wherein the surface converts the incident-wave to a desired radiation pattern.

In this holographic framework, the incident wave illuminating the IRS acts as
a reference-wave, whereas the desired IRS aperture field distribution that
generates the radiation pattern of interest can be considered as the objective
function. The role of the IRS is, therefore, to modulate the reference-wave
into the objective function when the IRS is illuminated by the reference-wave,
similar to an optical hologram. A crucial aspect within this holographic beam-
forming framework is that the objective function is required as a-priori
information to be able to calculate the IRS surface for a given reference-wave
incident. A particularly critical information needed in this process is the
direction of arrival (DoA) estimation in order to be able to retrieve the
direction of the end user and steer the radiation pattern of the IRS
accordingly.

Conventionally, DoA estimation requires a multi-channel detection unit formed
by means of an array topology [5, 6]. Because these techniques require raster
scanning on the receiver side, the DoA estimation is achieved by having a
full-phase control of each antenna forming the array aperture (phased array
technique) or by using antennas mechanically (or electronically) scanned to
synthesize an effective aperture. Mechanical scanning can significantly
increase the data acquisition time, posing a challenge for real-time
operation. On the other hand, phased arrays typically exhibit significant
complexity on the hardware layer due to the necessity to have a dedicated
phase shifter and power amplifier for each antenna element within the array
aperture. Recently, the authors have shown that a single-pixel, compressive
metasurface antenna can retrieve the DoA estimation in an all-electronic
manner by means of a simple frequency-sweep and using a single channel [7].
One of the significant advantages of this technique is that because it
requires a single channel to retrieve the DoA estimation, it can significantly
simplify the physical constraints associated with the hardware layer.

Currently, in wireless communications, IRS apertures are considered as a beam-
synthesis technology, leveraging the holographic principle depicted in Fig.
16. However, in order to synthesize a radiation pattern of interest using IRS
apertures, one needs to know the characteristics of the radiation pattern to
be radiated by the IRS. This aspect of the IRS design makes it necessary to
have a channel characterization capability built into the IRS design. As a
result, an IRS can be used to support multiple capabilities: (a) facilitate
compressive sensing to achieve DoA estimation and (b) synthesize a radiation
pattern of interest using the retrieved DoA estimation to satisfy the
characteristics of the desired channel.

##### Future developments to satisfy these challenges

One of the potential techniques that can be used to address these
aforementioned challenges is to use the IRS aperture to achieve both DoA
estimation and beam-synthesis. In this context, the IRS can first be designed
in such a way that the phase responses of the unit-cells forming the IRS
aperture can be modulated randomly to synthesize wave-chaotic bases to
facilitate spatio-temporally varying radiation patterns for compressive DoA
estimation. Once the DoA estimation is achieved, the IRS can be switched to
the holographic beam-synthesis mode, and using the estimated DoA information
as the objective function, the IRS can modulate the reference-wave to steer
its radiation pattern in the direction of the end user.

A significant challenge with this implementation is that both the DoA
estimation and the beam-synthesis steps need to be achieved in real-time by
the IRS to make sure that the IRS can reconfigure its operation mode and
radiation characteristics to capture the dynamic characteristics of the
channel that can change over time. This can be achieved using active
modulation schemes on the IRS layer facilitated by semiconductor elements with
fast switching times. Initial studies have shown that real-time retrieval can
be possible using PIN diodes as the switching mechanism [8].

Figure 17: An IRS aperture (a) operating in compressive DoA estimation mode.
Retrieved DoA pattern shown as inset (b) operating in beam-synthesis mode.

##### Conclusion

We have presented a roadmap on the application of metasurface type apertures
as IRS structures in wireless communication systems. Leveraging the
holographic beam-forming principle, an IRS can be designed to operate in a
dual-mode state. By randomizing the complex weights of the unit-cells to
facilitate compressive sensing, the IRS can synthesize wave-chaotic radiation
patterns that can be used for channel characterization. Once the channel
information is retrieved, the IRS can modulate an incident-wave into a desired
aperture wavefront, radiating in the direction of the end user using the
information provided by the DoA estimation step. Research fronts on IRS types
of apertures for beam-synthesis and wave-chaotic metasurface antennas for DoA
estimation have recently gained significant traction as two separate tracks.
Merging these two techniques into a single design to achieve IRS apertures
that can perform real-time channel characterization and beam-synthesis remains
as a disruptive technology to be developed in wireless communications.

## Acknowledgments

The work of O. Yurduseven was supported by a research grant from the
Leverhulme Trust under the Research Leadership Award RL-2019-019. The work of
M. Matthaiou was supported by a research grant from the Department for the
Economy Northern Ireland under the U.S.-Ireland R&D Partnership Programme.

## References

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## Ultra-compact ‘Optical-bench-on-a-chip’ Metasurface Toolkits for Ubiquitous
Optical Imaging

### Mitchell Kenney1* and George Gordon1

####  1Department of Electrical and Electronic Engineering,
University of Nottingham, Nottingham, UK

#### *Corresponding author<EMAIL_ADDRESS>
##### Abstract

We propose a roadmap to widely-deployable multimodality imaging devices that
are low-cost and ultra-compact enabled by _metasurface toolkits (MSTs)_ , an
emerging nanotechnology that can replace bulky traditional glass lenses. We
envisage MSTs will play a key role in emerging internet-of-things environments
performing tasks from examining road quality, to early diagnosis of disease.

##### Introduction

Optical technology is becoming ever more necessary in many walks-of-life, with
recent surveys estimating the multimodal imaging market worth £2.25Bn by 2024
[1]. A particular emphasis also lies upon its translation to smaller more
portable devices whilst still encapsulating the smart multifunctionality as
full-sized systems.

Smart-phones have heralded a revolution in hand-held optical imaging devices –
over 7 billion CMOS image sensors are shipped worldwide each year [5]. – with
applications from conducting biochemical assays to check for disease [2] to
identifying damage to roads [3] to low-cost widely-deployable screening of
water for dangerous pathogens [4]. With the rapidly expanding ‘internet of
things’ (IoT), devices with sensing capabilities are increasingly integrated
into countless environments. To achieve their full potential, image sensors
need to offer imaging modalities other than the traditional RGB intensity
imaging offered by smartphones. Techniques such as fluorescence,
multispectral, and polarisation-imaging showcase important additional
information about the physical world [6], but current approaches require bulky
optics made using centuries-old glass technology, akin to large bench-top
microscopes, which inhibits down-scaling of advanced imaging systems for
ubiquitous IoT devices.

_Metasurfaces_ (MSs) are intelligently patterned ultra-thin devices consisting
of optically-interacting nanostructures that control light in novel ways [7].
Metasurfaces exhibit enormous multifunctionality potential in replacing not
only conventional optical components but whole optical systems.

We propose a roadmap to widely-deployable advanced imaging devices, based
around an emerging concept: compact Metasurface Toolkits (MSTs). MSTs are
coin-sized ‘checkerboard’ samples composed of powerful bespoke metasurfaces,
each offering a different functionality or imaging modality that would
conventionally require a sizeable optical bench set-up, thus creating a
versatile ‘optical-bench-on-a-chip’ (shown in Figure 18). Such devices can be
produced at low-cost through high-volume industrial fabrication processes such
as nano-imprint or stepper lithography [8]. Further, recent advances in
polymer chemistry have enabled dynamically reconfigurable metasurfaces that,
when exposed to external stimuli (e.g. temperature, voltage), present
different optical behaviours. The imaging functionality can be further
increased by stacking multiple MSTs, creating powerful yet ultra-compact
systems.

These devices promise transformative applications where advanced imaging is
needed but resources and space are constrained, making them ideal for devices
as part of the burgeoning IoT. Additionally, the customisability of MSs bring
applications in fundamental optical research, quantum and communication
technologies, and point-of-care healthcare.

