Previous Webinars:

Seminar 38-S2: Applications of K-Theory in Materials Science

Speaker: Emil V Prodan (Physics Department, Yeshiva University, New York, USA)


Q & A:

Round Table

Abstract: Heisenberg formulation of quantum mechanics puts a focus on the physical observables which are organized as operator algebras. This approach and point of view has recently penetrated into metamaterials science. The goal of this talk is to explain this statement and to demonstrate the power of the theoretical tools that comes from the field of operator algebras, such as K-theory. As we shall see, the dynamical matrices of various classes of metamaterials generate specific topological algebras that can be computed explicitly. This will be exemplified using the class of periodic metamaterials, then that of quasi-periodic metamaterials and, lastly, that of metamaterials symmetric to a full space group. The talk will then introduce the notions of complete topological invariants and of stable homotopy. The equivalence class of a band projection with respect to the stable homotopy defines the complete topological invariant that can be associated with that projection and these equivalence classes lead to the K-group of the algebra of dynamical matrices. The last part of the talk exemplifies the K-groups for classes of metamaterials mentioned above. As we shall see, once the K-groups and their generators are known, one can produce a complete list of topological models which supply all topological phases supported by a particular class of metamaterials. Additional ways of using the K-groups will be presented.

Biography: Emil received BS and MS degrees in theoretical and mathematical physics from University of Bucharest. His advisor for the MS degree was mathematical physicists Gheorghe Nenciu. He received another MS degree in theoretical physics from University of Houston and then he graduated with a PhD from Rice University in theoretical physics. His advisor at Rice University was Peter Nordlander and his doctoral thesis was on large-scale quantum simulations of the plasmon response of nano-particles. Emil received further postdoctoral training at University of California Santa Barbara under the direction of Walter Kohn, a Nobel Laureate in theoretical chemistry. He was a fellow of the Princeton Center for Complex Materials at Princeton University, where he was sponsored by Roberto Car (2009 Dirac Medal) and Duncan Haldane (2016 Nobel Prize in Physics). Emil joined the Physics Department of Yeshiva University in 2007 and now he is a full professor of physics. While at Princeton, Emil witnessed Haldane’s effort on extending the concept of topological modes to photonic crystals, and he start working on the mechanical analog of the concept. The outcome, published in 2009 and co-authored with Camelia Prodan, was that Lagrangian systems containing q-dot-p terms can host Chern physics, a prediction confirmed experimentally in 2015. In about the same time, Emil’s research was profoundly influenced by the works of Jean Bellissard, who pioneered methods of analysis based on operator algebras, K-theory and non-commutative geometry. These days, together with many other enthusiasts, Emil is using these methods for search-and-discovery in materials science. He is also advertising what he calls Mathematical Engineering, where deep and utterly abstract concepts from pure mathematics are made concrete and applied, with a focus on advancing the technological progress rather than on just explaining observed phenomena.

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Seminar 37-S2: Maze balls and phoxonic metamaterials

Speaker: Oliver B. Wright (Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan)


Q & A:

Abstract: Controlling sound or light with metamaterials is a booming and illuminating field of research. Here we present two studies involving metamaterial structures. In the first study we propose an octagonal onion-like structure with interconnected labyrinthine shells that can reflect sub-kHz airborne sound when placed inside a cylindrical tube. The structure, fabricated by 3D printing, is found to stop 67% of the incident sound on resonance with a volume filling fraction of only 13%. In the second study we propose a new kind of metamaterial that is simultaneously acoustic and electromagnetic, which may have use as a new kind of wave modulator. Our design, verified by numerical simulation, is demonstrated in the audio acoustic and microwave electromagnetic range.
[1] ‘Compact acoustic metamaterial based on the 3D Mie resonance of a maze ball with an octahedral structure’, T. Zhang, E. Bok, M. Tomoda, O. Matsuda, J. Guo, X. Liu, and O. B. Wright, Appl. Phys. Lett. 120, 161701 (2022).
[2] ‘Simultaneously photonic and phononic metamaterials’, O. B. Wright, M. Tomoda, O. Matsuda, T. Zhang, and T. Ueda, Proc. AES 2022 Marrakesh – Morocco, The 8th International Conference on Antennas and Electromagnetic Systems, p. 236-7

Biography: Oliver B. Wright received his B.A. in physics at University College, Oxford and his Ph.D. in low-temperature solid-state physics at the Cavendish Laboratory, Cambridge. In 1982 he continued this research at CRTBT, C.N.R.S. in Grenoble, France. In 1984 he joined Schlumberger to work on optical sensors in Montrouge, Paris. In 1986 he moved to Nippon Steel Corporation, working as a Senior Researcher at their Electronics Research Laboratories, Sagamihara, Japan, mainly in the field of non-destructive characterization of materials using laser acoustic techniques and electromagnetic acoustic transducers. In 1994 he worked on related topics at C.N.R. Istituto di Acustica in Rome and in 1995 at C.N.R.S. in Besançon, France. Since 1996 he has been working as a professor in the Faculty of Engineering at Hokkaido University in Sapporo, Japan, specializing in particular on laser picosecond ultrasonics, surface acoustic wave imaging and acoustic metamaterials. In 2013 he founded the company Plum Science that makes novel waveguide-based desk lights and stand lights, on sale in many countries.

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Seminar 36-S2: Bessmertny ̆ı Realizations, Representations, and Related Problems in Multiphase Composites

Speaker: Aaron Welters (Department of Mathematical Sciences at Florida Institute of Technology, Melbourne, FL, USA)


Q & A:

Abstract: We discuss multivariate functions that can be represented as the Schur complement of a lin- ear (matrix-, tensor-, or operator-valued) pencil, i.e., the class of Bessmertny ̆ı realizable functions. We motivate this by showing that for multiphase composites, both the effective operator in the theory of composites as well as the DtN map for an electrical network are in this class in which the associated linear pencil is of positive semidefinite type. This naturally leads to multivariate (matrix-, tensor-, or operator-valued) Herglotz-Nevanlinna functions in this class and several open problems in realizability theory. Next, we present Bessmertny ̆ı realizations as the “universal” state- space model/realization [compared to others common in electrical engineering (e.g., Kalman-type, Fornasini-Marchesini, Givone-Roesser) that are just a special cases of the Bessmertny ̆ı realization]. Then we discuss our recent work1,2 on extensions of the Bessmertny ̆ı realization theorem for multivari- ate rational functions, Schur complement algebra and operations, and their application in symmetric determinantal representations of polynomials. Finally, we will show how the latter relates to the open realization problems above. This is based on joint work with Anthony Stefan (Florida Institute of Technology).

[1] A. Stefan, A. Welters. Complex Anal. Oper. Theory 15, pp. 1–74 (2021).

[2] A. Stefan, A. Welters. Linear Algebra Appl. 627, pp. 80–93 (2021).

Biography: Dr. Aaron Welters is an Assistant Professor in the Department of Mathematical Sciences at the Florida Institute of Technology. He received his Ph.D. in Mathematics from University of California at Irvine in 2011. During 2011-2012, he was a VIGRE Postdoctoral Researcher in the Department of Mathematics at Louisiana State University where he was part of the Mathematics of Material Science research group. From 2012-2014, he was an Applied Mathematics Instructor in the Department of Mathematics at Massachusetts Institute of Technology. He joined Florida Institute of Technology in 2014. His research interests include mathematical physics and applied mathematics with a focus on electromagnetics, material science, and dissipative systems. His research has been supported by the Air Force Office of Scientific Research (AFOSR) and, in particular, through the Air Force’s Young Investigator Research Program (YIP).

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Seminar 35-S2: Topological plasmonics: Ultrafast vector movies of plasmonic skyrmions and merons on the nanoscale

Speaker: Harald Giessen (4th Physics Institute, University of Stuttgart, Germany)

Abstract: We introduce a new technique, time-resolved vector microscopy, that enables us to compose entire movies on a sub-femtosecond time scale and a 10 nm scale of the electric field vectors of surface plasmon polaritons. Depending on the shape and geometrical phase, in combination with the helicity of the excitation beam, topological plasmonic quasiparticles are created: skyrmions, merons, as well as quasicrystalline excitations. We observe their complete field vector dynamics at subfemtosecond time resolution.

B. Frank et al., Science Advances 3, e1700721 (2017).
G. Spektor et al., Science 355, 1187-1191 (2017).
T. Davis et al., Science 367, eaba6415 (2020).

