davis  School of Physics, The University of Melbourne,
Parkville, VIC, 3010, Australia  Daniel E. Gómez<EMAIL_ADDRESS>RMIT University, Melbourne, VIC, 3000, Australia

###### Abstract

Near-perfect absorbers (NPAs) efficiently absorb visible light with a layered
nanostructure that is thinner than the diffusion lengths of photogenerated
charge carriers. We overcame existing limitations in fabricating their
nanoparticulate surface by depositing plasmene, a tightly-packed two-
dimensional lattice of metal nanoparticles formed through self-assembly. The
plasmene NPAs absorb up to 98% of incident visible light, with modelling
showing the improvement on existing NPAs arises from the structural ordering
of the plasmene. We also demonstrate control of NPAs’ absorption profile
through the use of anisotropic building blocks in plasmene. These property
enhancements may broaden the application of NPAs to structural colour, sensing
and photocatalysis.

###### keywords:

Plasmonics, metasurfaces, optical magnetic mode, perfect absorption

##  1 Introduction

Solar energy harvesting in photovoltaics and photocatalysis begins with the
absorption of light by matter 1. Light absorption creates electronically
excited states from which useful work can be extracted if the excited charge
carriers can readily access chemical (catalytic site) or physical (electrode)
interfaces. To maximize solar-energy conversion efficiencies, it is thus
desirable to create light-harvesting devices in which the thickness of the
absorbing layer is much smaller than characteristic charge-carrier scattering
lengths, whilst simultaneously preserving a high magnitude of light absorption
2.

Figure 1: The self-assembly of plasmene sheets on mirror/dielectric substrates
(supported on glass), resulting in the formation of near-perfect absorbers.

One class of structure that embodies these properties is the near-perfect
absorber (NPA), in which near-complete light absorption occurs on a sub-
wavelength scale due to optical impedance matching between the material and
free space. Optical impedance matching can be achieved by placing a layer of
nanoscale resonators at a specific distance from a reflector, leading to the
excitation of optical resonances that efficiently suppress the reflection of
light. The presence of the mirror eliminates transmission, and consequently
nearly all light is absorbed. This concept has been demonstrated using
metallic (plasmonic) nanostructures, resulting in strong absorption bands in
the infrared 3, 4, 5, 6 and visible 7, 8 range of the electromagnetic
spectrum. Notably, there are remarkable examples where broadband light
absorption has been achieved 9, 10, 11, 12, 5.

In most demonstrations of plasmonic NPAs, the metallic nanostructures have
been lithographically defined into periodic arrays or consist of randomly
distributed nanoparticles, which result from the vacuum deposition and
subsequent annealing of thin metal layers. In contrast, creating these
structures using colloidal suspensions of high quality nanoparticles would
enable the facile fabrication of NPAs using simple and scalable deposition
processes. A theoretical study suggested that for a planar periodic array of
lossy small particles (such as metal colloids) to exhibit perfect absorption,
the absorption cross-section of an individual member of said array must be
comparable to the area of the unit cell. 13 This implies that the use of metal
colloids as the building blocks of NPAs requires their assembly into surfaces
of moderate to high particle densities. To date, colloid-based plasmonic NPA
structures have been realized by the deposition of nanocubes using a self-
assembly approach driven by the electrostatic attraction of colloids to the
supporting substrates. However, this leads to relatively low surface coverages
($\sim$ 4.2% coverage 14) and parasitic light scattering from the formed
surfaces 14, 15, 8.

Plasmene is a highly ordered and tightly-packed two-dimensional sheet of metal
nanoparticles formed by spontaneous self-assembly at an air-water interface
16, 17, 18, 19, 20. These sheets are of single-particle thickness and form
over macroscopic (i.e. $\sim$3 mm) lateral dimensions. They also demonstrate
several unique fundamental properties, such as an unusually high mechanical
strength ($\sim$ 1GPa Young’s modulus) and the capacity to support both
propagating and gap plasmon modes, controllable by tuning the geometry of
plasmene’s unit cell 18.

Here, we demonstrate near-perfect absorbers made with a nanostructured
absorber layer of plasmene. The high surface coverage provided by plasmene
creates NPAs that absorb up to 98% of incident visible light. Furthermore,
engineering the geometry of the plasmene building blocks allows for control of
the wavelength of absorption.