Figure 18: (a) Schematic of individual metasurface devices (Inset: magnified
region showing individual nanostructures) being combined for a Metasurface
Toolkit (MST). A coin sized MST as a standalone “Optical-bench-on-a-chip”
consists of an assortment of both simple (e.g. lens, polariser) and complex
(e.g. optical-tweezer, vortex phase-plate) optical components. (b) Dynamic
MSTs which utilise hybrid nanotechnology. Examples of applications include bi-
focal lenses, with two focal lengths ($f$ and $f/2$) being switched.

##### Emerging challenges

There is evidently a need for imaging technology to continue reducing in size
while retaining advanced functionality. However, most optical components are
currently manufactured from bulky glasses, which presents a major roadblock.
The size of glass-based systems becomes problematic when multiple components
are combined together to implement advance imaging modalities, typically
requiring bench-sized setups. Additionally, glass components exhibit limited
functionalities and are often prohibitively expensive. Because of this, the
translation of imaging technologies from large-scale benchtop systems to hand-
held portable devices is severely hindered.

Efforts in miniaturizing optical technologies have attempted to address these
issues, resulting in well-known devices such as Fresnel lenses and Gradient
Index (GRIN) components. Whilst achieving some successes, these devices still
lack functionality and require difficult 3D fabrication steps.

Metasurfaces are an exciting area of optics research, which combine advances
in nanofabrication along with bespoke design through tailoring optical
properties of nanostructures (e.g. to control amplitude, phase, polarization).

Although growing interest in metasurface technology has produced impressive
results [9, 10, 11, 12], success in translating these to real-world
applications has been hindered due to three key hurdles – poor-efficiency;
difficulty in fabrication and up-scaling to large-area devices; and
functionality limited to single-operation devices (e.g. lenses, polarisers).

There have been great advances in metasurface technology for imaging
applications, many of which rely on recent developments in using dielectric
nanostructures for high efficiency transmissive devices. Only recently have
fabrication and computational capabilities advanced sufficiently to produce
nanostructures over large areas. Coupled with improved understanding of
metasurface performance, this has led to metasurface device efficiencies that
rival conventional optical devices. Now, through careful design using
nanoscale fabrication, numerous bespoke metasurfaces can be combined onto a
single sample – resulting in the proposed MSTs.

In the simplest case, different areas of the MST can be addressed to implement
different imaging modalities, such as wide-field, super-resolution, and
computational imaging [7]. Such designs can also be produced at low-cost due
to their compatibility with high-volume industrial fabrication processes such
as nanoimprint lithography [8]. The imaging functionality can be further
increased by producing 3D stacks of MSTs, creating powerful systems that allow
numerous optical processing steps in an ultra-compact device [13, 14, 15, 16].

##### Future developments to satisfy these challenges

To overcome the challenges of large systems composed of numerous bulky
components, we propose Metasurface Toolkits composed of checkerboards of
various analogues to conventional optical components, as well as bespoke
multifunctional devices that can not be achieved by any singular or
combination of conventional optics. Examples of these include bifocal lenses
for imaging at different depths, off-axis reflective or transmissive
holograms, or even polarisation-sensitive vortex lenses for Optical trapping.

These can miniaturise a whole optical system down to the size of a postage
stamp, functioning as an “Optical-bench-on-a-chip”. These modular devices can
be stacked, to produce further enhanced imaging and sensing modalities, such
as projection of holograms, through intelligent phase engineering.

Future developments we envision are using deep-learning enabled inverse design
approaches to design such stacked Multilayer MSTs (MMSTs) that perform complex
functions [17]. These designs could themselves implement passive neural
networks capable of light-field processing/sorting. MMSTs will address many
issue of single-layer devices, such as aberration correction and 3D imaging.
This future direction will combine advances in computer science, optical
technologies and modern fabrication techniques, representing a a highly inter-
disciplinary approach. Another promising future direction exploits recent
advances in nano-fabrication and polymer chemistry to enable dynamically
reconfigurable metasurfaces and MSTs that, when exposed to external stimuli
(e.g. temperature, voltage), present different optical behaviours [18, 19].
This further increases the range of optical imaging techniques that can
performed by an ultra-compact device.

Many of the approaches in this future-thinking development can be adapted to
the existing supply chain for fabrication; namely the micro-electronics
industry, which already carry out nanoscale fabrication _en masse_ using
techniques such as master-stamp lithography or extreme-UV (EUV) lithography.
Therefore, they are well suited to enable future scaling up of these advanced
device designs.

##### Conclusion

We propose the development of Metasurface Toolkits - bespoke postage stamp
sized devices composed of nanotechnology-driven metasurface technology, where
each metasurface is, by itself, capable of novel and powerful imaging
modalities, and when stacked together will unlock even more complex and yet to
be realised imaging systems - rivalling standard benchtop systems - resulting
in an "‘optical-bench-on-a-chip"’. Through intelligent design using deep
learning, these systems can be optimised for exciting new science and
applications. Finally, the hybridisation of these MSTs with polymer technology
will result in dynamic devices that respond to changes in external stimuli
(temperature, voltage) leading to switchable operation. These MSTs have
potential applications in IoT systems, where multimodality and compactness is
extremely desirable.

## References

  * [1] https://tinyurl.com/3am746ez Accessed 22-03-2021.
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  * [19] M. Choi, J. Choi, S. Kim, et al.  _Nature Photonics_ , 7(12):987, 2013\.

## Metasurface Based Wireless Localization

###  Orestis Georgiou1* and Cam Ly Nguyen2

####  1Department of Electrical and Computer Engineering, University of
Cyprus, Nicosia, Cyprus

####  2Wireless System Laboratory, Corporate Research & Development Center,
Toshiba Corporation, Kawasaki, Japan

#### *Corresponding author<EMAIL_ADDRESS>
##### Introduction

While metasurfaces are posed to revolutionize wireless communications, their
potential use for wireless localization has received very limited attention to
date.

Traditional localization is usually achieved via a Global Positioning System
(GPS). This however introduces additional production costs and power
requirements to mobile devices, typically consuming about 30mA at 3.3V.
Moreover, GPS is not accurate indoors thus failing to meet the Federal
Communications Commission’s (FCC’s) mandate requiring network operators to
locate those calling 911 to within certain accuracy requirements (50m
horizontally and $\pm$3m vertically). This, together with the need for
position-related services, such as, logistics, smart factories, smart cities,
autonomous vessels, vehicles, and localized sensing has seen a wealth of other
wireless localization methods being developed and widely deployed. These are
broadly classified as database, angle-based, range-based, and range-free
methods [1].

Recent advances in metasurface design are promising to inject many new
capabilities into next-generation wireless communication systems (6G)
including enhanced wireless localization and positioning both in and outdoors
while also also unlocking novel sensing applications (e.g., Fig. 19) [2]. This
promise has been enabled through the remarkable ability of reconfigurable
intelligent surfaces (RIS), namely, to manipulate the propagation of incident
electromagnetic waves in a robust and programmable manner thus transforming
the wireless channel into a controllable system block that can be engineered
and dynamically optimized; the result of many years of R&D in physics, optics,
and material science domains, culminating with the integration of control
circuitry into RIS design and unlocking the smart radio environment (SRE)
vision. In the SRE vision, a swarm of low-profile, low-cost, and low-power RIS
are densely deployed in- and outdoors and can collaborate and support existing
telecommunications infrastructure to: suppressing interference, overcome non-
line-of-sight blockage, enhance coverage, improve multi-user throughput and
enhance wireless power transfer.

All of these challenges and opportunities are still in their early days and
are discussed in other sections of the present roadmap article. But how does
one exploit the added degrees of freedom afforded by dense RIS deployments for
improved wireless localization of people and devices?