Biography: Harald Giessen (*1966) graduated from Kaiserslautern University with a diploma in Physics and obtained his M.S. and Ph.D. in Optical Sciences from the University of Arizona in 1995 as J.W. Fulbright scholar. After a postdoc at the Max-Planck-Institute for Solid State Research in Stuttgart he moved to Marburg as assistant professor. From 2001-2004, he was associate professor at the University of Bonn. Since 2005, he is full professor and holds the Chair for Ultrafast Nanooptics in the Department of Physics at the University of Stuttgart. He is also co-chair of the Stuttgart Center of Photonics Engineering, SCoPE. He was guest researcher at the University of Cambridge, and guest professor at the University of Innsbruck and the University of Sydney, at A*Star, Singapore, as well as at Beijing University of Technology. He is associated researcher at the Center for Disruptive Photonic Technologies at Nanyang Technical University, Singapore. He received an ERC Advanced Grant in 2012 for his work on complex nanoplasmonics. He was co-chair (2014) and chair (2016) of the Gordon Conference on Plasmonics and Nanophotonics. He was general chair of the conference Photonics Europe (Strasbourg 2018) and is co-chair of the biannual conference NanoMeta in Seefeld, Austria. He is on the advisory board of the journals “Advanced Optical Materials”, “Nanophotonics: The Journal”, “ACS Photonics”, “ACS Sensors”, and “Advanced Photonics”. He is a topical editor for ultrafast nanooptics, plasmonics, and ultrafast lasers and pulse generation of the journal “Light: Science & Applications” of Nature Publishing Group. He is a Fellow of the Optical Society of America. In 2018, 2019, 2020 and 2021, he was named „Highly Cited Researcher“ (top 1%) by the Institute of Scientific Information. In 2021, he was elected as a Full Member into the Honor Society Sigma Xi. In 2021, he was awarded the Gips-Schüle Research Prize together with Simon Thiele and Alois Herkommer for his pioneering work on 3D printed microoptics. His research interests include Ultrafast Nano-Optics, Plasmonics, Metamaterials, 3D Printed Micro- and Nano-Optics, Medical Micro-Optics, Miniature Endoscopy, Novel mid-IR Ultrafast Laser Sources, Applications in Microscopy, Biology, and Sensing.

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Seminar 34-S2: A new look on periodic homogenization methods towards generalized continua and applications to architectured materials

Speaker: Jean-François Ganghoffer (Université de Lorraine, France)


Q & A:

Abstract: The seminar aims to provide a classification of generalized continua constructed by a micromechanical approach, relying on an extension of Hill macrohomogeneity condition for the micromorphic effective medium. Starting from the Cauchy balance equations holding at the microscopic level, equilibrium equations for a micromorphic effective medium are derived. The construction of the static macroscopic variables conjugated to the introduced macroscopic kinematic degrees of freedom relies on the additive decomposition of the microscopic displacement into a homogeneous part and a fluctuation. The homogeneous part represents in an exact manner the effective micromorphic medium, and the fluctuation corrects for its deviation from the initially heterogeneous periodic medium. The homogenized micromorphic constitutive law is derived based on suitable variational principles and the solution of the so-called unit cell BVP’s. Examples of architected media representative of some of the constructed effective generalized media illustrate the proposed homogenization method. An enhanced Timoshenko microstructured beam model is constructed, exhibiting couplings between different deformation modes induced by the response of its underlying tetrachiral microstructure. The ranking of the different effective media with respect to the small-scale parameter (ratio of lattice size to a macroscopic dimension) is established, based on the asymptotic expansion of the homogeneous part of the microscopic displacement.

Alavi et al. J. Mech. Phys. Solids, Vol. 153, 104278 (2021).
H. Reda, et al, 2021. Homogenization towards chiral Cosserat continua and applications to enhanced Timoshenko beam theories. Mechanics of Materials, 2021. In print.

Biography: Jean-François Ganghoffer received a PhD degree from Ecole des Mines (Nancy, France) in 1992, after a joined international collaboration (PICS) with the Dpt of Mechanical Engineering at Linköping University of Technology (Sweden). His research activities were devoted to the micromechanics of solid-solid phase transformations and Nickel based superalloys. In 1992, he was involved as a post-doctorand student in an international project (PICS CNRS) with the INM Institute in Saarland University on the setting up of constitutive models for structural relaxation in glass, implemented in the FE code Sysweld. From 1992-2000, he held a researcher position in CNRS, France, where he carried out research activities in the fields of adhesion, damage and fracture mechanics. He spent one year (1996) in Civil Engineering at TU Delft, where he carried research on the mechanics of generalized continua. He joined ENSEM (Nancy, France) as a full Professor in 2000. He has been invited to delivers lectures in more than 40 internatioal conferences. He has organized about 25 conferences or Minisymposia in international conferences. He is the frequent referee in more than 25 journals. He has published about 250 papers and 25 book chapters. He has received the Beltrami international prize given by MeMoCS in 2017 (

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Seminar 33-S2: Metallic or Dielectric Metasurfaces? Which one is better?

Speaker: Mohsen Rahmani (Advanced Optics & Photonics Laboratory, Department of Engineering, School of Science & Technology, Nottingham Trent University)


Q & A:

Abstract: Metasurfaces are an array of periodic subwavelength nanostructures that resonantly couple to the incident light. Such nanostructured surfaces can reproduce the functions of bulk optics, and on occasions, offer new functionalities that are not possible with conventional diffractive optics. Metallic metasurfaces, employing resonant oscillation of surface-plasmons, can confine light in the nanoscale gaps, so-called hot spots, with extreme sensitivity to the refractive index of the environment. However, the price of such characteristics is the high ohmic losses of metallic nanoparticles. On the other hand, high-index dielectric and semiconductor metasurfaces are lossless. They can stimulate Mie resonances in a multipolar fashion, applicable to both linear and nonlinear regimes, although they produce much weaker hot spots. The benefits of metallic or dielectric metasurfaces have been a subject of debate in the last decade. In this seminar, I review my journey in employing metallic to dielectric and semiconductor metasurfaces in both linear and nonlinear regimes. I will discuss the benefits of each of them for certain applications ranging from ultra-sensitive detection to near-infrared imaging.

Biography: Mohsen Rahmani is a Professor at Nottingham Trent University. His research activities span over light-matter interactions with various subwavelength nanoparticles for applications in flat optics, near-infrared imaging, bio-sensing, etc. He obtained his PhD from the National University of Singapore in 2013, followed by a postdoc fellowship at Imperial College London and the Australian Research Council Early Career Fellowship at the Australian National University (ANU). In 2020, he moved to Nottingham Trent University as a Royal Society Wolfson Fellow, followed by the UK Research and Innovation Future Leaders Fellowship. Rahmani has published more than 70 peer-reviewed journal papers (H-index=36). He is the recipient of several prestigious awards and prizes, including the Australian Eureka Prize, Early Career Medal from the International Union of Pure and Applied Physics, and the Australian Optical Society Geoff Opat Award.

About the University/College: Nottingham Trent University (NTU), in the UK, is creating the University of the future. Through our Research Peaks, Centres and Themes, we’re delivering ground-breaking research that has a profound real-world impact on individuals, communities, businesses and policies. NTU has the third largest number of postgraduate students in the UK studying professional qualifications, and we have over 320 experts working across 52 distinct areas of research and analysis. NTU has a growing reputation for research excellence and has recently been ranked 14th in REF2021 General Engineering based on overall Grade Point Average. We were awarded the Queen’s Anniversary Prize for our outstanding research (2021 and 2015), the Guardian University of the Year 2019, Times Good University Guide Modern University of the Year 2018 and the Times Higher University of the Year 2017.

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Seminar 32-S2: Asymptotic analysis of time-dependent subwavelength resonators

Speaker: Erik O. Hiltunen (Yale University, USA)


Q & A:

Abstract: We study wave propagation inside metamaterials consisting of high-contrast subwavelength resonators whose material parameters oscillate periodically in time. The main result is a capacitance matrix characterization of the band structure, which generalizes previous recent work on static subwavelength metamaterials. This characterization provides both theoretical insight and efficient numerical methods to compute the dispersion relationships of time-dependent structures. We exemplify this in several structures exhibiting interesting wave manipulation properties. Specifically, the time-modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may induce exceptional points or open into non-symmetric, unidirectional band gaps.

Biography: Dr. Erik O. Hiltunen is a Gibbs Assistant Professor at Yale University, USA. Dr. Hiltunen’s research focuses on developing the mathematical understanding of wave propagation in materials governed by local or non-local PDEs, using tools from PDE theory, harmonic analysis, and solid-state physics. Before moving to Yale, Hiltunen earned his PhD from ETH Zurich under the supervision of prof. Habib Ammari, where his dissertation was recently awarded the ECCOMAS award for best PhD theses on Computational Methods in Applied Sciences.

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Seminar 31-S2: Mie-resonant metaphotonics and metasurfaces

Speaker: Yuri Kivshar (Nonlinear Physics Centre, Australian National University, Canberra, Australia)


Q & A:

Abstract: Recently emerged field of Mie-resonant metaphotonics (also called “Mie-tronics”) employs the resonances in high-index dielectric nanoparticles and dielectric metasurfaces aiming for novel applications of subwavelength optics and photonics. High-index subwavelength resonant dielectric structures benefit from low material losses, and they provide a simple way to realize optically induced magnetic response which enables efficient devices outperforming the capabilities of bulk components. Here I plan to discuss the physics of Mie resonances, optical structures employing such resonances, and their link to photonic bound states in the continuum. Also, I aim discussing some applications of these resonances and dielectric metasurfaces.

Biography: Yuri Kivshar is a world leader in photonics and metamaterials, and one of the founders of the field of all-dielectric resonant metaphotonics governed by the physics of Mie resonances in dielectric nanoparticles with high refractive index. He is Fellow of the Australian Academy of Science, OSA, APS, SPIE, and IOP.

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Seminar 30-S2: Hybrid Quantum Photonics Empowered by Metamaterials and Plasmonics

Speaker: Vladimir M. Shalaev  (School of Electrical and Computer Engineering, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute, Purdue University, USA)


Q & A:

Abstract: We discuss how various ideas and notions from the field of metamaterials can benefit the emerging area of quantum science and technology. Specifically, we show that the enhancement and speedup enabled by plasmonic metamaterials open up a means to outpace dephasing and thus make quantum systems immune to decoherence. We also discuss new opportunities for SiN quantum photonic circuitry enabled by our recent discovery of single-photon sources in this technologically important material platform. Our findings spark further studies of quantum emitters toward deeper understanding of their nature, deterministic formation, and scalable integration with on-chip quantum photonic circuitry. We also demonstrate how hybrid quantum sensors with record-high sensitivity can be developed, by employing spin qubits controlled by light and coupled via magnons. The important role of machine-learning designs for quantum photonic circuitry will be also discussed.

