Seminar 24: Scattering electromagnetic eigenstates of a two-constituent composite and their exploitation for calculating a physical field
Speaker: David Bergman (School of Physics and Astronomy, Tel Aviv University, Israel)
Q & A:
Abstract: The spectral representation of an electric field in a two-constituent composite medium is revisited. A theory is developed for calculating the electromagnetic (EM) eigenstates of Maxwell’s equations for such a composite where the magnetic permeability as well as the electric permittivity have different uniform values in the two constituents. The physical electric field E(r) produced in the system either by a given incident field or by a given source current density is expanded in this set of biorthogonal eigenstates for any position r. If the microstructure consists of a cluster of separate inclusions in a uniform host medium then the EM eigenstates of all the isolated inclusions can also be used to calculate E(r). Once all these eigenstates are known for a given host and a given microstructure then calculation of E(r) only involves performing three-dimensional integrals of known functions and solving sets of linear algebraic equations.
Biography: I was born in 1940 in Tel Aviv, then in Palestine which was governed by a British mandate from the League of Nations. I got my BSc and MSc degrees from the Hebrew University of Jerusalem, and my PhD in 1968 from the Wezmann Institute of Rehovot, Israel. After two years as a post-doc at UCSD in La-Jolla, CA I joined the academic faculty of Tel Aviv University in 1969. During 2003–2011 I held the Joseph & Rebecca Meyerhoff Chair in Solid State Theory & Thermodynamics, Tel Aviv University (TAU). In 2008 I became Emeritus Professor at the School of Physics & Astronomy of TAU. Since then I have continued my research in theoretical physics at TAU. In 2015 I was awarded a Landauer Medal by the International ETOPIM Society. I am currently president of that society since 2018. I am Fellow of the Israel Physical Society (IPS) and of the American Physical Society (APS).
Here is a brief description of some of my major discoveries in physics: In 1977 I introduced a new approach to the analysis of composite materials. This resulted from the observation that the macroscopic moduli of such a material are analytic functions of the constituent moduli. As a result of this, new bounds for the macroscopic moduli of such materials, where the microstructure is disordered and not precisely known, were evolved. The poles of these analytic functions were shown to be the eigenvalues of the homogeneous Maxwell Equations. An approach for calculating the physical electromag- netic fields based upon the eigenstates of those equations was developed and is known in the community as the “Bergman-Milton spectral representation”. More recently I discovered surprising new properties of transport and optical response of a composite medium which are brought about by the presence of a strong magnetic field B. For example, in a mixture of metals with different but comparable resistivities, the macro- scopic Ohmic resistivity ρe can sometimes keep increasing as B2 without any saturation when the Hall resistivities of the constituents are greater than their Ohmic resistivities and keep increasing as |B|. This occurs when the microstructure is periodic. Moreover, ρe then depends very strongly on the precise direction of B with respect to the periodic microstructure. These properties can be exploited for developing new types of magnetic field sensors.
Seminar 23: New results on the range of responses that two-phase composites can have to time varying fields
Speaker: Graeme Milton (Department of Mathematics, University of Utah, USA)
Q & A:
Abstract: It is now slightly more than 40 years since David Bergman and myself obtained bounds on the effective complex dielectric constant of isotropic composites of two isotropic phases mixed in given proportions. This constant governs the quasistatic response to electromagnetic waves of fixed frequency. Hence it also controls the absorption and refraction of radiation by these composites. There has been renewed interest in these old bounds, in part because they also give shape independent bounds in quasistatics on the amount of energy dielectric or metallic particles of given volume can absorb. Our bounds on the effective complex dielectric constant consisted of a lens shaped region in the complex plane bounded by circular arcs. We show that one bound can be tightened and that the corresponding circular arc corresponds to an assemblage of doubly coated spheres. New hierarchical laminate geometries that attain additional points on the remaining arc are described. Consequently, we see that this bound is very tight, almost optimal. We also bound the quasistatic response to applied electromagnetic fields, or antiplane elastic fields, that can have any variation in time, not necessarily a fixed frequency one. Curiously, judicious choices of the applied field can directly yield the volume fractions of the phases from measurements at specific times. We show how applied fields can be tailored to have this property. The work is joint with my wonderful and energetic collaborators: Christian Kern, Ornella Mattei, Owen Miller, and Mihai Putinar.