An initial answer to the above question was attempted by several authors in a
point-to-point communication setting (i.e., a transmitter and receiver pair)
mediated by a RIS that applies phase differences to the composite wireless
channel, the performance gains of which can be captured through the Cramer-Rao
lower bound (CRLB) [3, 4]. The CRLB represents the minimum variance of the
error associated with an unbiased estimator, and can be obtained through the
inverse of the Fisher information matrix. Mathematical and numerical analysis
of the CRLB for wireless localization and orientation estimation accuracy
suggest considerable accuracy improvements with increasing RIS antenna element
count, RIS physical size, and multi-RIS spatial distribution, as one would
probably expect. Multiple trade-offs have also been identified between the
different deployment strategies, but a clear winner remains unresolved;
further analysis is needed.

Other intricacies of similar RIS-aided localization setups have also been
considered, such as the possibility of RIS elements having discrete phase
shifts and finite amplitudes [5], or the possibility of jointly optimizing
communication gains (e.g., improved data-rate) and localization capabilities
[6]. It was concluded that phase resolution is more important to localization
accuracy than amplitude sampling density, while adaptive phase shifters could
be efficiently designed and implemented based on hierarchical codebooks and
feedback from the terminal. Authors have very recently also proposed joint
positioning, synchronizing, and beam training algorithms, thus capitalizing on
RIS ability to focus and improve SNR while employing low-complexity iterative
maximum likelihood estimators thus avoiding exhaustive computational search
and reducing signaling overheads [7].

##### Emerging challenges

Most research on RIS-aided wireless localization has assumed that the
underlying channel is largely geometric, comprising of paths of rays that
connect a wireless source, the RIS elements, and the terminal while ignoring
any rays bouncing off other environmental objects, and also ignoring any
mutual EM coupling between RIS elements. Better channel models are therefore
urgently needed both in the far and near field. Moreover, most proposed
approaches, while indeed concluding that significant gains are possible thanks
to the RIS focusing abilities and large element count, they do not fully
exploit the added spatial and temporal degrees of freedom afforded by the RIS
in controlling the proximal electromagnetic field. Non-standard localization
methods should therefore be explored. Finally, to go beyond algorithmic
optimization, more accurate models, and novel localization methods, we must
begin to experiment with RIS prototypes in controlled test-beds and practical
localization settings in order to truly evaluate performance, discover any
possible limitations or novel business opportunities.

##### Future developments to satisfy the challenges

A promising approach towards better channel models is already underway by
formulating equivalent end-to-end channels in terms of impedance voltages at
transmitter/receiver ports which are propagated by electromagnetic fields and
mutually coupled among the sub-wavelength unit cells of the RIS [8]. Building
upon such efforts and embedding such models into engineering analysis and
optimization is expected to deliver great insights to the field. Further, it
will enable investigations into RIS geometry and periodicity design and their
effect on localization performance. Channel models could also be extended to
capture near-field effects such as wave-curvature as well as uncertainties and
peculiarities of the electronics used to control the RIS, e.g., hardware
impairments and frequency/polarization dependencies.

A different and highly promising approach leverages the RIS ability to alter
the radio environment in a controlled and predictable manner. Coupled with
dynamic large databases and machine learning, novel fingerprinting
localization solutions have been proposed to exploit the spatial and temporal
variability introduced by RIS not only at a single terminal but to the whole
deployment region [9, 10]. Benefits in localization accuracy and coverage
using just a single RIS are comparable to what was previously possible through
the costly installation of multiple additional access points and antennas.

Figure 19: Further applications of metasurface based indoor (left figure) and
underground localization (right figure).

Finally, metasurface based localization can unlock novel applications that
traditional localization cannot (see Fig. 19). For example, we envision
conformal, wearable, and even implantable RIS affecting the electromagnetic
properties of its host. Further, the dense deployment of metasurfaces can
enable localization coverage expansions, e.g, in GPS-unavailable environments
such as inside tunnels and buildings while assisted by existing wireless
infrastructure.

##### Conclusion

The past decade has witnessed a fast development of reconfigurable
metasurfaces, recently posed by wireless engineers as a key technology for
next generation communication systems (6G). The high focusing capabilities of
RISs, their ability to alter/encode waveforms onto impinging signals as well
as their unique capacity of producing differential spatiotemporal radio maps
can be capitalized for finely estimating the location of mobile terminals and
devices. To that end, we envision that in the next few years we will see more
accurate yet tractable channel models, new system architectures, methods and
localization algorithms exploiting novel RIS waveform designs, generative
spatial diversity, and fast temporal modulations for improved localization and
sensing applications. Along with a wealth of theoretical and numerical
results, we also hope to see prototypes and test-beds being deployed,
exploring both the fundamental and practical capabilities while utilizing new
conformal, wearable and even implantable RIS designs, thus enabling novel
localization applications and use cases.

## Acknowledgment

The authors would like to acknowledge funding from the EUs H2020 research and
innovation programme under the Marie Skłodowska-Curie project NEWSENs, No
787180; and Vingroup Joint Stock Company (Vingroup JSC), Vingroup and Vingroup
Innovation Foundation, No VINIF.2020.DA09.

## References

  * [1] Z. Xiao _et al._ , “An overview on integrated localization and communication towards 6g,” _arXiv preprint arXiv:2006.01535_ , 2020.
  * [2] M. Di Renzo _et al._ , “Smart radio environments empowered by reconfigurable intelligent surfaces: How it works, state of research, and road ahead,” _arXiv preprint arXiv:2004.09352_ , 2020.
  * [3] S. Hu _et al._ , “Beyond massive mimo: The potential of positioning with large intelligent surfaces,” _IEEE Transactions on Signal Processing_ , vol. 66, no. 7, pp. 1761–1774, 2018.
  * [4] H. Wymeersc _et al._ , “Beyond 5g wireless localization with reconfigurable intelligent surfaces,” in _ICC 2020-2020 IEEE International Conference on Communications (ICC)_. IEEE, 2020, pp. 1–6.
  * [5] J. V. Alegría _et al._ , “Cramér-rao lower bounds for positioning with large intelligent surfaces using quantized amplitude and phase,” in _2019 53rd Asilomar Conference on Signals, Systems, and Computers_. IEEE, 2019, pp. 10–14.
  * [6] J. He _et al._ , “Adaptive beamforming design for mmwave ris-aided joint localization and communication,” in _2020 IEEE Wireless Communications and Networking Conference Workshops (WCNCW)_. IEEE, 2020, pp. 1–6.
  * [7] W. Wang _et al._ , “Joint beam training and positioning for intelligent reflecting surfaces assisted millimeter wave communications,” _arXiv preprint arXiv:2009.03536_ , 2020.
  * [8] G. Gradoni _et al._ , “End-to-end mutual-coupling-aware communication model for reconfigurable intelligent surfaces: An electromagnetic-compliant approach based on mutual impedances,” _arXiv preprint arXiv:2009.02694_ , 2020.
  * [9] H. Zhang _et al._ , “Metaradar: Indoor localization by reconfigurable metamaterials,” _IEEE Transactions on Mobile Computing_ , 2020.
  * [10] C. L. Nguyen _et al._ , “Wireless Fingerprinting Localization in Smart Environments Using Reconfigurable Intelligent Surfaces,” _IEEE Access_ , vol. 9, pp. 135526-135541, 2021.

## Sensing the Environment by Surface Wave Based
Metasurfaces

### Enrica Martini1 and Stefano Maci1*

####  1Department of Information Engineering and Mathematics, University of
Siena, Siena, Italy

#### *Corresponding author<EMAIL_ADDRESS>
The new generation of connectivity systems based on a smart electromagnetic
environment will be enabled by non-invasive, cognitive, low-power and low-
complexity intelligent metasurfaces (MTSs) to be integrated within, or on top
of, objects, machines and/or structural building elements. MTSs are artificial
surfaces constituted by electrically small elements that collectively exhibit
equivalent homogeneous boundary conditions to any interacting electromagnetic
fields. In the years 2000-2010, MTSs for radio frequency (RF) applications
were essentially uniform in space and realized by periodically printing
elements on a dielectric slab. This was the first generation of MTSs. In a
second generation (2010-2020) MTSs are designed to create spatially variable
boundary conditions to further tailor the interaction with the incident field.
Today, we are facing a transition to the third generation of MTSs, where MTSs
change boundary conditions in both space and time in intelligent way, opening
new perspectives for the next generation of communications. This section of
the roadmap focuses on envisioning surface wave-based sensing MTSs as a
complement to the re-routing MTSs, in the context of an intelligent
connectivity environment.