Biography: Scientific Director for Nanophotonics at Birck Nanotechnology Center and Distinguished Professor of Electrical and Computer Engineering at Purdue University, specializes in nanophotonics, plasmonics, optical metamaterials and quantum photonics. Prof. Shalaev has received several awards for his research in the field of nanophotonics and metamaterials, including the APS Frank Isakson Prize for Optical Effects in Solids, the Max Born Award of the Optical Society of America for his pioneering contributions to the field of optical metamaterials, the Willis E. Lamb Award for Laser Science and Quantum Optics, IEEE Photonics Society William Streifer Scientific Achievement Award, Rolf Landauer medal of the ETOPIM (Electrical, Transport and Optical Properties of Inhomogeneous Media) International Association, the UNESCO Medal for the development of nanosciences and nanotechnologies, and the OSA and SPIE Goodman Book Writing Award. According to Google Scholar, his h-index is 112 with over 60,000 citations in total to his publications. He is a Fellow of the IEEE, APS, SPIE, MRS and OSA.


Seminar 29-S2: Nonlinear Helmholtz equations with sign-changing diffusion coefficient

Speaker: Zoïs Moitier  (Department of Mathematics, Karlsruhe Institute of Technology, Germany)


Q & A:

Abstract: In this talk, we are interested in the combine effect of metamaterial and Kerr non-linearity. More precisely, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains of the form −div(σ(x) ∇u)−λ u=u3−div(σ(x)∇u)−λu=u3. Using weak T-coercivity theory, we can establish the existence of an orthonormal basis of eigenfunctions of the linear part −div(σ(x) ∇u)−div(σ(x)∇u). Then, all eigenvalues are proved to be bifurcation points, and we investigate the bifurcating branches both theoretically and numerically. As a fundamental example, we look at some one-dimensional model, we obtain the existence of infinitely many bifurcating branches that are mutually disjoint, unbounded, and consist of solutions with a fixed nodal pattern.

Biography: I am a postdoctoral researcher under the supervision of Rainer Mandel in the department of mathematics of the Karlsruhe Institute of Technology (Germany). Before that, I was a postdoctoral researcher under the supervision of Camille Carvalho in the departement of applied mathematics at the University of California, Merced (USA). I did my PhD student under the supervision of Stéphane Balac and Monique Dauge in the numerical analysis IRMAR team at the University of Rennes 1 (France).


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Seminar 28 – S2: Non-Hermitian elastodynamics without gain and loss

Speaker: Gal Shmuel (Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Israel)


Q & A:

Abstract: Exceptional points are singular states of non-Hermitian systems that generate counterintuitive physics, such as unidirectional transmission and negative refraction. The common approach to access them is by designing parity-time symmetry, which requires a challenging balance between material gain and loss. In this talk, I will show how the unique nature of elastodynamics can be harnessed to mimic gain and loss, generate exceptional points and exotic non-Hermitian wave phenomena, using nothing more than isotropic elastic layers.
If time permits, I will briefly show another special feature of elastodynamics, when considering piezoelectric composites. I will show that these composites have effective coupling that does not exist at the microscale, in addition to the Willis coupling. This so-called electromomentum coupling reflects another knob to design the dynamics of the medium, and must be included in order to obtain a physical constitutive description.

Biography: Gal Shmuel is an associate professor at the Faculty of Mechanical Engineering, Technion, Israel. Shmuel’s group studies the mechanics of active-, soft- and heterogeneous media. He is the 2021 ERC consolidators grant recipient for his current focus on metamaterials in elastodynamics. His recent contributions include the discovery of the electromomentum coupling in piezoelectric metamaterials, and more generally cross-coupling of Willis type in active composites; and the realization of exceptional points and non-Hermitian phenomena in conservative elastodynamics.

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Seminar 27 – S2: Tunability of electrically controlled piezoelectric phononic crystals

Speaker: Anne-Christine Hladky-Hennion (Univ. Lille, CNRS, Centrale Lille, Univ. Polytechnique Hauts-de-France, Junia, UMR 8520 – IEMN, F-59000 Lille, France)


Q & A:

Abstract: Phononic Crystals (PCs) (i.e. periodic arrangements of several materials) have received a great deal of interest for the last two decades because of the unusual properties that they can exhibit. Classically, depending on material properties and geometrical arrangement, PCs can produce band gaps, i.e. frequency ranges where the propagation of waves is forbidden (i.e. waves are evanescent). These Bragg band gaps offer several potential applications such as sonic insulators or filters, from the kHz to the GHz range depending upon the spatial periodicity.
In this presentation, the general case of PCs made of piezoelectric materials is studied where the band gaps may be tuned by changing the electrical boundary conditions. First, a stack of piezoelectric rods, poled along their thickness is considered [S. Degraeve et al, J. Appl. Phys. 115, 194508 (2014)]. This device exhibits Bragg gaps that depend on the electrical boundary conditions chosen on periodically placed electrodes. An analytical model is developed that is compared to finite element results, validating the model. Depending on the electrical boundary condition, tunability is clearly demonstrated, i.e. an increase or a decrease of the width and the position of the stop bands. Ultrasonic experiments are presented, showing a good agreement with the theoretical predictions. Then, more complex control involving space-time modulation of electrical boundary conditions give access to tuning/control of nonlinear physical effects such as non reciprocity [C. Croenne et al, Appl. Phys. Lett. 110(6), 061901 (2017)].
The second part of this presentation concerns the extension of this concept to surface acoustic waves (SAW). In fact, SAW devices are constituted of piezoelectric phononic crystals due to the periodicity of the metallization patterns. We have shown that their working frequencies can be modified by a change of the electrical conditions on the electrodes that constitute the mirrors of a single-port SAW resonator. Numerical as well as experimental results are presented that underline a shift of the resonance frequency by a change of the electrical condition. It allows the development of new strategies for tunable components, compatible with RF microfabrication.

Biography: Anne-Christine Hladky-Hennion was awarded the diplome d’ingenieur (five-year engineering degree) of the Institut Superieur de l’Electronique et du Numérique in 1987 and the Ph D degree in materials science from the Universite des Sciences et Technologies de Lille in 1990. She is currently a principal scientist at the CNRS and at the Institute of Electronics, Microelectronics and Nanotechnology (IEMN UMR 8520 CNRS), France. Her main research interest is the study of phononic structures and acoustic metamaterials and particularly tunable piezoelectric metamaterials. She received the Silver Medal of CNRS in 2018 for her research activities on acoustic metamaterials, and the French Medal of the French Acoustical Society (SFA) in 2019.


Seminar 26 – S2: Mixed methodology approach for ergonomic and multiphysical characterisation of metamaterials

Speaker: Gioia Fusaro (Department of Industrial Engineering, University of Bologna)


Q & A:

Abstract: Metamaterials have paved so far the way towards higher freedom of design of building’s features as their physical characteristics depend on the geometry rather than the constituent material. At this point, the research has reached an overall assessment of such innovative materials and applications are now arising within the engineering field. However, many building engineering applications have to address multiple physical constraints and mechanical responses while being tailored for ergonomic management by the final users. At this moment there is no clear indication of how these systems may interact with i) different environmental conditions and ii) different indoor and outdoor functions of the building. In this talk, I will first highlight our recent work to draw a new experimental method outlying the impact of metamaterials on the user’s perception through both ergonomics, psychoacoustics, and soundscape. In the second part of the presentation, I will introduce a new method in development to include different environmental conditions (in terms of temperature for example) to this ergonomic/human perception approach. Such methods could be used to make metamaterials more affordable from the engineers, designers, industries, and users’ point of view with a significant improvement in the industrial design applicability.

Biography: Dr Gioia Fusaro graduated from the Sheffield School of Architecture, Acoustics Group (UK) and Institute of High Performance Computing (IHPC), A*STAR Institute (Singapore). She is currently a Postdoctoral Research Fellow at the University of Bologna, Industrial Engineering Department, Applied Physics Research Group. She is a Fellow of the Higher Education Academy (UK). Her main interests in research are building and environmental acoustics, materials and metamaterials, ergonomics, and industrial design, and social sciences. Her master’s degree background is in Building Engineering (the University of Perugia, IT) and before starting her PhD, she worked for local architectural and engineering companies, keeping on the collaboration with Italian and international research centres. She is a Chartered Building Engineer and Architect. She is a member of UKAN (UK Acoustics Network) and YAN (Young Acousticians Network) of EAA (European Acoustics Association).
Coming from a Building Engineering background, through her PhD she managed to broader her knowledge in the social science field and the implication of architectural design on the final users (either if this is a single person or a community). On the other hand, through a 2 years’ attachment to the IHPC in Singapore, she gained more experience in the AMMs field from both analytical, numerical, and experimental sides and including multiphysical and architectural application aims. At this stage of her career, she is trying to develop a more inclusive methodology to use metamaterials of various physical effects in the building design with benefits from the applied physics, architectural, ergonomics and social points of view.