##  2 Results and Discussion

The basic architecture of the plasmene NPAs, shown in Figure 1, consists of
three distinct layers: a mirror, a thin dielectric spacer, and a single layer
of plasmene. Plasmene sheets with building blocks of Au nanocubes (shown in
Figure 2B) were synthesized following well-established protocols (Figure 2A)
21, 20. Suspensions of these nanocrystals in water exhibit extinction bands in
the visible that are characteristic of the excitation of localized surface
plasmon resonances (Figure 2D) 22.

Figure 2:  A The drying-mediated self-assembly of plasmene. Electron
microscope images of B Au nanocubes (side length $\sim$ 40 nm), and C a
plasmene sheet. The scale bar corresponds to 100 nm in both images. D
Normalized absorption spectra of Au nanocubes in solution and the extinction
(1-T) spectrum of a Au nanocube plasmene sheet on glass. Inset. Calculated
lowest-order degenerate eigenmodes $\sigma_{m}(\boldsymbol{r})$ of Au
nanocubes.

In solutions of low particle concentration, the inter-particle distances
between neighboring particles is much larger than the near-fields generated by
individual particle plasmons. Consequently, the optical properties of these
particles are well-described by considering the interaction of an isolated
nanocube with an incident light field. This interaction excites localized
surface plasmon resonances, creating a surface charge distribution
$\sigma(\boldsymbol{r})$. Given that the nanoparticle dimensions are
significantly smaller than the wavelength of visible light, this charge
distribution can be written in terms of the (electrostatic) eigenmodes
$\sigma_{m}(\boldsymbol{r})$ (or self-sustained oscillations) of the particle
according to
$\sigma(\boldsymbol{r})=\sum_{m}a_{m}(\omega)\sigma_{m}(\boldsymbol{r})$,
where $a_{m}(\omega)$ are the excitation amplitudes that describe the coupling
of the incident light field with a particular eigenmode (here $m$ is an index
that indicates the $m$-th mode sustained by the nanoparticle). Modes with
strong dipolar character couple strongly with uniform electric fields and thus
have large values of $a_{m}(\omega)$. Consequently, these are manifest in
optical extinction spectra, as shown in Figure 2D corresponding to Au
nanocubes in Figure 2B. The calculated lowest-order (three-fold) degenerate
eigenmodes $\sigma_{m}(\boldsymbol{r})$ of the nanocubes clearly have a strong
dipolar character, with charge accumulation at each of the three orthogonal
directions of the cube (Figure 2D inset). For these particles, the
electrostatic eigenmode description (particles in a uniform medium with the
refractive index of water; eigenvalue for this mode 1.728) predicts that these
dipole resonances occur at 560 nm, which is in good agreement with the
experimental value.

Plasmene is formed by the deposition of a chloroform solution of Au
nanoparticles onto the surface of a water droplet. A change in polarity
resulting from the evaporation of the chloroform results in self-assembly into
an extended two-dimensional array on the surface of the water droplet, with
subsequent evaporation yielding a quasi-crystalline lattice of plasmene 23
(Figure 2A, more detail in the Methods Section). The extinction spectrum
($1-T$) of a plasmene layer on a glass surface clearly demonstrates a strong
modification to the nanostructures’ interaction with light (Figure 2D). This
results from a combination of at least two effects: the interaction of the
nanoparticles with a flat substrate, as well as inter-nanoparticle
interactions. When the nanocubes are placed on a substrate, the degeneracy of
the dipolar modes shown in Figure 2D is lifted, leading to hybridisation
between bright (dipolar) and dark (multipolar) plasmon modes. In the case of
Ag nanocubes, it has been shown that this results in substantial spectral red-
shifts and the emergence of resonances that were absent in the solution
spectrum 24, 25.

Inter-nanoparticle interactions also lead to plasmon hybridization 26; the
surface electron charge oscillations $\sigma(\boldsymbol{r})$ that result from
the interaction with light are delocalized over the array of particles. This
forms a collective plasmon mode with a resonance frequency red-shifted with
respect to that of the isolated particle.

Figure 3: A Absorption spectra of plasmene NPAs made with Au nanocubes / TiO2
/ Al mirror, with varying TiO2 thicknesses affecting the absorption spectra. B
Effect of mirror type on the absorption spectra of plasmene near-perfect
absorbers (TiO2 thickness fixed at 30 nm.)