##### Introduction

The awareness capability of a smart radio-environment consists on the ability
to capture the instantaneous electromagnetic (EM) status by using a set of
independent EM sensorial surfaces connected through a controlled electronic
network, whose aim is to perceive the localization of the network players
(e.g., access-points and users). The instantaneous amplitude and phase of the
EM field is transduced into electrical quantities at individual ports
connected by an electronic intelligence behind.

The simplest EM receiving smart device is a sensing MTS, properly emulating
impedance boundary conditions (IBCs) that convert EM space wave from the
environment into a surface wave (SW), whose energy is collected at one or more
points on the surface. In literature, these devices are called SW-based
modulated MTSs [1]. At microwaves, a SW-based MTS is composed of a grounded
dielectric slab with many small metallic printed elements, often referred to
as “pixels”, arranged in a regular lattice (Figure 20). The SW is collected by
an elementary sensor embedded in the MTS itself, that can be as simple as an
elementary monopole. MTS receiving antennas have therefore a simple, low
profile structure. This mechanism is the reciprocal of the one for which a
Leaky Wave (LW) originates from a monopole-excited cylindrical SW which
interacts with periodic or quasi-periodic IBCs [2]. By changing the
geometrical characteristics of the inclusions, the surface can be adapted to
receive external fields from different arrival directions, or from multiple
simultaneous directions [3], and arbitrary polarization [4]. This feature has
fostered the research on dynamically adaptive MTS, which are able to steer or
reconfigure the beams to reach the maximum reception at the sensor
point/points [5]. The main concept is to dynamically change the IBCs offered
by the MTS by acting on the inclusions composing the MTS through active
electronic devices or tunable materials [6].

Figure 20: MTS antennas based on SWs. The MTS is formed by a texture of
patches printed on a grounded dielectric slab.

SW-based MTSs are cost effective, easily manufactured with standard PCB
techniques, light, low profile and conformable to different kinds of physical
surfaces. These are intriguing features for smart environment connectivity.
Moreover, they can be applied on a wide range of fractional-bandwidth (B) and
gain (G). Figure 21 shows the region occupied by MTS antennas in a G-B
diagram, in comparison with other types of antennas.

The most recent achievement is the large bandwidth performance, i.e. pattern
stability in frequency [7]. Pattern bandwidth is limited by the dispersion-
induced mismatch between the SW wavelength and the periodicity of the IBCs
occurring when the operational frequency changes. By using a non-uniform
modulation period one can enlarge the bandwidth, at the price of a lower, but
still significant, antenna efficiency. This habilitates the designer to play
with high gain and reduced bandwidth or viceversa, thus, spanning the large
area of the diagram in Fig. 21. Overall, the bandwidth performance of these
antennas are quite robust with respect to alternative printed dipole
technology (i.e. single substrate patch arrays, reflectarrays, and
transmitarray) with single feed-point. Furthermore, reflectarrays or transmit-
MTSs are not really flat because of the presence of an external feeder.

Figure 21: MTS antenna area in a GB diagram in comparison with other types of
PCB antennas. The insets show the layout of antennas realized with high-gain
and small bandwidth (40dB, 5%) and large product bandwidth-gain (30 dB, 17%)

##### Emerging challenges

The main challenge for intelligent MTSs able to localize the network players
(e.g., access-points and users) is represented by the complexity of the
electronics. Two different architectures can be conceived to minimize it. The
first one is based on a dynamic configuration with active control switches.
The second one is based on a static configuration with overlapped holographies
and multiple receiving points. The two architectures are described next.

A. Uniform MTS with controllable switches and single pin

Any electrically small constituent element of the MTS is connected to a switch
that allows to change the particle status with two bits (zero-one). The
distribution of switches in status “on” is changed continuously maintaining a
density of half-wavelength. The distribution is able to re-design a holography
of “on” switches capable of sensing one direction of arrival at a time, so as
the SW coupled energy will be maximized at the single collector point ([6,
5]). The inclusions of the MTS are loaded with active devices or they include
phase changing materials, such as liquid crystals or vanadium dioxide. The
electric features of the inclusions become voltage controlled, and, hence, the
IBCs offered by the MTS can be properly adjusted by an external control.
However, this solution needs to be improved in terms of efficiency. In fact,
active devices or phase changing materials yield an increase of the antenna
losses, with a consequent reduction of gain and increase of power demand;
losses become more important when working at higher frequencies (e.g. Ka-
band): frequency scalability is indeed another future challenge. Also, phase
changing materials suffer of temperature instability. Alternative strategies
make use of optical pumping of silicon or gallium arsenide substrates to alter
the electrical properties of the inclusions. Losses become less critical when
dealing with a mechanical reconfiguration. The use of micromechanical systems
or piezoelectric devices have been proposed, but they may suffer of low
reliability and an intelligent MTS based on such devices might be too
sensitive to the external vibrations if installed on moving vehicles.

B. Multi-pin overlapped holographies

It has been demonstrated [3] that a MTS can be designed in such a way to
simultanously couple waves coming from different directions maximizing power
at individual collector points. This is done by a proper optimization of
overlapping contributions that maximize the power received from different
directions. This approach exhibits low-complexity, since no switches are
needed, and it offers the possibility of detecting simultaneously more
directions of arrival (DoA), distinguishing them by ports. However, the main
drawback with respect to the solution A is the smaller effective area of
collection for each DoA, which translates in a reduction of precision in the
DoA detection.

##### Future developments to satisfy these challenges

Advances in phase changing materials would bring a significant benefit to MTS
antennas in terms of efficiency, switching speed and temperature stability.
MTSs with integrated active devices, instead of discrete active devices, would
also bring advantages in terms of reliability, losses and performance.
Realizing integrated devices on a wide area, in turn, will require an
improvement of the accuracy of the realization processes.

##### Conclusion

SW based MTS antennas constitute an innovative concept for sensing the EM
smart environment in non-invasive, cognitive, and low-complexity manner.
Space-time tailoring of MTSs is obtained with active devices or phase changing
materials.

## References

  * [1] B. H. F. et al., “Scalar and tensor holographic artificial impedance surfaces,” _IEEE Trans. Antennas Propagat._ , vol. 58, no. 10, pp. 3212–3221, 2010.
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## Waveform-Selective Metasurfaces and Their Potential Applications in
Wireless Communications

### Hiroki Wakatsuchi1,2* and Sendy Phang3

####  1Department of Electrical and Mechanical Engineering, Graduate School of
Engineering, Nagoya Institute of Technology, Nagoya, Aichi, 466-8555, Japan

####  2Precursory Research for Embryonic Science and Technology (PRESTO),
Japan Science and Technology Agency (JST), Saitama 332-0012, Japan

####  2George Green Institute of Electromagnetics Research, Faculty of
Engineering, University of Nottingham, Nottingham NG7 2RD, UK

#### *Corresponding author<EMAIL_ADDRESS>
##### Introduction

In this Roadmap, we introduce recently developed waveform-selective
metasurfaces [1, 2] and explain how they potentially fit in emerging
issues/technologies in wireless communications. Composed of subwavelength
conducting elements connected by lumped circuits, waveform-selective
metasurfaces are capable of sensing a particular incident wave among others
even at the same frequency depending on their waveforms or, more specifically,
on their pulse widths. Such a waveform selectivity is made possible by
coupling electromagnetic resonant mechanisms of metasurfaces with transient
phenomena well known in classic direct-current (DC) circuits. Specifically,
diodes are used to rectify electric charges induced on conductors and to
generate an infinite set of frequency components including zero frequency. The
energy converted to zero frequency is then controlled by other lumped circuit
components such as capacitors and inductors over a time period much longer
than a cycle of an incident wave (see more detail in the literature [1, 3,
4]). Waveform-selective metasurfaces were so far reported to preferentially
sense various types of waveforms [3, 5] and vary their absorptances [1, 3, 6],
scattering parameters [4, 7], and polarization changes [4] at a normal/oblique
angle [8, 9] with/without tuning systems [4]. Besides conventional frequency
selectivity, such a waveform selectivity provides an additional degree of
freedom to address existing electromagnetic issues as discussed below.