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Seminar 25 -S2: Energetic and geometric variational principles for computational homogenization and applications

Speaker: Cédric Bellis (Aix Marseille Univ, CNRS, Centrale Marseille, LMA, Marseille, France)


Q & A:

Abstract: The homogenization of periodic elastic composites can be addressed through the reformulation of the local equations of the mechanical problem into energetic variational principle. We review such principles and describe a computational, FFT-based, approach that has shown effective on a variety of problems. Building on these tools, we propose a novel geometric variational formulation of the problem. This relies on the definition of Hilbert spaces of kinematically and statically admissible tensor fields, whose orthogonality and duality properties will be recalled. These are endowed with specific energetic scalar products that make use of a reference and uniform elasticity tensor. The corresponding strain and stress Green’s operators are introduced and interpreted as orthogonal projection operators in the admissibility spaces. In this context and as an alternative to classical minimum energy principles, two geometric variational principles are investigated with the introduction of functionals that aim at measuring the discrepancy of arbitrary test fields to the kinematic, static or material admissibility conditions of the problem. By relaxing the corresponding local equations, this study aims in particular at laying the groundwork for the homogenization of composites whose constitutive properties are only partially known or uncertain. The local fields in the composite and their macroscopic responses are computed through the minimization of the proposed geometric functionals. To do so, their gradients are computed using the Green’s operators and gradient-based optimization schemes are discussed. A FFT-based implementation of these schemes is proposed and they are assessed numerically on a canonical example for which analytical solutions are available.

Biography: After a MSc in Mechanical Engineering at the École Normale Supérieure, Cachan (France) and a MSc in Applied Mathematics at the University of Paris 6, Cedric Bellis obtained in 2010 a joint PhD in Mechanics & Civil Engrg at the École Polytechnique (France) and the University of Minnesota. He then held a postdoctoral position at Columbia University before joining the Laboratory of Mechanics and Acoustics, Marseille (France) as a CNRS Research Scientist. He is also an associate professor at the Dept of Mechanics of Ecole Polytechnique since 2019. Most of his work is related to the theoretical and computational aspects of inverse problems and homogenization as they arise in wave propagation, imaging, and material science. 

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Seminar 24 -S2: Bringing metamaterials to practice: influence of base material and novel applications

Speaker: Anastasiia O. Krushynska (University of Groningen, the Netherlands)

DOI: 10.52843/meta-mat.knhv6s

Q & A:

Abstract: Phononic materials enable unprecedented control over acoustic waves in solids. In real structures, their expected functionalities can however be severely affected by the mechanics of base material. The first part of the talk discusses the influence of linear viscoelasticity on wave attenuation by polymer phononic materials. The accuracy of the mechanical models commonly used to model viscoelastic behavior of polymers is discussed and validated experimentally for conventionally and additively manufactured phononic structures. Next, two application prospects for metamaterials are proposed. These are metamaterial surface patterns for manipulating the aerodynamic and acoustic characteristics of artificial wings and kirigami metasheets as modular actuator arrays in adaptive optics.

A. Krushynska, Adv. Funct. Mater. 31, 2103424 (2021)
A.Krushynska, Mater. Design 205, 109714 (2021)
I. Zhilyaev, Bioinspir. Biomim. 17, 025002 (2022)
A. E.M. Schmerbauch, Phys. Rev. Appl., in press (2022)

Biography: Dr. Anastasiia O. Krushynska is an assistant professor on Dynamics and Vibration at the Engineering and Technology Institute Groningen, University of Groningen (the Netherlands) and a former Cofund Marie Sklodowska-Curie Research Fellow (2015-2016) at University of Torino (Italy). With a Ph.D. degree in Mechanics of Deformable Solids from Kiev National Taras Shevchenko University (Ukraine), she worked as a post-doctoral researcher in Ukraine, the Netherlands, and Italy. Her research interests are in the field of wave dynamics of elastic solids, acoustics, material science, and mechanics with the focus on mechanical, acoustic and phononic metamaterials. Her research was distinguished by several individual research grants.

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Seminar 23 -S2: A T-matrix approach to describe them all: materials, metamaterials, and metasurfaces

Speaker: Carsten Rockstuhl (Karlsruhe Institute of Technology, Institute of Theoretical Solid State Physics, Germany)

DOI: 10.52843/meta-mat.q784q2

Q & A:

Abstract: A T-matrix, also called transition matrix, expresses how an object converts an incident into a scattered field. The object can be classical, like a traditional scatterer for which the T-matrix can be obtained from Maxwell’s equations, or a molecule, which prompts a quantum-chemical treatment to capture its T-matrix. When combined with a renormalization of the T-matrix upon periodically arranging the object, many properties can be analytically expressed. Examples of such properties aee effective material parameters or expressions of how a metasurface diffracts light. Both can be used to design optical materials inversely. In this contribution, I describe the latest developments along these lines and emphasize the combined consideration of ordinary molecular materials and materials.

Biography: Carsten Rockstuhl received a Ph.D. degree from the University of Neuchâtel, Switzerland, in 2004. After a PostDoc period at AIST in Tsukuba, Japan, he has been since 2005 with the Friedrich Schiller University Jena, Germany. In 2013, he was appointed full professor at the Karlsruhe Institute of Technology, Karlsruhe, Germany. He is heading groups at the Institute of Theoretical Solid State Physics and the Institute of Nanotechnology. His research interests cover many aspects in the context of theoretical and computational nano-optics. He works on nanostructured photonic materials, plasmonics, scattering theory, integrated photonics, quantum optics, and nonlinear photonics.

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Seminar 22 -S2: Partial order can make photonic nanomaterials different

Speaker: Rémi Carminati (Institut Langevin, ESPCI Paris, PSL University, France)

DOI: 10.52843/meta-mat.9jq9fq

Q & A:

Abstract: Light scattering from disordered materials has been extensively studied, but the influence of short and long-range spatial correlations in the disorder has been often overlooked. The possibility to engineer partially ordered materials (i.e. between completely amorphous and perfectly periodic) opens new perspectives for the control of light-matter interaction. We will discuss light propagation and absorption in partially ordered materials made of discrete scatterers in a transparent matrix. As an example, we will show that transparency, or almost perfect absorption, is expected for a specific type of partial order known as hyperuniform disorder. Finally, we will present recent approaches to the fabrication of partially ordered materials by bottom-up self-organization processes.

Biography: Rémi Carminati is a Professor of Physics at ESPCI Paris, PSL University. He leads the group of Mesoscopic and Theoretical Optics at the Langevin Institute ( His works cover the fields of nanophotonics and light scattering in complex media. Rémi Carminati received the Fabry-de-Gramont prize of the French Optical Society in 2006 and the Research award from the iXCore Research Foundation in 2009. He was elected a Fellow of the Optical Society of America in 2015.

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Seminar 21 -S2: 3D printing technologies and application in  seismic testing of structures

Speaker: Michalis Vassiliou (Department of Civil, Environmental and Geomatic Engineering (DBAUG), ETH Zürich)

DOI: 10.52843/meta-mat.mhh0qs

Q & A:

Abstract: The seismic behavior of structures is not yet under-stood sufficiently. Use of 3D printing technologies can substantially facilitate experimental studies of their behaviour allowing fabrication of model structures at a small scale (e.g.: scaled-down masonry, and reinforced concrete). Mechanical properties can be modulated by controlling the micro-geometry of the printed material. Ongoing research at ETH aims to achieve validated structural models for use in the newly constructed centrifuge. The goal is to reduce the cost of shaking table testing via using very small scale specimens thereby allowing conduction of an adequate number of tests for statistical analysis of structural performance. 

Biography: Michalis Vassiliou is currently an Assistant Professor and holds the Chair of Seismic Design and Analysis, at the Institute of Structural Engineering (IBK), of the Department of Civil, Environ-mental and Geomatic Engineer-ing (DBAUG), ETH Zürich. He is a Civil Engineer and has studied in NTU Athens (Diploma 2004), UC Berkeley (MSc 2006), and University of Patras (PhD 2010). Since 2012 he has been a Postdoc and a Senior Assistant in the ETH. In 2019, he was hired as an Assistant Professor in the ETH after receiving an ERC Starting Grant. His research interests lie in the fields of Earthquake Engineering, Applied Mechanics, and Nonlinear Dynamics, with a special focus on rocking, seismic isolation, ground motion analysis, and applications of 3D printing on seismic testing of structures. At the ETH, he is teaching courses on Structural Dynamics and Seismic Isolation.

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Seminar 20 -S2: Metamaterials that Compute

Speaker: Martin van Hecke (Università degli Studi di Cagliari, Italy)

Abstract: Collections of two-state hysteretic elements called hysterons describe the intricate pathways, hysteresis loops and memory effects observed in crumpled sheets and amorphous media. Such hysterons also naturally arise in many mechanical metamaterials and are then associated with buckling and snapping. Here we bridge these two fields, and explore, in experiments on corrugated sheets, on metamaterials, and in models, the pathways that these systems exhibit. In particular, we show that
interactions between hysterons make these systems process information, and show examples of elementary mechanical computations such as counting.

Refs: M.van Hecke, PRE 104, 054608 (2021)
H. Bense and M van Hecke, PNAS 118 e2111436118 (2021)

See also: 

Biography: Martin van Hecke is a group leader at AMOLF, Amsterdam, and a professor of physics at Leiden University. Since 2011, his research has focussed on mechanical metamaterials, from patterned elastic media to origami. In particular he has developed new design techniques to make complex metamaterials that straddle the boundary between material and machine, and that form complex patterns or can self-fold when compressed. He is a fellow of the APS and was awarded an ERC-advanced grant in 2021. He is now exploring if and how complex materials – from metamaterials to crumpled sheets – can store and process information.