To experimentally realize plasmene near-perfect absorbers of light, the mirror
and spacer layer were deposited by physical vapor deposition. The spacer layer
consisted of TiO2, a dielectric with a high refractive index that is
transparent to visible light. Self-assembly of a plasmene sheet on the TiO2
thin film completed the structure. Figure 3A shows the measured absorption
spectra of two samples constructed using Al as the mirror, Au nanocubes as the
plasmene building blocks, and TiO2 of different thicknesses. These spectra
were determined by measuring the transmission ($T$) and reflection ($R$)
spectra of each sample (the latter carefully referenced to a surface with a
known reflectance spectrum), giving the absorption ($A$) as: $A=1-R-T$ by
virtue of the conservation of energy (more detail in the Methods Section, the
transmission spectra are shown in Figure S.1). With a dielectric spacer of 30
nm thickness, the spectrum showed two dominant absorption bands at 480 and 703
nm reaching absorption magnitudes of 86% and 91%, respectively. Increasing the
dielectric spacer thickness to 58 nm slightly improved the maximum absorption
to 94% at 700 nm. Interestingly, whilst the absorption band at $\sim$700 nm
underwent a slight hypsochromic shift, the higher energy band ($\sim$480–500
nm) showed a bathochromic shift as the TiO2 thickness increased, consistent
with a distance-dependent interaction between the plasmene sheet and the metal
layer 15. Changing the chemical composition of the mirror layer in the NPA
from Al to Au caused a hypsochromic shift in the low energy absorption band
(approx. 10 nm) along with a small increase in magnitude (Figure 3B). When
compared to the extinction spectrum of a nanocube plasmene sheet deposited on
glass (Figure 2C), the absorption bands of Figures 3 are noticeably sharper.

Figure 4: Effect of plasmene building block geometry on optical properties.
Electron microscope images of A Au bipyramids in solution (scale bar 100 nm)
and B a plasmene sheet made with Au bipyramids (scale bar 400 nm),
illustrating the lattice orientation that is responsible for the observed
polarization dependence. C (Normalized) absorption spectrum of Au bipyramids
in solution and absorption spectrum of a plasmene near-perfect absorber made
with bipyramids. D Absorption spectra for plasmene sheets made with Au
bipyramids measured for two polarizations. The black line corresponds to the
measured dark-field scattering spectrum. For the cases shown here, the mirror
was made with Al and the spacer consisted of 30 nm of TiO2. Inset. Optical
microscope images of the measured regions demonstrating a drastic change in
color.

The absorption spectrum of plasmene is spectrally tailored by the geometry of
the nanoparticle building blocks. This effect is illustrated in Figure 4,
where we show NPAs made with bipyramidal-shaped Au nanocrystals. Due to their
long aspect ratio (Figure 4A), Au bipyramid nanoparticles exhibit multiple
localized surface plasmon resonances (Figure 4C). A plasmene NPA incorporating
bipyramidal building blocks exhibited an absorption band with a maximum of 98%
incident light absorption at 524 nm. (A second absorption band is expected to
occur at higher wavelengths, beyond the detection range of the instrumentation
used). Nanobipyramids can self-assemble to form plasmene sheets in four
different packing orders 21, and due to their high structural aspect ratio,
these assemblies can form plasmene sheets with optical properties that are
sensitive to the polarization of the incident electromagnetic field (Figure
4D). These changes are also clearly visible to the naked eye under an optical
microscope (Figure 4D inset).

The scattering of light imposes a lower limit on the reflectivity at the peak
absorption. Scattering can occur as a consequence of structural disorder or
the existence of edges in the plasmene lattice. The former may arise from the
size distribution of the building blocks, whilst the latter may occur due to
the finite extent of the plasmene sheets or the unintentional formation of
stacked multiple layers. Figure 4(D) shows a comparison between the measured
absorption and dark-field scattering spectra of a plasmene near-perfect
absorber, which were measured against surfaces of known reflectance and
calibrated scattering amplitude, respectively. The figure shows clearly that
scattering amounts to $<$ 1% of the total incident power, indicating that it
is strongly suppressed due to the regular ordering of the nanocrystal building
blocks in the plasmene layer 14.

Theory For metasurfaces with a nanostructured layer, in which the inter-
particle spacings are larger than the spatial extent of the plasmonic near-
fields, perfect absorption has been modelled with a coupled-mode theory 27,
28, wherein each individual mirror-coupled nanocube reacts like a magnetic
dipole. The collective action of an ensemble of these nanocubes results in an
effective magnetic response, which enables almost complete impedance matching
between the metasurface and free space, resulting in near-perfect absorption
14, 15, 8. In metasurfaces with a sparse surface coverage, these magnetic
modes can be both excited and scattered at the edges of the nanocube, allowing
for some of the radiation to escape and couple into free space.