Figure 22: (a) Waveform-selective metasurface and (b) its absorbing profile at
the “same” frequency of 4.2 GHz [1].

##### Applications proposed in the literature

A metallic enclosure composed of shielding conductor walls can be used to
protect sensitive electronic devices from strong electromagnetic fields. Such
an enclosure, however, is known to generate stronger internal fields than
external ones due to its cavity resonance [10]. This electromagnetic
interference issue can be readily mitigated by including an absorbing material
inside the enclosure [11]. However, this solution also weakens communication
signals generated from the inside of the cavity. A conducting cavity composed
of a waveform-selective transmitting metasurface simultaneously achieves a
strong shielding effect for a continuous wave and an enhanced transmission
effect that rather exploits the cavity resonance to transmit a short pulse for
a longer distance even at the same frequency [4]. In addition, waveform-
selective metasurfaces can be used to directly cover an antenna. This scheme
can be used to eliminate a coupling between individual antenna elements and
design advanced intelligent array systems [12]. Another interesting
application reported so far is seen in signal processing where a large
reflective screen consists of different types of pixelated waveform-selective
metasurfaces [13]. By mathematically solving the relationship between time-
varying multiple inputs and outputs, an incident signal can be restored as a
temporal ghost imaging. We also emphasise that waveform-selective metasurfaces
can control not only fundamental electromagnetic properties but also
communication characteristics such as bit-error-rates [3, 14]. In the
following part of this Roadmap, we particularly discuss how these metasurfaces
are aligned with emerging issues/technologies in wireless communications.

##### Potential applications in wireless communications

The number of wireless communication devices keeps increasing in modern
society. For instance, internet of things (IoT) devices are newly installed at
a pace of more than two billion a year over the world [15]. While these
devices enrich the quality of our life, a new technique is necessary for
accommodating such a vast number of devices within a single network and
ensuring concurrent connection. In this context, various multiaccess and
multiplexing techniques were proposed using frequency, space, time, etc as
their modulation variables [16, 17]. Waveform selectivity can potentially add
a new degree of freedom that is conceptually orthogonal to any of these
variables and thus contributes to enhancing network capacities and connection
performances. Another issue seen here is how advanced IoT systems composed of
an extremely large number of sensors are maintained if the sensors are highly
dispersed in space. In this case, ideally each sensor is expected to be free
of a battery for less maintenance and collect its driving energy from
surrounding electromagnetic fields [18]. Waveform-selective metasurfaces store
rectified energy in internal circuit components such as capacitors, which can
empower IoT sensors.

Also, the Fifth generation (5G) of mobile communications provide high-speed
communication services by using a quasi-millimeter wave band, which at the
same time narrows a coverage area, compared to that of a lower frequency band
around a few GHz. A promising solution to this issue is introducing wavefront-
shaping panels that reflect incident waves to non-line-of-sight devices [19].
Although such a reflection profile usually remains unchanged, a metasurface
combining a wavefront-shaping functionality with waveform selectivity enables
dynamic steering, thereby further increasing a coverage area. Moreover,
waveform selectivity can be more usefully exploited together with cloaks in
the generation of the post 5G, where the main frequency domain is supposed to
be in the THz regime. Especially, for indoor scenarios, surface waves may be
more often used to effectively send signals to distant receivers than ever
before as free-space wave propagation has a limited travelling distance range.
However, a practical design of wireless communication environment involves
inevitable scattering objects or columns. These scatterers can be bypassed by
using a cloak. Moreover, if the cloaking system is composed of waveform-
selective metasurfaces and contains an antenna, waveform-selective
communications and cloaking are simultaneously realised.

##### Conclusion

In conclusion, we have briefly covered recent studies on waveform-selective
metasurfaces that vary their responses depending on incident waveforms or
pulse widths. We explained their fundamental characteristics and applications
with a strong focus on wireless communications. Nevertheless, the concept of
waveform-selective metasurfaces is simple and versatile to be applied to other
existing electromagnetic issues as well.

## Acknowledgment

H.W. acknowledges support from the Japan Science and Technology Agency (JST)
under Precursory Research for Embryonic Science and Technology (PRESTO) No.
JPMJPR193A and the Japanese Ministry of Internal Affairs and Communications
(MIC) under Strategic Information and Communications R&D Promotion Program
(SCOPE) No. 192106007.

## References

  * [1] H. Wakatsuchi, S. Kim, J. J. Rushton, D. F. Sievenpiper, “Waveform-Dependent Absorbing Metasurfaces”, _Phys. Rev. Lett._ , 111, 24, 245501, 2013.
  * [2] G.V. Eleftheriades, “Protecting the Weak from the Strong”, _Nature_ , 505, 490, 2014.
  * [3] H. Wakatsuchi, D. Anzai, J. J. Rushton, F. Gao, S. Kim, D. F. Sievenpiper, “Waveform Selectivity at the Same Frequency”, _Sci. Rep._ , 5, 9639, 2015.
  * [4] H. Wakatsuchi, J. Long, D. Sievenpiper, “Waveform Selective Surfaces”, _Adv. Funct. Mater_ , 29, 11, 1806386, 2019
  * [5] H. Wakatsuchi, “Time-Domain Filtering of Metasurfaces”, _Sci. Rep._ , 5, 16737, 2015.
  * [6] H. Wakatsuchi, J. J. Rushton, J. Lee, F. Gao, M. Jacob, S. Kim, D. F. Sievenpiper, “Experimental Demonstration of Nonlinear Waveform-Dependent Metasurface Absorber with Pulsed Signals”, _Electron. Lett._ , 49, 24, 1530, 2013.
  * [7] H. Wakatsuchi, “Numerical Demonstration of Non-Reciprocal Waveform-Selective Metasurfaces”, _Electron. Lett._ , 55, 6, 312, 2019.
  * [8] H. Wakatsuchi, “Waveform-Selective Metasurfaces with Free-Space Wave Pulses at the Same Frequency”, _J. Appl. Phys._ , 117, 16, 164904, 2015.
  * [9] H. Wakatsuchi, F. Gao, S. Yagitani, D. F. Sievenpiper, “Responses of Waveform-Selective Absorbing Metasurfaces to Oblique Waves at the Same Frequency”, _Sci. Rep._ , 6, 31371, 2016.
  * [10] C. Christopoulos, _Principles and Techniques of Electromagnetic Compatibility_ , CRC Press Taylor & Francis Group, London, U.K., 2007.
  * [11] H. Wakatsuchi, J. Paul, C. Christopoulos, “Performance of Customizable Cut-Wire-Based Metamaterial Absorbers: Absorbing Mechanism and Experimental Demonstration”, _IEEE Trans. Antennas Propag._ , 60, 12, 5743, 2012.
  * [12] S. Vellucci, A. Monti, M. Barbuto, A. Toscano, and F. Bilotti, “Waveform-Selective Mantle Cloaks for Intelligent Antennas”, _IEEE Trans. Antennas Propag._ , 68, 3, 1717, 2020.
  * [13] M.F. Imania and D.R. Smith, “Temporal Microwave Ghost Imaging Using a Reconfigurable Disordered Cavity”, _Appl. Phys. Lett._ , 116, 054102, 2020.
  * [14] D. Ushikoshi, M. Tanikawa, K. Asano, K. Sanji, M. Ikeda, D. Anzai, H. Wakatsuchi, “Experimental Demonstration of Waveform-Selective Metasurface Varying Wireless Communication Characteristics at the Same Frequency Band of 2.4 GHz”, _Electron. Lett._ , 56, 3, 160, 2020.
  * [15] Ministry of Internal Affairs and Communications, Japan, Information and communications in Japan, White Paper 2020, (https://www.soumu.go.jp/johotsusintokei/whitepaper
/eng/WP2020/2020-index.html).