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Seminar 19 S2: Metamaterials for concealment and scattering reduction in acoustics and elasticity

Speaker: Davide Enrico Quadrelli (Department of Mechanical Engineering, Politecnico di Milano, Italy)

DOI: 10.52843/meta-mat.zmhgd9

Q & A:

Abstract: Avoiding detection from echolocation is one of the most interesting applications of acoustic metamaterials. Transformation Acoustics can be used to obtain perfect cloaking when a suitable mapping can be written, which is typically easy to find only for a restricted set of cases. In our work, we try to achieve scattering reduction and partial invisibility in a set of scenarios where practical feasibility is preventing perfect cloaking. First, we address the problem of underwater scattering reduction of elliptic obstacles, by applying suitable mapping defined in elliptical coordinates, which allow for practical realization and experimental testing of a non-axisymmetric, anisotropic pentamode near-cloak. Then, we approach the problem from a different perspective: specifically, we use PDE-constrained optimization aiming at cloaks obtained with isotropic materials only, which can be implemented with distributions of scatterers in the background fluid. The formulation of the optimization problem is done in such a way as to consider practical limits in the obtainable homogenized properties. In the same way of thinking i.e., isotropic materials are easier to implement than other exotic material distribution, we address elastic cloaking with isotropic materials, going back to Transformation Theories and exploiting conformal mapping, underlining the limits of applicability of such method to obtain cloak that works for Rayleigh waves.
Finally, a different type of concealment can be conceived as being able to listen to what others say, without being listened to. This implies achieving nonreciprocal acoustic wave propagation. We derive the prescription for material properties that need to be implemented for non-reciprocal wave propagation of 2D cylindrical acoustic waves.
[1] D.E. Quadrelli, M.A. Casieri, G. Cazzulani, S. La Riviera, F. Braghin, “Experimental validation of a broadband pentamode elliptical-shaped cloak for underwater acoustics”, Extr. Mech. Letters (2021)
[2] D.E. Quadrelli, R. V. Craster, M. Kadic, F. Braghin, “Elastic wave near-cloaking”, Extr. Mech. Letters (2021)
[3] D.E. Quadrelli, G. Cazzulani, S. La Riviera, F. Bragin, “Acoustic scattering reduction of elliptical targets via pentamode near-cloaking based on transformation acoustics in elliptic coordinates”, J. of Sound and Vibr.. (2021)
[4] S.Cominelli, D.E. Quadrelli, C. Sinigaglia, F. Braghin, “Design of arbitrarily shaped acoustic cloaks through partial differential equation-constrained optimization satisfying sonic-metamaterial design requirements”, Proc. Royal Soc. A (2022)
[5] D.E. Quadrelli, E. Riva, G. Cazzulani, F. Braghin, “Omindirectional Non-Reciprocity via 2D Modulated Radial Sonic Crystals”, Crystals (2020)
[6] C. Sinigaglia, D.E. Quadrelli, A. Manzoni, F. Braghin, “Fast, active thermal cloaking through PDE-constrained optimization and Reduced-Order Modelling, Proc. Royal Soc. A (2022)
[7] E. Riva, D.E. Quadrelli, G. Cazzulani, F. Bragin, “Tunable in-plane topologically protected edge waves in continuum Kagome lattices”, J. of App. Phys. (2018)

Biography: Davide Enrico Quadrelli is a Mechanical Engineer that has been PhD student in the group of Prof. Francesco Braghin at Politecnico di Milano (Italy). He is interested in acoustic metamaterials, acoustic/structure interaction, and vibration control with piezoelectric materials.

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Seminar 18 S2: Revisiting topological materials: crystal optics and the Chern number

Speaker: Simon Horsley (Department of Physics and Astronomy, University of Exeter, UK)

DOI: 10.52843/meta-mat.k2gw6l

Q & A:

Figure 1: Illustration of the effect of a material with zero index in a complex direction. (a)  an interference between waves in free space leads to an interference pattern where energy can circulate in either sense of rotation (shown as + and – vortices). (b) when the refractive index vanishes in a complex direction the energy can only circulate e.g. anticlockwise as shown here.  

Abstract: It is now well established that the number and direction of interface waves trapped between different materials can be calculated using topology. Typically we use the wave-vector k as coordinates on a closed surface (a torus for example), and then compute the first Chern number from the waveform at each value of k. If this number differs between two materials, it indicates the presence of trapped states at their interface. Useful and fascinating as this is, there is also a great deal of mystery here: what exactly is the Chern number recording? and could we have found these modes in a simpler way?

This talk attempts to answer these questions. I will begin by briefly reviewing the mathematics underlying these topological calculations, showing that the Chern number is recording special points in the dispersion relation where an effective refractive index vanishes. Examining these points of vanishing index using good old fashioned crystal optics, we find that the refractive index is zero in a complex direction. The complexity of the direction indicates a direction of allowed circulation (analogous to circular polarization), as required for a one-way interface state. Using examples from near field optics, elasticity, and coupled resonator theory, it is then shown that this zero index condition provides a shortcut to the results from equivalent topological calculations.

[1] S. A. R. Horsley and M. Woolley, Nat. Phys. 17, 348 (2021)

Biography: Simon Horsley is a Royal Society TATA University Research Fellow at the University of Exeter in the UK.  He completed his PhD in 2009 at the University of York and worked at the University of St Andrews and the European Laboratory for Non Linear Spectroscopy before joining the metamaterials group at Exeter.  He is interested in waves of all kinds, and the strange things they can do in the right kind of materials.

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Seminar 17 S2: Nonreciprocal and non-Hermitian material response inspired by semiconductor transistors

Speaker: Mário Silveirinha (Instituto Superior Técnico and Instituto de Telecomunicações, University of Lisbon, Portugal)

DOI: 10.52843/meta-mat.7s886r

Q & A:

Abstract: In this talk, I will present an overview of the ongoing research work of my group on novel nonreciprocal and non-Hermitian metamaterials that have a bulk electromagnetic response inspired by the operation of a MOSFET transistor. We will show that such metamaterials enable rather exotic physics and can have potential applications in electromagnetic isolation or as wave amplifiers [1]. 

[1] S. Lannebère, D. E. Fernandes, T. A. Morgado, M. G. Silveirinha, “Nonreciprocal and non-Hermitian material response inspired by semiconductor transistors”, Phys. Rev. Lett. 128, 013902, (2022).

Biography: Mário G. Silveirinha received the Licenciado degree in Electrical Engineering from the University of Coimbra, Coimbra, Portugal, in 1998, and the Ph.D. degree in Electrical and Computer Engineering (with a minor in Applied Mathematics) from the Instituto Superior Técnico (IST), Technical University of Lisbon, Lisbon, Portugal, in 2003. Currently, he is a Professor at the University of Lisbon, Portugal and a Senior Researcher at Instituto de Telecomunicações.
Mário Silveirinha is an IEEE Fellow, and OSA Fellow and an APS Fellow. He is a founding editor of the APS journal Physical Review Applied. He was a Visiting Professor at the University of Pennsylvania during several periods in 2004-2005 and 2010-2011, and a Chercheur CNRS en Physique at the University of Montpellier in 2017.
His research interests include electromagnetism, plasmonics and metamaterials, quantum optics, and topological effects (

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Seminar 16 S2: MetasurMetasurfaces and metabuildings in megacities: Cloaking of body and surface seismic waves

Speaker: Jean-François Semblat (ENSTA Paris | Institut Polytechnique de Paris & IMSIA | Institute of Mechanical Sciences and Industrial Applications, France

DOI: 10.52843/meta-mat.7mhpqd

Q & A:

Abstract: Seismic waves propagate in complex heterogeneous geological structures and may be strongly amplified when reaching the free surface. Due to strong velocity contrasts, seismic waves are particularly amplified in alluvial basins thus leading to extensive surface waves generation.
Such surface waves may interact with buildings at the local scale (soil-structure interaction/SSI) as well as the scale of an entire city (site-city interaction/SCI).
In this talk, we emphasize on the quantification of such surface waves through the Normalized-Inner Product allowing an efficient time-frequency extraction. Various modeling strategies are then discussed to analyze wave-structures interaction in alluvial basins at various scales: 1DT-3C approach, impedance functions, macroelement formulations, homogenization methods (either for foundations or structures), fast-Boundary Element Methods, large site-city models for actual urban environments.
The main issues are the complexity and the efficacy of these various approaches. The final goal being to answer this crucial question: is site-city interaction beneficial or detrimental?

Biography: Jean-François Semblat is Professor at ENSTA-Paris, Institut Polytechnique de Paris (IP-Paris). He is head of the Department of Mechanics and Energetics of IP-Paris and coordinator of the master program in Mechanics. His field of research ranges from seismic wave propagation in complex media to dynamic soil-structure interaction and site-city interaction through various modelling approaches (FEM, BEM, macroelements, homogenization).

He is member of the editorial board of Soil Dynamics and Earthquake Engineering and International Journal of Geomechanics (ASCE). He is also member of the Technical Committee 203 of the International Society of Soil Mechanics and Geotechnical Engineering (ISSMGE) and former vice-President of the French Society for Earthquake Engineering (AFPS). He has been involved in a number of research projects at the national and international level (Isolate, Modulate, ERC CoQuake, SINAPS@, Series, EuroSeisRisk).