In order to gain a physical insight into the mechanism that enables almost
complete impedance matching in plasmene NPAs, we have modelled the optical
properties of a nanocube plasmene NPA using a finite element approach for
solving Maxwell equations. The model material consisted of a periodic array of
nanocubes of side length 40 nm ordered in a cubic lattice with a 100 nm period
and a 30 nm spacer layer. Figure 5 shows the calculated absorption spectrum
for this configuration with two bands that closely match the experimental
data, along with the calculated maps of the magnitude of the electric ($|E|$)
and magnetic ($|H|$) fields for each band. The electric field is strongly
localized at the edges of the nanocube distant from the dielectric film, for
the short–wavelength absorption band (located at $\sim$ 540 nm). For the long-
wavelength absorption band (located at $\sim$700 nm), the electric field is
strongly localized at the edges of the cube in contact with the dielectric
film, and the magnetic field exhibits strong localization in the TiO2 layer,
in a way similar to a magnetic dipole 3. This optical magnetic response
originates from the interaction of the induced oscillating surface charges on
the cube with their mirror images on the metal support. The radiation from the
latter can cancel that produced by the induced dipole located on the
nanoparticles, leading to suppression of reflection and causing the
nanoparticles to absorb the energy, given that the mirror support prevents
transmission of light 29. Given the deep sub-wavelength separation between the
building blocks, the plasmene sheet can be rationalized to consist of an
effective magnetic metasurface, that is different from a metal film of a
similar thickness (see Figure S.2).

Figure 5: Numerically simulated optical absorption spectrum for a perfectly-
ordered array of Au nanocubes on a TiO2–Au mirror support. The insets show
spatial maps of the magnitude of the electric ($|E|$) and magnetic ($|H|$)
fields. The magnetic field distribution for the absorption peak located at
$\sim$700 nm clearly shows that at this wavelength, normally-incident light
excites a magnetic mode in the structure.

##  3 Conclusion

In summary, we have fabricated and measured the absorption spectra of plasmene
near-perfect absorbers of light. We demonstrate that these materials can
absorb up to 98% of incident visible light. The intense electromagnetic near-
fields resulting from this near total extinction of light may find application
in surface-enhanced spectroscopy, chemical and biological sensing, and
plasmonic hot-carrier extraction. Notably, as the mirror and TiO2 layers can
be deposited by solution-based approaches (such as electroplating, spin-
coating and sol-gel methods), this report provides a pathway for the scalable,
vacuum-free fabrication of NPAs.

##  4 Methods

Methods

Require a general materials section. Also, should note that all solutions are
aq. unless otherwise noted, this is ambiguous.

Synthesis of Nanocrystal Building Blocks Synthesis of Au nanocubes A seed-
mediated method was used to synthesize Au nanocubes 30.. Briefly, a seed
solution was prepared by adding NaBH4 (0.6 ml, 0.01 M) to an aqueous solution
prepared by mixing HAuCl4 (0.1 ml, 25 mM) and cetyltrimethylammonium bromide
(CTAB) (7.65 ml, 0.1 M). The seed solution was then kept at 30 ∘C for 1 hour.
The growth of Au nanocubes was triggered by adding 5 $\mu$l of a 10-fold
diluted seed solution into a growth solution prepared by adding CTAB (1.6 ml,
0.1 M), HAuCl4 (0.2 ml, 7 mM), and ascorbic acid (1.2 ml, 0.1 M) to Milli-Q
water (8 ml). The resulting solution was then left undisturbed overnight,
followed by centrifugation at 7830 rpm for 10 min and redispersal in Milli-Q
water (10 ml) for further use.

Synthesis of Au Nanobipyramids (NBP) The synthesis of Au nanobipyramids
involved a seed-meditated method and a three-step purification, as reported
21. A Au-seed solution was synthesized by adding NaBH4 (1 ml, 100 mM) to a
solution prepared by adding HAuCl4 (0.4 ml, 25 mM) to aqueous trisodium
citrate (40 ml, 0.25 mM). The resulting solution was then kept stirring at
room temperature for 2 hours. Later, a portion of this seed solution (0.8 ml)
was added to 100 ml of growth solution that contained aliquots of CTAB (0.1
M), HAuCl4 (2 ml, 25 mM), AgNO3 (1 ml, 10 mM), HCl (2 ml, 1.0 M), and ascorbic
acid (0.8 ml, 0.1 M). The growth solution was kept at 30 °C overnight, and
then centrifuged at 7830 rpm for 10 min, with the precipitate redispersed in
an aqueous solution of CTAC (100ml, 80 mM). Purification of the Au NPBs was
achieved using a three-step method reported previously 21. The final solution
was washed and redispersed in Milli-Q water for further use.