  * [16] L. Hanzo, S.X. Ng, T. Keller, and W. Webb, _Quadrature Amplitude Modulation: From Basics to Adaptive Trellis-Coded, Turbo-Equalised and Space-Time Coded OFDM, CDMA and MC-CDMA Systems_ , Wiley-IEEE Press, Chichester, U.K., 2004.
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  * [18] F. Erkmen, T.S. Almoneef, and O.M. Ramahi, “Scalable Electromagnetic Energy Harvesting Using Frequency-Selective Surfaces”, _IEEE Trans. Microw. Theory Techn._ , 66, 5, 2433, 2018
  * [19] N. Yu and F. Capasso, “Flat Optics with Designer Metasurfaces”, _Nat. Mater._ , 13, 139, 2014.


We present a new local-search algorithm for the $k$-median
clustering problem. We show that local optima for this algorithm
give a $(2.836+\epsilon)$-approximation; our result improves upon
the $(3+\epsilon)$-approximate local-search algorithm of Arya et
al. <cit.>. Moreover, a computer-aided analysis
of a natural extension suggests that this approach may lead to an
improvement over the best-known approximation guarantee for the

The new ingredient in our algorithm is the use of a potential
function based on both the closest and second-closest facilities to
each client. Specifically, the potential is the sum over all
clients, of the distance of the client to its closest facility, plus
(a small constant times) the truncated distance to its
second-closest facility.  We move from one solution to another only
if the latter can be obtained by swapping a constant number of
facilities, and has a smaller potential than the former. This
refined potential allows us to avoid the bad local optima given by
Arya et al. for the local-search algorithm based only on the cost
of the solution.

§.§ Acknowledgments

We thank Amit Kumar, Ola Svensson, and Justin Ward for fruitful
discussions. Special thanks to Guru Guruganesh, with whom we obtained
some early results on this problem. LH is supported by NSF Award IIS-1908774 and a
VMware fellowship. This work was conducted in part while LH was an
undergraduate at Tsinghua University visiting CMU and TTI-Chicago.

Supported in part by NSF awards CCF-1907820, CCF1955785, and CCF-2006953.

This work was [partially] funded by the grant ANR-19-CE48-0016 from the French National Research Agency (ANR).


# Backflipping motion of air bubbles colliding with a tilted wall

Alireza Hooshanginejad  Department of Biological and Environmental
Engineering, Cornell University, Ithaca, New York, USA.  School of
Engineering, Brown University, Providence, Rhode Island, USA.  Anuj Baskota
Department of Biological and Environmental Engineering, Cornell University,
Ithaca, New York, USA.  Sunghwan Jung<EMAIL_ADDRESS>Department of
Biological and Environmental Engineering, Cornell University, Ithaca, New
York, USA.

###### Abstract

Oblique collision of solid particles with surfaces has been a topic of
extensive study in Newtonian mechanics, which also explains the motion of
bubbles and droplets to some extent. Here, we observe that air bubbles exhibit
a backflipping behavior when they collide with a tilted surface. Our
experiments reveal that bubbles with radii 0.6-0.7 mm undergo backflipping
when they collide with surfaces at an angle of up to $15^{\rm{o}}$ with the
strongest backflipping at $3^{\rm{o}}$. Particle image velocimetry reveals
that the backflipping behavior is caused by wake-induced circulation around
the bubble, which applies a lift force on the bubble. We develop a theoretical
model that incorporates potential flow theory to characterize the circulation
caused by the interaction between the bouncing bubble and its wake. The
theoretical results are in good agreement with the experiments confirming the
key role of the wake-induced lift force in backflipping. Finally, we show that
the backflipping behavior of air bubbles can be leveraged for sustainable
cleaning of a biological surface coated with a protein solution.

The laws of collision proposed by Newton and other scientists of his era
including Wallis, Wren, and Huygens provide the foundation for our
understanding of elastic collision Birch (1756). In his famous book, the
Mathematical Principles of Natural Philosophy, Newton discussed about the
oblique collision of two spherical bodies that “if bodies are moving in
different right lines impinging obliquely one upon the other, … the parallel
motions are to be retained the same after reflexion as before Newton  _et al._
(1729).” According to Newton’s law of collision, during an oblique elastic
collision between a rigid ball and a solid surface, the angle of incidence
equals the angle of reflection Birch (1756). However, this is no longer true
for inelastic collisions of an elastic ball impinging obliquely on a smooth
surface Garwin (1969); Kharaz  _et al._ (2001). Despite the differences in
angles of incidence and reflection during inelastic collisions, the ball still
retains its motion along the parallel direction during reflection as long as
no spinning is enforced before collision Penner (2002); Vollmer and Möllmann
(2011); Cross (2015, 2018).

Collision of an air bubble with a solid surface is considered as an inelastic
collision due to the high deformation of the bubble during collision Zenit and
Legendre (2009). While the dynamics of air bubbles colliding with a flat
surface have been studied extensively Krasowska and Malysa (2007); Zenit and
Legendre (2009); Klaseboer  _et al._ (2014); Manica  _et al._ (2015); Zawala
(2016); Zawala  _et al._ (2016); Wang  _et al._ (2017), there are only few
studies on air bubbles colliding with a tilted surface Maxworthy (1991); Tsao
and Koch (1997); Podvin  _et al._ (2008); Norman and Miksis (2005); DeBisschop
_et al._ (2002); Barbosa  _et al._ (2019). Oblique collision of air bubbles
with tilted surfaces in an aqueous medium is of great recent importance due to
the urgent need for sustainable cleaning methods in the sanitization of
agricultural produce to reduce foodborne illnesses Jung and Eifert (2016); Lee
_et al._ (2018); Esmaili  _et al._ (2019); Hooshanginejad  _et al._ (2022a,
b). Although in the case of large surfaces, the shear stress associated with
steady sliding of bubbles determines the average shear force Hooshanginejad
_et al._ (2022b), the magnitude of the shear force associated with the
transient bouncing regime is much larger than the shear force during steady
sliding Esmaili  _et al._ (2019). Hence, bouncing bubbles offer a better
cleaning outcome for small contaminated areas. However, the downside of using
the bouncing phase in cleaning is the spatial gaps between the collision
points which leave the surface intact Hooshanginejad  _et al._ (2022b). Here,
we report an intriguing behavior by an air bubble of a certain size range,
where it bounces backward after its first collision with a tilted wall. We
show that this novel backward motion of the bubble does not follow Newton’s
laws of collision, which is due to the hydrodynamic interaction between the
bouncing bubble and its rising wake. While few studies have shown the
transverse motion of a bubble rising next to a vertical wall due to a
transverse lift force Takemura  _et al._ (2002); Takemura and Magnaudet
(2003), the backward motion of bubbles along a tilted surface has never been
explored to the best of our knowledge.

Figure 1:  (a) The schematic of the experimental apparatus. (b) At
$\theta=5^{\rm{o}}$, a bubble with radius $a=0.7$ mm bounces backward and
collides the surface below the first collision point. (c) At
$\theta=10^{\rm{o}}$, the bubble bounces backward, but ultimately collides at
a point above the first collision point. (d) At $\theta=20^{\rm{o}}$, the
bubble no longer undergoes backflipping. The corresponding videos are included
in Ref. Sup .