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Seminar 15 S2: Responsive Mechanical Metamaterials for Unprecedent Wave Control and Odd Elasticity

Speaker: Guoliang Huang (Department of Mechanical and Aerospace Engineering University of Missouri, Columbia, MO 65211, USA)

DOI: 10.52843/meta-mat.jgj1n8

Q & A:

Abstract: Biological and artificial machinery systems have utilized the approach made by sensing, actuating, and information processing to adapt themselves to environmental changes, maintain dynamic equilibrium, and execute particular functions. In this talk, we present how to leverage this approach to construct active and responsive mechanical metamaterials for enabling a range of unprecedent wave phenomena and mechanical properties. The active mechanical metamaterials are composed of piezoelectric sensors and actuators connected with digital electronic circuits. The electrical circuits implemented allow for precisely and independently modulating mechanical properties of the metamaterial through programmable transfer functions. By developing active theory, numerical simulations and conducting experimental testing, we systematically demonstrate their application in broadband wave mitigation, independently wave transmission and reflection control, non-local dynamics, wave mode conversion and odd micropolar elasticity for realizing non-Hermitian mechanics and dynamics.

Biography: Dr. Guoliang Huang is currently a Huber and Helen Croft Chair professor of mechanical and aerospace engineering at University of Missouri-Columbia. He received his Ph.D. degree from University of Alberta, Canada, in 2004. Dr. Huang’s research interests include wave propagation and mechanics in elastic/acoustic metamaterials and structural materials, topological and active mechanics, structural dynamics, machine learning, vibration and sound wave mitigation. Dr. Huang’s research has been funded by NSF, Air Force of Scientific Research, Army Research Office, Office of Naval Research, DURIP, Department of Energy, NASA, and major industries.  He has authored one book, 4 book chapters and more than 140 journal papers.

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Seminar 14 S2: Modal approximations for plasmonic resonators in the time domain and applications to super-localisation

Speaker: Alice Vanel (ETH Zurich, Switzerland)

DOI: 10.52843/meta-mat.2yvcjt

Q & A:

Abstract: We study the possible expansion of the electromagnetic field scattered by a strictly convex metallic nanoparticle with dispersive material parameters placed in a homogeneous medium in a low-frequency regime as a sum of modes oscillating at complex frequencies (diverging at infinity), known in the physics literature as the quasi-normal modes expansion. We show that such an expansion is valid in the static regime and that we can approximate the electric field with a finite number of modes. We then use perturbative spectral theory to show the existence, in a certain regime, of plasmonic resonances as poles of the resolvent for Maxwell’s equations with non-zero frequency. We show that, in the time domain, the electric field can be written as a sum of modes oscillating at complex frequencies. We introduce renormalised quantities that do not diverge exponentially at infinity.
We present numerical simulations in two dimensions to corroborate our results. We illustrate
the usefulness of our method on the super-localisation of a point-like emitter in a resonant environment.

Biography: Alice Vanel is an applied mathematician, who uses a combination of analytic, asymptotic and numerical techniques to model wave propagation in complex media.
She worked as a postdoc in Professor’s Habib Ammari research group, based in the Department of Mathematics at ETH Zurich. Before that she was a PhD student under the supervision of Professor Richard Craster and Dr Ory Schnitzer at Imperial College London.

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Seminar 13 S2: MRI metamaterials

Speaker: Marc Dubois (Mutliwave Imaging SAS, France)

DOI: 10.52843/meta-mat.2cnm24

Q & A:

Abstract: Magnetic resonance imaging (MRI) relies on a precise control of spin magnetic moments in the body tissues. To achieve such control, one needs to induce a uniform radiofrequency (RF) magnetic field flux (B1+) across the imaged volume. In 7T MRI scanners, the proton (1H) Larmor frequency reaches 300 MHz. Due to the high relative permittivity of human tissues, the associated RF wavelength can shrink down to 11 cm, which is comparable to the dimensions of some human organs. Consequently, spatially varying phase and amplitude of the RF fields generate signal inhomogeneities across the image. For head imaging, signal losses become strongly visible in the temporal lobes and cerebellum regions of the brain.
Different approaches have been implemented to improve B1+ field uniformity of transmit coils such as passive and active RF shimming. Active RF shimming is based on coils with multiple independently controllable transmit elements or channels. These additional degrees of freedom can be exploited to mitigate B1+ inhomogeneities. But, it raises challenges in terms of workflow and patient safety (specific absorption rate). In contrast, passive RF shimming relies on the insertion of passive structures between the subject and the coil. Devices based on high-permittivity dielectric materials and/or metamaterials have seen strong developement in the past years. Induced currents (displacement or conduction currents) generate a secondary RF field that corrects the initial B1+ field. This talk will review some of the achievements and remaining challenges of RF passive shimming in high field MRI applications.

Biography: Marc joined Multiwave Imaging from the French National Research Agency laboratory Institut Fresnel in 2020. Prior to assuming the role of CEO, he led research and development activities for Multiwave Imaging with a focus on developing MRI devices that would drastically improve standards of care in hospitals and clinics around the world.
Marc completed his PhD at Institut Langevin in Paris at Université Paris Diderot-Paris VII and was later trained in world leading laboratories on wave control and metamaterials including at University of California, Berkeley where he spent 2 years as a post-doctoral researcher.
Upon his return to France, he first joined the renowned French National Research Agency laboratory Institut Fresnel where he combined his knowledge of metamaterials with his deep interest in magnetic resonance imaging. With funding from consecutive European projects of excellence in MRI, he joined the Center of Magnetic Resonance in Biology and Medicine (CRMBM) where he honed his skills in MRI across all magnetic field strengths.

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Seminar 12 S2: Wave propagation in gyro-elastic microstructured media

Speaker: Michele Brun (Università degli Studi di Cagliari, Italy)

DOI: 10.52843/meta-mat.yktb9t

Q & A:


Abstract: In this talk, wave propagation in gyro-elastic structured media are presented. The system is a lattice composed of periodically placed masses interconnected by elastic rods and attached to gyroscopic spinners. The analysis is based on an asymptotic model that describes the interaction between a gyroscopic spinner and a mass embedded in a truss system. Several examples are given that illustrate the transient features of special dynamic phenomena, including unidirectional interfacial waves and highly localised waveforms.
In the second part of the talk Rayleigh waves are analysed in elastic lattices incorporating gyroscopic effects. The vector problems of elasticity for a triangular lattice and its long-wavelength/low-frequency continuum approximation are considered. The analytical procedure gives explicit solutions for the Rayleigh waves for both the discrete and continuous systems. Despite the symmetry of the dispersion curves with respect to the wavenumber, the introduction of the inertial coupling breaks the symmetry of the eigenmodes and makes the system non- reciprocal.

Biography: Michele Brun is Associate Professor of Solids and Structural Mechanics at the Department of Mechanical, Chemical and Materials Engineering of the University of Cagliari Italy. He graduated in Structural Civil Egnineering at the University of Brescia (Italy) (1999, grade 110/110) and got a PhD in Mechanics of Materials and Structures at the University of Trento. He held several positions in international Universities (postdoc at Ecole Polytechnique in Palaiseau and University of Trento, Marie Curie Fellow at the University of Liverpool, Research Associate at the University of Colorado at Boulder, University of Liverpool and Laboratoire d’Acoustique de l’Université du Mans). Since 2006 he is working at the University of Cagliari.

He is author of more than 60 papers on international peer reviewed journals, plus several conference proceedings and book chapters. He has been Principal Investigator of several international and national projects (total income ~ 103 k€), in particular he has been PI in the EU project H2020-MSCA-IF- 2016: 747334 CAT-FLAPP and Principal Researcher in FP7- PEOPLE-2011-IEF: 302357 DYNAMETA. He has given invited seminars in several high-rank universities (including Harvard University, Imperial College and Ecole Polytechnique). He has supervised 2 postdocs, 5 PhD students, 19 MSc and 2 BSc students.

His interest is in the broad area of solid and structural mechanics, wave propagation in elastic solids and structures, metamaterials, micro-structured media, contact mechanics, composites materials, continuum mechanics (finite elasticity), numerical methods (BEM, Fortran code, FEM), instability (bifurcations in elastic structures, surface instability, shear bands), fundamental solutions and Green’s functions, atomistic models (MEAM), fracture mechanics in anisotropic media, variational formulations, integration algorithms in structural dynamics, dynamic propagation of structural failure.

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Seminar 11 S2: Topological Photonics

Speaker: Mordechai (Moti) Segev (Solid State Institute and Physics Department, Technion – Israel Institute of Technology)

DOI: 10.52843/meta-mat.k8rkqd

Q & A:

Abstract: I will present an overview on the field of Topological Photonics, with an emphasis on the Foundations, on Topological Insulator Lasers, and on current challenges.

Biography: Moti Segev is the Robert J. Shillman Distinguished Professor of Physics and Electrical Engineering, at the Technion, Israel. He received his BSc and PhD from the Technion in 1985 and 1990. After postdoc at Caltech, he joined Princeton as Assistant Professor (1994), becoming Associate Professor in 1997, and Professor in 1999. Subsequently, Moti went back to Israel, and in 2009 was appointed as Distinguished Professor.
Moti’s interests are mainly in photonics, solitons, lasers, and quantum optics. He won numerous international awards, among them the 2007 Quantum Electronics Prize of the European Physics Society, the 2009 Max Born Award of the Optical Society of America, and the 2014 Arthur Schawlow Prize of the American Physical Society. In 2011, he was elected to the Israel Academy of Sciences, in 2015 to the National Academy of Science (USA), and in 2021 to the American Academy of Arts and Sciences. In 2014 Moti Segev won the Israel Prize (highest honor in Israel) and in 2019 he has won the EMET Prize.
Above all his achievements, Moti takes pride in the success of his graduate students and postdocs, among them are currently 23 professors in the USA, Germany, Taiwan, Croatia, Italy, India, China and Israel, and many holding senior R&D positions in the industry.