Biography: Graeme Milton is a distinguished (or maybe extinguished) professor of mathematics at the University of Utah, well known in the field of metamaterials for his 2002 book on the theory of composites, his contributions to bounds on the response of composites, realizability of those bounds, and for co-developing a systematic theory of exact relations for composites which are microstructure independent formulae satisfied by effective moduli. Notable contributions, often with coauthors, include: the first rigorous proof that isotropic elastic materials could have a negative Poisson ratio; the conception of pentamode materials useful for guiding stress; the construction of microgeometries that have reversed Hall coefficient compared to the phases; the discovery in 1994 of anomalous resonance essential to the understanding of superlens imaging; the finding in 2005 of cloaking due to anomalous resonance; and later developments on active cloaking. Additionally, he has obtained bounds on the response of inhomogeneous bodies, not necessarily with microstructure, and used these bounds to estimate the volume fractions of the phases. Other interests include the responses of electric, electromagnetic, and spring-mass networks, and their role in understanding the unusual responses of metamaterials. He is the recipient of Sloan and Packard fellowships, the Prager Medal, the Ralph Kleinman prize, the Landauer Medal, and the Levi-Civita prize among other awards.
Seminar 22: Wave Control for Wireless Communications: From Time-Reversal to Reconfigurable Intelligent Metasurfaces
Speaker: Mathias Fink (Langevin Institute, ESPCI Paris, PSL University, CNRS, France)
Q & A:
Abstract: In this talk, I will show how the works performed at Langevin Institute have led 8 years ago to the seminal concept behind large reconfigurable intelligent surfaces (RIS) that is currently a topic of great interest in the wireless communication community and that is proposed as a new paradigm for the sixth generation (6G) of communication networks. Starting with the first demonstrations of ultrasonic time-reversal focusing in complex media, I will underline how these ideas were transposed later, for electromagnetic waves, into the concept of massive multi-user multiple-input multiple-output (MIMO) for the 5G communication networks. Then, I will explain how, working on the concept of wavefront shaping using spatial light modulators in optics, we propose an equivalent for the microwave domain, using tunable metasurfaces, a concept that would solve the drastic price problem of active techniques like time reversal MIMO. By smartly tuning the signal reflection of large metasurfaces, reconfigurable tunable metasurfaces are capable of dynamically altering wireless channels in disordered environments to enhance the communication performance. Using reconfigurable metasurfaces placed inside any complex environment, we tune the medium complexity to obtain the best communication performance. Compared to the well-known massive multiple-input multiple-output (MIMO) technique, RIS can provide excellent system performance without requiring power-hungry components such as power amplifiers.
Biography: Mathias Fink is the George Charpak Professor at the Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris). He is member of the French Academy of Science. His area of research is concerned with the propagation of waves in complex media and the development of numerous instruments based on this basic research. 6 start-up companies with more than 300 employees have been created from his research (Echosens, Sensitive Object, Supersonic Imagine, Time Reversal Communications, Cardiawave and Greenerwave).
Seminar 21: Tailoring thermal emission with metasurfaces
Speaker: Jean-Jacques Greffet (Université Paris-Saclay, CNRS, France)
Q & A:
Abstract: With the advent of fabrication and imaging at the nanoscale, many unexpected properties of thermal radiation have been explored in the last twenty years. The first part of the talk will be devoted to a review of key features including spatial and temporal coherence of incandescent sources. In the second part of the talk, recent results on an incandescent source that can be modulated beyond 10MHz, six orders of magnitude faster than commercially available hot membranes, will be presented.
Biography: Jean-Jacques obtained his PhD from university Paris-Sud Orsay in 1988 in solid state physics and the Habilitation in 1992. Jean-Jacques Greffet was a professor at Ecole Centrale Paris between 1994 and 2008. He is currently a professor at Institut d’Optique, Université Paris Sud and a senior member of Institut Universitaire de France. He has made a number of contributions in light scattering by random systems. Between 1994 and 2005, he worked on the theory of image formation in near-field optics. Since 1998, he investigated thermal radiation at the nanoscale and demonstrated spatial coherent thermal sources and a giant radiative heat transfer at the nanoscale. His current research interests include nanophotonics (nanoantennas, quantum plasmonics, metasurfaces for light emission) and the design of smart IR incandescent sources. He has coauthored 200 refereed papers with more than 17000 citations. He is an OSA fellow and the recipient of the Ixcore foundation prize and the Servant prize of the french Academy of Science.
Seminar 20: Acoustic Metamaterial Wizardry
Speaker: Oliver B. Wright (Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Japan)
Q & A:
Abstract: Acoustic metamaterials are non-naturally occurring structures consisting of arrays of sub-wavelength resonators designed to manipulate the propagation of sound, exhibiting effective negative density or modulus [1,2]. Counterintuitive metamaterial properties such as acoustic negative refraction, superlensing and cloaking have been demonstrated.
Another example is extraordinary acoustic transmission, i.e. the passage of more acoustic energy than expected through a small sub-acoustic-wavelength aperture acting as an acoustic meta-atom. This has been be demonstrated in a variety of systems, having first been shown in optics. I will first present our experimental work in this field using kHz airborne acoustics , in which case we find giant transmission, with enhancements up to ~60, by use of an aperture closed with a membrane. I will then show how gigantic transmission enhancement, by more than a factor of 500, can be achieved in solid acoustics [4,5].