We perform experiments in a tank filled with deionized water to visualize the
bubble motion while colliding with a tilted smooth surface. We place a custom-
made needle at the bottom of the tank connecting the needle to a syringe pump
(New Era) through a 3D-printed mount and tubing as depicted in Fig. 1 (a). The
needle is made to generate bubbles of uniform radius at low pump flow rates
with a standard deviation of less than 0.02 mm. We then use a 3D-printed tower
that has a manual pulley design to hold a clean glass slide at the desired
inclined angle, $\theta$, on top of the needle as shown in Fig. 1 (a). The
distance between the needle and the lowest edge of the glass slide is
approximately 12 cm to ensure that the bubbles reach their terminal velocity
before collision. We use a high-speed camera (Photron SA-Z), a macro lens
(Nikkor 105 mm), an extension bellows (Nikon PB-6), and a 10x magnifying lens
(Neewer) to record the bubble behavior near the collision zone. We test three
different bubble radii, $a\simeq 0.6$, $0.65$, and $0.7$ mm. We note that
bubbles of the current size range have an oblate spheroid shape during the
rising phase, but retain a spherical shape after the collision. We also note
that all bubbles rise along a straight path as the associated Reynolds number
(i.e. ${\rm{Re}}=\rho U_{\rm{T}}a/\mu\sim 180-250$) is below the threshold of
path instability (i.e. $\rm{Re_{cr}}\sim 300-400$) Clift  _et al._ (2005).
Here, $\rho$ denotes the density of water, $\mu$ the dynamic viscosity of
water, and $U_{\rm{T}}$ the terminal velocity of the bubble. In addition to
different bubble sizes, we test different $\theta$, ranging from $0^{\rm{o}}$
to $20^{\rm{o}}$.

Figure 1(a) shows different trajectories of an air bubble with $a=0.7$ mm from
the first collision at $t=t_{0}$ to the second collision at $t=t_{\rm{1}}$. We
define a dimensionless time, $\tau=(t-t_{0})/(t_{\rm{1}}-t_{0})$, normalized
by its period between the two bounces (i.e., $t_{\rm{1}}-t_{0}$). At
$\theta=0^{\rm{o}}$, the bubble bounces normal to the surface (video 1 in Ref.
Sup ). As we tilt the surface at a low angle $\theta$, the bubble initially
bounces forward like an elastic collision, but then reverses and moves
backward until it collides with the surface at a location behind the first
collision spot, as shown in Fig. 1(b) for $\theta=5^{\rm{o}}$ (video 2 in Ref.
Sup ). We herein define the backward motion of the bubble as backflipping as
shown in Fig. 1(b). As we increase $\theta$ to $10^{\rm{o}}$, the bubble still
exhibits a backflipping behavior; however, the bubble collides on a point past
the first collision point, as shown in Fig. 1(c) (video 3 in Ref. Sup ). We
refer to such a backflipping motion of the bubble as weak backflipping.
Finally, at $\theta=20^{\rm{o}}$, the bubble no longer backflips as shown in
Fig. 1(d) (video 4 in Ref. Sup ).

Figure 2:  (a) Time sequential images of a bouncing bubble with $a=0.7$ mm at
$\theta=5^{\rm{o}}$ for $\tau=0-1$ (video 5 in Ref. Sup ). The yellow circle
following the particles on the bubble surface indicates a counterclockwise
circulation around the bubble. (b) The vorticity map from PIV around the
bubble at $\tau=0.3$ for a bubble with $a=0.7$ mm and $\theta=1^{\rm{o}}$
(video 6 in Sup ). (c) Schematic showing the use of a reference bubble rising
continuously to model the interaction between the bouncing bubble and its own
rising wake. (d) The average vorticity, $\overline{\omega}$, around the bubble
surface over time for $a=0.7$ mm, and $\theta=1^{\rm{o}}$.

To understand the key flow features associated with backflipping, we visualize
the flow around the collision zone by adding 10 $\mu\rm{m}$ hollow glass
particles to the tank and using a 100 milliwatt laser sheet (Laserland Co.) to
illuminate the bubble motion in a 2D plane. We leave the seeding particles to
rest in water; therefore, some particles aggregate on the surface of the
tilted glass wall. Figure 2(a) shows a bubble with $a=0.7$ mm colliding with a
surface at $\theta=5^{\rm{o}}$ from $\tau=0$ to $\tau=1$ (video 5 in Ref. Sup
). When the bubble collides with the surface, the particles on the surface
detach and follow the bouncing bubble. Specifically, these particles show a
signature of counterclockwise circulation around the bubble, as shown in Fig.
2(a). To characterize the circulation around the bubble, we perform more
rigorous particle image velocimetry (PIV) experiments. Figure 2(b) shows the
vorticity distribution, $\omega(X,Y)$, in a laboratory frame, $XY$, around a
bouncing bubble with $a=0.7$ mm, and $\theta=1^{\rm{o}}$ at $\tau=0.25$ (video
6 in Supplementary Materials Sup ). The vorticity colormap of Fig. 2(b) shows
that the bouncing bubble moves through a shear flow structure created in the
past, as illustrated in Fig. 2(c).

As the bubble approaches the surface for the first collision, it generates an
axisymmetric flow in its wake. Note that we neglect any unsteadiness in the
wake of the rising bubble as the current range of bubble size remains below
the threshold of vortex-induced path instability Haberman and Morton (1956);
Duineveld (1995). The circulation caused by the shear flow in the background
induces a lift force on the bubble that is always pointed towards the bubble’s
trajectory prior to the first collision. Figure 2(d) shows that the time-
averaged vorticity around the bubble surface, $\overline{\omega}(\tau)$, first
increases in time, and then decays. It is worth noting that
$\overline{\omega}$ starts to decay at the moment when the centroid of the
bubble crosses the central axis of the rising bubble. This is due to the
opposite direction of the shear flow over the bubble as depicted in the inset
schematic of Fig. 2(d).

We mathematically model the wake from the free rising phase of the bubble as a
potential flow. To find the wake-flow profile around the bubble at each time,
we consider an image bubble after collision. The image bubble continuously
rises with $U_{\rm{T}}$ behind the surface wall, hence separating from the
real bubble bounced upon collision. Then, the potential flow induced by the
rising image bubble represents the primary flow around the real bubble induced
by its own wake during the bouncing phase, as depicted in Fig. 3(a). We note
that we neglect the secondary flow from the reflection of the rising wake
flow. By approximating the bubble as a sphere, the velocity potential
associated with the image bubble yields
$\phi=-U_{\rm{T}}(a^{3}/2)Z/(r^{2}+Z^{2})^{3/2}$ where $r$ and $Z$ are the
radial and axial variables of a cylindrical coordinate moving with the
centroid of the image bubble also shown in Fig. 3(a). Therefore, the
tangential velocity $u_{\rm{s}}$ along the bubble surface is given at any
position of the bubble where $s$ denotes the circumferential length in the
$xy$ plane. The average circulation around the bubble is then given by
$\overline{\Gamma}=(1/2a)\varoiint u_{\rm{s}}dsdz$, where $z$ denotes the out-
of-plane coordinate as shown in Fig. 3(a). The lift force is correlated with
the circulation around the bubble as $\bm{F_{\rm{l}}}=(4\pi
a^{3}/3)C_{\rm{l}}\bm{\overline{\omega}}\times\bm{U}$ Legendre and Magnaudet
(1998) where $\bm{U}(\tau)$ denotes the velocity at the center of the bubble,
$\bm{\overline{\omega}}(\tau)=\overline{\Gamma}(\tau)/\pi a^{2}$ denotes the
average vorticity around the bubble, and $C_{\rm{l}}$ denotes the lift
coefficient that is kept constant following previous studies Tomiyama  _et
al._ (2002); Adoua  _et al._ (2009); Esmaili  _et al._ (2019). Further details
of the potential flow model are provided in Supplementary Material Sup .