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Seminar 10 S2: Hierachical geomaterials and seismic metamaterials: tracks for implementation

Speaker: Stéphane Brûlé (Menard – Région Rhône-Alpes & Auvergne, France)

DOI: 10.52843/meta-mat.w21xc6

Q & A:

Abstract: The transposition of the principles of periodic media to materials as specific as terrestrial materials requires rigorous definition of the validity conditions. In particular, the elasticity condition, the full complexity of the attenuation in viscoelastic material, the pattern of the sedimentary basin, the strong antagonism between amplification and attenuation, the soil-structure interaction, etc.

Indeed the possibilities of diffraction phenomena have been revealed by experiments on a real scale. The lenses tested are explored as phononic crystals and metamaterials. By the effects observed, we point out the diffraction including Bragg reflection and double image of the source as a result of the negative refraction of a flat lens. However, a metamaterial is defined as an artificial composite material made from the assembly of resonators of smaller dimensions, whose wavelength at resonance is much greater than their physical dimension. These possibilities of local resonances are verified for Helmholtz resonators or very soft soils with rigid inclusions.

On a macroscopic scale, a metamaterial is likely to exhibit properties that are not found in nature, such as negative refractive index. In addition to these early interpretations, there is an analysis of the modification of the polarization of surface waves. This new reading of the data opens the discussion on other descriptions of phenomena such as the existence of local resonances of rigid elements placed in a soil, and no longer of empty cylinders, as well as on static or dynamic homogenization approaches, dynamic anisotropy, transformational optics, surface resonators, etc. The modification of the signal by the fact of a structured soil and surface resonators are the link with Civil Engineering and the soil-structure interaction practiced in Earthquake Engineering. Research subjects converge in seismology and on the effects of secondary sources generated by surface buildings. The coupling of buildings such as surface resonators with structured soils constitutes an opportunity for development in the trapping of mechanical energy. In the era of energy transition, any free source of energy is of interest.

S. Brûlé et al. (2014) Experiments on Seismic Metamaterials: Molding Surface Waves. Physical Review Letters, 112(13)

S. Brûlé et al. (2017) Flat lens effect on seismic waves propagation in the subsoil. Scientific Reports, 7(1)

S. Brûlé and S. Guenneau (2021) Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space–time modulations. Comptes Rendus. Physique, 21(7-8)

B. Ungureanu et al. (2015) Auxetic-like metamaterials as novel earthquake protections. EPJ Applied Metamaterials, 2

Y. Achaoui et al. (2017) Clamped seismic metamaterials: ultra-low frequency stop bands. New Journal of Physics, 19(6)

T. Varma et al. (2021) The Influence of Clamping, Structure Geometry, and Material on Seismic Metamaterial Performance. Frontiers in Materials, 8

Biography: Stéphane Brûlé, contributor in the field of seismic metamaterials, is a researcher in seismic risk assesment, soil dynamics, soil-structure interaction and geotechnical engineering, holder of a master’s degree research from École Normale Supérieure de Paris and Pierre and Marie Curie University and an engineering diploma in geotechnics of Grenoble-Alpes University in the field of soil mechanics, ground improvement and deep foundations. Stéphane Brûlé is the Phd studend of Stefan Enoch, director of research at CNRS, and was the leading author of the foundation paper for the field of seismic metamaterials [Physical Review Letters 112, 133901, 2014]. He also led with Sébastien Guenneau and Stefan Enoch, and others, the first experiment on lensing of surface Rayleigh waves via negative refraction [Scientific Reports 7, 18066, 2017].
He is also teaching in Universities and Engineering Schools (ENS Lyon, Polytech Grenoble, EOST, ESITC Paris, École des Mines d’Alès, Polytech Clermont), is a member of the International Technical Committee 203 « Geotechnical Earthquake Engineering and Associated Problems », and is also an active boardmember of the French committee of soil mechanics (CFMS) and of the French earthquake engineering association (AFPS).

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Seminar 9 S2: Multiple scattering analysis of quasi-periodic clusters of scatterers

Speaker: Daniel Torrent Martí (Physics Department, Universitat Jaume I, Spain)

DOI: 10.52843/meta-mat.ypxv1d

Q & A:

Abstract: We will apply multiple scattering theory to the analysis of resonant modes of finite clusters of scatterers for flexural waves. It will be shown that this method allows the calculation of the real and imaginary part of the eigenfrequencies of finite structures, so that we can determine not only the resonant frequency but also its quality factor. We will apply this method to the study of two-dimensional clusters forming moiré lattices and to the quasi periodic infinite line, showing that both types of structures present a large amount of resonances of high quality. It will be shown therefore that quasi-periodic clusters are a promising family of structures for the design of wave-localization devices, since these results are in principle applicable to any kind of classical wave.

Biography: Daniel Torrent studied physics at the University of Valencia and obtained his PhD in the Electronics Engineering Department of the Polytechnic University of Valencia, on July 25th 2008. During his career he has contributed to the development of both theoretical and experimental tools to understand the propagation of acoustic, elastic and electromagnetic waves in complex media. After four years of research stays in the University of Lille (France) and the Univeristy of Bordeaux – CNRS (France), he has been awarded by the “Ramón y Cajal” Fellowship, and currently is working as a researcher at the “Univeritat Jaume I” in Castellón de la Plana (Spain).

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Seminar 8 S2: Mathematical analysis of subwavelength metamaterials: sensors, biomimicry and topological edge modes

Speaker: Bryn Davies (Department of Mathematics, Imperial College London, UK)

DOI: 10.52843/meta-mat.g0hhml

Q & A:

Abstract: The aim of our work is to conduct rigorous analyses of subwavelength scattering problems and use these results to establish the mathematical foundations for the design of high-contrast metamaterials. We will present results that characterise a system’s resonance in terms of the eigenstates of the generalized capacitance matrix. We will use this theory to explore applications including the design of cochlea-inspired metamaterials, enhanced sensors based on exceptional points and tuneable topological wave guides. The talk will discuss results developed in collaboration with Habib Ammari, Erik Orvehed Hiltunen and Sanghyeon Yu, who are all former colleagues from Bryn’s time at ETH Zurich.

Biography: Dr Bryn Davies is a Research Associate in the Department of Mathematics at Imperial College London. His research concerns the analysis of wave propagation in complex media. He has used integral methods and asymptotic techniques to study problems from the fields of topological insulators, subwavelength waveguides, enhanced sensing and bio-inspired metamaterials.

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Seminar 7 S2: Acoustic and elastic wave propagation in microstructured media with interfaces: homogenization, simulation and optimization

Speaker: Marie Touboul (Department of Mathematics, University of Manchester, UK)

DOI: 10.52843/meta-mat.h0srxz

Q & A:

Abstract: The design of media at a microstructured scale allows to control wave propagation in a fine way and to obtain exotic effects at the macroscopic scale. Thanks to homogenization methods, the microstructure can be advantageously replaced, at the macro scale, by a homogeneous effective medium. Then, it raises the question of optimization tools in order to design the microstructure that allows to achieve a desired macroscopic effect. In this context, the consideration of interfaces (microstructured interfaces, imperfect interfaces) can lead to modifications in the homogenization methods, the numerical methods, or the optimization methods classically used. Two different cases of interfaces will be presented (PhD work, supervised by Cédric Bellis and Bruno Lombard):
(i) Homogenization and optimization are first carried out for microstructured interfaces. The homogenization of a highly contrasted, and therefore resonant, microstructured interface is studied in the time-domain and leads to resonant jump conditions on an effective interface (coll: Kim Pham, Agnès Maurel, Jean-Jacques Marigo). The introduction of auxiliary variables allows to get a local evolution problem in time which is then solved numerically to perform time-domain simulations for the effective resonant meta-interface. Finally, the sensitivity of the effective non-resonant model to the geometry of the microstructure is determined using topological derivatives (coll: Rémi Cornaggia) in order to develop a topological optimization of the microstructure.

(ii) Homogenization of solids with imperfect interfaces of the spring-mass type is then performed (coll: Raphaël Assier). The wavefields are approximated at low-frequency for possibly nonlinear cracks. An approximation of both the wavefields and the dispersion relation is also obtained at higher frequencies for a 1D array of linear cracks.

Biography: Marie Touboul has just received her PhD from the University of Aix-Marseille (supervisors: Cédric Bellis and Bruno Lombard at the Laboratory of Mechanics and Acoustics). She is currently working as a postdoctoral researcher with Professor William Parnell in the Mathematics of Waves and Materials research group (Department of Mathematics, University of Manchester). Her work lies at the interface of applied mathematics, waves, and mechanics of solids.