Preparation of Metal-Semiconductor Substrates All films were deposited in an
electron beam evaporation system (Intlvac, Nanochrome II) using a 10 kV power
supply in a Class 10,000 cleanroom. Glass substrates were cleaned by
sequential ultra-sonication in acetone and isopropanol, and then dried under a
stream of nitrogen gas. The substrates were also cleaned by a plasma treatment
step prior to the deposition of the metal-semiconductor films. In order to
achieve good adhesion of the mirror layer to the substrate, a thin layer of Cr
(5 nm, deposited 0.5 Å/s) was deposited. The Al or Au mirrors (100 nm,
deposited 1.0 Å/s), and TiO2 spacer (30 or 60 nm, deposited 0.5 Å/s) were
deposited sequentially. Dielectric film thickness was confirmed by
spectroscopic ellipsometry (J. A. Woolam Co., M-2000DI).

Fabricated of Plasmene Sheets Plasmene was fabricated by a drying-mediated
self-assembly method at an air-water interface 20. First, a two-step ligand-
exchange method was used to replace CTAB ligands with thiol-terminated
polystyrene (SH-PS) (Mn=50,000 for Au nanocubes and 20,000 for NBP). Briefly,
10 ml of the CTAB-capped Au nanocube solution (or 12 ml of the Au NBP
solution) was centrifuged and redispersed in 5 ml (or 6 ml for Au NBP) SH-PS-
THF (4 mg/ml) solution. The solution was then kept at room temperature
overnight and purified by repeated centrifugation-precipitation cycles to
remove uncapped ligands and precipitate the SH-PS capped nanoparticles.
Finally, the solution was concentrated and redispersed in a small amount of
chloroform. To assemble a plasmene sheet, one drop of nanoparticle solution
was deposited onto a water droplet sitting on the mirror/spacer substrate.
After the full evaporation of the water and chloroform, a plasmene sheet was
obtained.

Characterization Normal incidence images of the resulting structures were
obtained by scanning electron microscopy (FEI, NovaNanoSEM 430). SEM images of
plasmene were obtained by a FEI Helios Nanolab 600 FIB-SEM operating at 5 kV.

Optical Measurements The optical transmission and reflectance spectra of the
NPA plasmene sheets were measured using an upright microscope (Nikon LV100),
coupled to a spectrograph (Andor, SR-303i-A) equipped with a CCD (iDUS
DU420A-BEX2-DD). For all the measured spectra, the light source was a
broadband 100 W halogen lamp. The illumination and collection of reflectance
($R$) was done with a ${50}\times$ objective (NA 0.55), and these measurements
were referenced to a mirror with a known reflectance spectrum (Thorlabs
BB1-E02). The transmission ($T$) spectra were calibrated using a bare glass
substrate. The absorption data shown in this paper were calculated as:
$A=1-R-T$ and are consequently not arbitrary values 10. Scattering spectra
were measured using the same objective but placing a dark-field iris in front
of the light source. These spectra were referenced to a white diffuse
Reflectance Standard (Labsphere, Spectralon SRS-99-020).

Numerical Simulations The numerical simulations shown in Figure 5 were
undertaken using the Finite Element Method implemented in COMSOL Multiphysics
5.3a. We used tabulated data for the refractive index of Au 31 and Al 32 for
the substrate, and 1.0 for the medium above the structure. The refractive
index of the TiO2 layer was assumed to be 2.4. Periodic boundary conditions
were assumed on the sides and a port boundary was used at the excitation
surface. The normally incident plane was assumed to be linearly polarised
parallel to one of the horzontal edges of the cubes. The other surface of the
model adjacent to the Al was taken to be a scattering boundary. No apparent
backscattering from the terminating boundaries was apparent. The cubes were
rounded to have a radius of curvature of 2 nm.

Acknowledgements This work was performed in part at the Melbourne Centre for
Nanofabrication (MCN) in the Victorian Node of the Australian National
Fabrication Facility (ANFF). We acknowledge the ARC for support through a
Future Fellowship (FT140100514) and a Discovery Project (DP160100983).

Competing financial interests The authors declare no competing financial
interests

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Figure S.1: Measured transmission spectra of for the plasmene absorbers
corresponding to Figure 3 of the main text, for the case of an (top) Al and a
(bottom) Au mirror. Figure S.2: Calculated absorption spectrum of a 40 nm
thick Au film placed on top of a 30 nm thick TiO2 / Au mirror support.