Figure 3:  (a) The schematic for the potential flow model and the freely
rising image bubble. (b) The force balance schematic for the bouncing bubble.
(c) The bubble trajectory from the experiments and the model for $a=0.7$ mm,
and varying $\theta$. (d) The schematic showing geometrical parameters
characterizing the backflipping behavior. Comparison between the experiments
and the model for (e) $\lambda$ vs $\theta$, (f) $\eta$ vs $\theta$, and (g)
$h_{\rm{m}}$ vs $\theta$ at varying $a$. The error bars correspond to 5 trials
for each case.

We develop a simplified model for bubble motion from the first collision to
the second collision that incorporates the effect of wake-induced lift force
on bubble motion. Figure 3(b) shows the free-body diagram for the bouncing
bubble. We consider the buoyancy force, $\bm{F_{\rm{b}}}$, the drag force,
$\bm{F_{\rm{d}}}$, and the lift force, $\bm{F_{\rm{l}}}$, to be the primary
forces that affect the bouncing bubble. We also consider an added mass term
due to accelerating or decelerating motions of the bubble. After some
algebraic manipulations, the force balance in the $xy$ plane yields

$\frac{{\rm{d}}\bm{U}}{{\rm{d}}\tau}=\bm{S}\bm{U}+\bm{B},$ (1)

where $\bm{S}$ is a rank-two tensor corresponding to lift and drag forces as

$\bm{S}=\frac{1}{C_{\rm{m}}}\begin{bmatrix}-\frac{\pi}{4}{C_{\rm{d}}}\mu
a\rm{Re}&{C_{\rm{l}}}\overline{\Gamma}(\tau)\\\
-{C_{\rm{l}}}\overline{\Gamma}(\tau)&-\frac{\pi}{4}{C_{\rm{d}}}\mu
a\rm{Re}\end{bmatrix},$ (2)

and $\bm{B}$ denotes the body force vector associated with buoyancy effects,

$\bm{B}=\frac{g}{C_{\rm{m}}}\begin{bmatrix}\sin{\theta}\\\
\cos{\theta}\end{bmatrix}.$ (3)

Here, $C_{\rm{d}}$ and $C_{\rm{m}}$ denote the drag coefficient and the added
mass coefficient, respectively. The values of all coefficients are chosen
following previous studies Esmaili  _et al._ (2019); Hooshanginejad  _et al._
(2022b). Equation 1 is numerically solved with different values of $a$ and
$\theta$. We use the initial velocity as
$\bm{U}(t=0)=(U_{0}\sin{2\theta},U_{0}\cos{2\theta})$, where $U_{0}$ denotes
the initial speed of bouncing at $\theta=0^{\rm{o}}$ from the experiments for
each bubble size. Figure 3(c) shows the comparison of the bubble trajectory
between the model results and the experiments for $a=0.7$ mm with different
$\theta$. As indicated in Fig. 3(c), the simplified model qualitatively
matches the experiments in capturing strong backflipping, weak backflipping,
and no backflipping behaviors. To characterize the backflipping behavior more
quantitatively, we define a collision distance, $\lambda$, that denotes the
distance between the second collision and the first collision locations along
$x$. As demonstrated in Fig. 3(d), the negative value of $\lambda$ corresponds
to the strong backflipping behavior, while the positive value of $\lambda$
includes both weak backflipping and no backflipping behaviors. Figure 3(e)
shows $\lambda$ from theory for three different bubble sizes, $a=0.6$, 0.65,
and 0.7 mm at different $\theta$ ranging from $0^{\rm{o}}$ to $20^{\rm{o}}$ in
good agreement with the experiments. As shown in Fig. 3(e), the backflipping
behavior becomes pronounced as $\theta$ increases in the beginning and then
starts to decay until the bubble transitions to the weak backflipping regime.
We note that bubbles smaller than the presented range do not show any
backflipping behavior as a result of their weaker wake. In addition, bubbles
larger than the current range exhibit 2D or 3D rising motion before collision,
which makes controlling the collision angle extremely complicated.

Figure 4:  (a) A sample glass slide double-coated with a protein soil solution
before and after the test [$a=0.7$ mm, and $\theta=1^{\rm{o}}$]. The
processing area is marked with a green box centered by the first collision
point marked with the red circle. The scale bar represents 4 mm. (b) The
transmission factor, $I$, for varying $\theta$. $I=1$ refers to a completely
clean surface while $I=0$ refers to the original coated surface. The error
bars correspond to 3 trials for each case.

The weak backflipping regime cannot be differentiated from the no backflipping
regime with the parameter, $\lambda$. Hence, we define a new parameter,
$\eta$, as the maximum distance traveled backward along $x$ when $\lambda>0$
as illustrated in Fig. 3(d). We note that $\eta=0$ and $\eta>0$ correspond to
no backflipping and weak backflipping, respectively. Figure 3(f) shows the
model predictions for $\eta$ vs. $\theta$ for different $a$. Both the model
and the experiments show a decaying trend for $\eta$ in the weak backflipping
regime. In addition, as the bubble size decreases, both $\eta$, and the range
of $\theta$ for the weak-backflipping behavior decrease. While the model
predicts the threshold of the no backflipping behavior in good agreement with
the experiments, we note that the $\eta$ predictions from the model are
slightly smaller than the experiments for $a=0.7$ mm. This is presumably due
to the secondary effect of bubble deformations, which becomes pronounced as
the bubble size increases. Finally, Fig. 3(g) shows the maximum bouncing
height, $h_{\rm{m}}$, from the surface for both the experiments and the model
in good quantitative agreement. Overall, as $\theta$ increases, $h_{\rm{m}}$
decreases as the normal component of the collision velocity scales as
$U_{\rm{T}}\cos{\theta}$.

To test the efficacy of backflipping behavior in cleaning biological surfaces,
we run a series of experiments on surfaces coated with a protein solution. We
first double-coat glass slides with a protein soil solution using a spin-
coater Hooshanginejad  _et al._ (2022a). We then designate an area of 4
mm$\times$4 mm, and target its center for the first collision of the bubbles.
We continuously inject bubbles from the needle with a frequency of $\sim$20
bubbles per minute for 15 minutes (i.e. $\sim$ 300 total bubbles). We use a
white LED background to image the clean surface before coating, the coated
surface before the test, and the surface after the test. The average values of
the grayscale images corresponding to each are denoted with $I_{0}$, $I_{1}$,
and $I_{2}$, respectively. Then, we define the normalized intensity as
$I=(I_{2}-I_{1})/(I_{2}-I_{0})$ as the efficacy of the cleaning experiments.
Figure 4(b) shows that the best cleaning efficacy (i.e. maximum $I$) happens
for $a=0.7$ mm, and $\theta=3^{\rm{o}}$ which coincides with the maxima in
$\lambda$ shown in Fig. 3(d). Further details about the cleaning test method
are included in the Supplementary Material Sup .

As bubbles bounce backward in the strong backflipping regime, more surface
area is exposed to bubbles and gets cleaned due to the shear forces.
Therefore, the cleaning efficacy are more pronounced in the target area when
the bubbles backflip. The backflipping phenomenon can be used in the design of
sustainable devices for sanitizing surfaces where an array of nozzles can be
used to target different points on the surface. As discussed above, the key to
getting backflipping bubbles is to control the bubble size and collision
angle. It is noteworthy that the wake-induced circulation discussed here is
not exclusive to the current system and can have potential applications in
other systems where redistributing particle aggregates on a surface is of
interest.

The authors thank B. Cooke, T. J. Sheppard, and P. Xu for their help in making
the spin coater and surface coatings. We also thank D. Koch, R. Zenit, and J.
Magnaudet for fruitful discussions. The authors acknowledge funding from the
National Science Foundation under Grants No. CBET-1919753, and No.
CBET-2042740.

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