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Seminar 6 S2Bringing metamaterials to creative industries and hospitals

Speaker: Gianluca Memoli (School of Engineering and Informatics, University of Sussex)

DOI: 10.52843/meta-mat.hlx12h

Q & A:

Abstract: According to different recent market research reports, acoustic metamaterials are quickly going up the TRL scale, moving to applications. In this talk, I will therefore present two examples of applications: one relative to sound delivery and one to noise management, both for audible frequencies in air.
First, I will describe how combinations of metasurfaces can be used to achieve sound delivery with wavelength precision at variable distances, for creative applications. I will touch on the possibility of applying the thin-lens equation and on the verification of COMSOL simulations using human volunteers.
Secondly, I will discuss how my team came to design meta-material based movable panels to COVID wards. I will touch on the criticality of noise in hospitals, on the specific combination of unit cells that we used and on the challenges to test the performance of our panels using standard techniques, both in the laboratory and in-situ.

Biography: Gianluca Memoli is a Senior Lecturer at the University of Sussex and the acting CEO of Metasonixx Ltd. A physicist and an engineer, he fell in love with metamaterials in 2016, when he arrived at Sussex from the National Physical Laboratory and used metasurfaces to levitate objects without transducer arrays. A passionate science communicator and a proud father of two, he holds a UKRI fellowship whose aim is to bring metamaterials to creative industries. He co-chairs (with Tim Starkey) the Special Interest Group on Acoustic Metamaterials shared between the UK Acoustic Network and the UK Metamaterials Network.

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Seminar 5 S2Towards scalable Photonic Neural Networks with (3+1)D integrated optics

Speaker: Daniel Brunner (Institut FEMTO-ST, Université Bourgogne Franche-Comté CNRS UMR 6174, Besançon, France)

DOI: 10.52843/meta-mat.njw217

Q & A:

Abstract: Integrated photonic architectures have the potential to revolutionize neural network computing. However, conventional 2D lithography strongly limits the size of integrated photonic neural networks due to fundamental scaling laws. We want to overcome this problem by integrating neural networks using 3D printed photonic waveguides. For that we demonstrate complex 3D multimode waveguide networks based on polymer waveguides surrounded by air. Furthermore, we recently developed a (3+1)D direct laser writing technique where we dynamically and locally control the writing power in order to realize single mode step or graded index waveguides.

Biography: Daniel Brunner is a CNRS researcher with the FEMTO-ST, France. His interests include novel computing using quantum or nonlinear substrates with a focuses on photonic neural networks. He was received several University and the IOP’s 2010 Roys prize and the IOP Journal Of Physics:Photonics emerging leader 2021 prize. He edited one Book and two special issues, has presented his results 45+ times upon invitation and has published 50+ scientific articles.

Home – Prof. Daniel Brunner

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Seminar 4 S2Self-collimation, Veselago lens, Dirac cones and embedded states in continuum in acoustics without phononic crystals and metamaterials

Speaker: Alexei Maznev (Department of Chemistry, Massachusetts Institute of Technology, USA)

DOI: 10.52843/meta-mat.3cvw3b

Q & A:

Self-collimation a.k.a. phonon focusing of surface acoustic waves on Ge (111)

Abstract: The concepts of photonic crystals and metamaterials initially appeared in optics and electromagnetism, and were subsequently extended to acoustic waves. However, a number of phenomena thought to be specific to these “artificial” media have been observed in solid state acoustics with conventional materials – in some cases well before the advent of metamaterials and photonic/phononic crystals. In this talk, which will cover both historical and recent research, we will discuss several such phenomena: (i) “self-collimation” of bulk and surface acoustic waves in natural crystals; (ii) negative group velocity, Veselago lens and Dirac cones exhibited by guided acoustic waves in plates; (iii) robust embedded states in continuum on natural crystal surfaces and in simple layered structures.

Biography: Alex Maznev received Diploma in physics from the Moscow Institute of Physics and Technology and PhD from the General Physics Institute of the Russian Academy of Sciences (thesis on laser-generated SAWs including the first experimental observation of surface phonon focusing). He held postdoctoral positions at the Freie Universität Berlin, as an Alexander von Humboldt Fellow, and at MIT, where he developed an optical heterodyning scheme for laser-induced transient grating experiment currently used in many labs. Subsequently, he worked as an industrial researcher (mainly at Philips Electronics North America) developing metrology systems for semiconductor industry using optical and optoacoustic techniques, before returning to MIT as a staff scientist.  His current interests involve a broad range of topics pertaining to wave propagation phenomena, primarily in acoustics and related fields such as phonon-mediated heat transport on micro/nanoscale.  He is collaborating with many groups around the world and has held visiting positions at Université du Maine in France, Hokkaido University in Japan, University of Witwatersrand in South Africa, and Universität Heidelberg in Germany.

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Seminar 3 S2: Manipulating water waves using bathymetric plate arrays

Speaker: Richard Porter (School of Mathematics, University of Bristol, UK)

DOI: 10.52843/meta-mat.rw4q8c

Q & A:

Abstract: This talk will describe how closely-spaced arrays of vertical plates protruding from the bed of an incompressible fluid can be used to produce interesting effects on water waves propagating on the surface of the fluid. We will consider how both fully depth dependent and depth-averaged (shallow water) models are formulated and how they compare and illustrate their use in a number of different settings. For instance, we can generate examples of bathymetric devices which represent all-frequency all-angle refractive devices which allow negative refraction and for which the phase velocity is directed towards the source. Other examples include the use of bathymetric plate arrays to perfectly transmit energy through bends in waveguides and, when formed into a cylinder, act as a bathymetric lens.

Biography: Richard Porter has worked at the University of Bristol for over 25 years, first as a Research Assistant before becoming a lecturer in Applied Mathematics. His research interests mainly focus on the interaction of water waves with marine structures and developing mathematical tools for approximating solutions to the boundary-value problems that arise. The principle topics of interest include trapped and near-trapped waves, the design and modelling of ocean wave energy converters, the influence of floating ice and cracks in ice sheets on wave propagation and, more recently, metamaterials and their application in water wave settings.
He has published six papers with his father, been known to cycle to overseas conferences, and appeared in a BBC documentary which he has never watched.

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Seminar 2 S2: Valley-Hall topological acoustics

Speaker: Zhiwang Zhang (School of Physics, Nanjing University, China)

DOI: 10.52843/meta-mat.7b1523

Q & A:

Abstract: The discrete valley degree of freedom, i.e., quantum states of energy extrema in momentum space, is attracting growing attention because of its potential as a new type of information carrier like spins in spintronics. Transferring the valley concept to classical wave systems through valley-like frequency dispersions, has been made possible using engineered artificial lattices such as photonic and sonic crystals. 

In this webinar, we will start with a brief introduction on valley-projected topological acoustics and then discuss our recent works in this topic, which include the experimental realizations of the topological acoustic delay line[1], the directional acoustic antenna[2] and the valley-projected edge states based on the subwavelength soda cans[3]. Lastly, in this context, we also consider non-Hermiticity combining sonic crystals with gain[4]. Here, we take advantage of electro-thermoacoustic coupling from biased carbon nanotube films used as lattice coatings. We construct a topological whispering gallery made out of such coated lattice and show how the mode chirality can be broken and a topological “saser”, the analogous topological “laser” in acoustics, can be realized.

[1] Zhang, Z. et al. Phys. Rev. Appl. 9, 034032 (2018).

[2] Zhang, Z. et al. Adv. Mater. 30, 1803229 (2018).

[3] Zhang, Z. et al. Research 2019, 5385763 (2019).

[4] Hu, B. et al. Nature597, 655 (2021).

Biography: Zhiwang Zhang is currently a postdoctoral researcher in Department of Physics, Nanjing University under the support of the China National Postdoctoral Program for Innovative Talents. He received his Laurea (2015) and PhD (2020) from Nanjing University, China, and visited Universidad Carlos III de Madrid, Spain, as a joint training PhD student (2018-2019). He majors in acoustics and focus on physical acoustics and acoustic metamaterials. His current researches mainly concern the topological protected states in 2D/3D acoustic systems and achieving the functional device based on the topological acoustics.

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Seminar 1 S2Odd robotic matter

Speaker: Corentin Coulais (Van der Waals-Zeeman Instituut, Faculty of Science, University of Amsterdam, Netherland)

DOI: 10.52843/meta-mat.pjfy9h

Q & A:

Abstract: Controlling how waves propagate, attenuate and amplify in simple, scalable geometric structures is a daunting challenge for science and technology. In this talk, I will discuss how odd media—media in which energy conservation and chiral symmetries are simultaneously broken—can be used to steer mechanical waves in unprecedented ways. Combining experiments on mechanical lattices of distributed robots with wave physics and continuum mechanics, I will discuss the emergence of unidirectionally amplified waves, of topological waves and of one-way solitons in odd media. I will further show how these odd waves can be used to induce locomotion and unusual responses to impacts and hence pave the way towards a novel generation of materials with animate properties.

Biography: Corentin Coulais is Associate Professor at the University of Physics of the University of Amsterdam. Coulais’ Machine Materials group investigates designer soft materials, with a particular emphasis on how mechanical metamaterials can programmed to achieve advanced mechanical tasks. Coulais explores the structure-property relationship in metamaterials with highly nonlinear degrees of freedom, by combining additive manufacturing, precision-desktop experiments, numerical methods and theory inspired from condensed matter. Recent highlights include shape-changing (2016), non-reciprocal topological (2017), self-folding (2018) and multifunctional (2021) metamaterials. He has recently pioneered robotic materials, which combine the notions of emergence and symmetries inherent to condensed matter with the capabilities of robotics. This has led to early experimental observations of non-Hermitian wave phenomena such as unidirectional amplification (2019) and non-Hermitian topology (2020). Coulais has received the NWO VENI (2015), ERC Starting (2019) and leads multiple collaborations with industry. More information on his research activities can be found at

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