Closely related to extraordinary acoustic transmission is the phenomenon of enhanced transmission between acoustically mismatched media. I will review experimental work on the enormously enhanced passage of acoustic waves from water to air based on the use of a kHz acoustic metasurface .
Finally, I will present recent kHz experiments on acoustic metabeams  and metarods  with perfect bandgaps that prevent all vibrations from passing along them at certain frequencies. The era of metawands that do not vibrate is upon us.
 Z. Liu, X. Zhang, Y. Mao, Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng, Science 289, 1734 (2000).
 S. H. Lee and O. B. Wright, Phys. Rev. B 93, 024302 (2016).
 J. J. Park, K. J. B. Lee, O. B. Wright, M. K. Jung and S. H. Lee, Phys. Rev. Lett. 110, 244302 (2013).
 S. Mezil, K. Chonan, P. H. Otsuka, M. Tomoda, O. Matsuda, S. H. Lee and O. B. Wright, Sci. Rep. 6, 33380 (2016).
 T. Devaux, H. Tozawa, P. H. Otsuka, S. Mezil, M. Tomoda, O. Matsuda, E. Bok, S. H. Lee and O. B. Wright, Sci. Adv. 6, 8507 (2020).
 E. Bok, J. J. Park, H. Choi, C. K. Han, O. B. Wright and S. H. Lee, Phys. Rev. Lett. 120, 044302 (2018).
 K. Fujita, M. Tomoda, O. B. Wright and O. Matsuda, Appl. Phys. Lett. 115, 081905 (2019).
 A. Ogasawara, K. Fujita, M. Tomoda, O. Matsuda,, O. B. Wright, Appl. Phys. Lett. 116, 241904 (2020).
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.
Seminar 19: Reflectionless Modes: an alternative spectrum for wave scattering
Speaker: Vincent Pagneux (Laboratoire d’Acoustique de l’Université du Maine, CNRS, France)
Q & A:
Figure: two examples of reflectionless modes with real frequency, with an incident wave from the left and perfect transmission to the right (a case of “PT-symmetry” for the reflectionless operator)
Abstract: To characterize scattering resonances, a useful tool is the complex resonance spectrum corresponding to eigenmodes (QNM) able to leak energy. However, for reflection/transmission problems (e.g. waveguides, gratings or screens), the complex resonance spectrum does not directly quantify transmission efficiency, and the question of good or perfect transmission is of tremendous importance in many topics of intense study in wave physics: extraordinary optical transmission, topological states immune to backscattering, perfect transmission resonances, transmission eigenchannels through disordered media, reflectionless metamaterials or metasurfaces.
We present here an alternative spectrum allowing one to identify situations where perfect transmissions occur . The operator yielding the spectrum of reflectionless modes is non-selfadjoint, and it is PT-symmetric for systems with spatial mirror symmetry. Eigenmodes (reflectionless modes) and eigenvalues (reflectionless complex frequencies) will be presented in various scattering situation, from the simplest 1D setup to several 2D waveguide geometries.
 A.-S. Bonnet-Ben Dhia, L. Chesnel, V. Pagneux. Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem. Proc. R. Soc. A, 474(2213), 20180050 (2018)
Biography: Dr. Vincent Pagneux has received his PhD in 1996 from the Université du Maine in France. He is currently Director of Research Scientist at CNRS-LAUM. His research focuses on wave physics, acoustics and metamaterials.
Seminar 18: Wave Interaction with Subwavelength Resonators
Speaker: Habib Ammari (ETH Zürich)
Q & A:
Abstract: In this lecture, the speaker reviews recent results on subwavelength resonances. His main focus is on developing a mathematical and computational framework for their analysis. By characterizing and exploiting subwavelength resonances in a variety of situations, he proposes a mathematical explanation for super-focusing of waves, double-negative metamaterials, Dirac singularities in honeycomb subwavelength structures, and topologically protected defect modes at the subwavelength scale. He also describes a new resonance approach for modelling the cochlea which predicts the existence of a travelling wave in the acoustic pressure in the cochlea fluid and offers a basis for the tonotopic map.
Biography: Habib Ammari is a Professor of Applied Mathematics at ETH Zürich. Before moving to ETH, he was a Director of Research at the Department of Mathematics and Applications at Ecole Normale Supérieure in Paris. He received a Bachelor’s degree in 1992, a Master’s degree in 1993, and a Ph.D. in applied mathematics in 1995, all from the Ecole Polytechnique, France. Following this, he received a Habilitation degree in Mathematics from the University of Pierre & Marie Curie in Paris three years later. Habib Ammari is a world leading expert in wave propagation phenomena in complex media, mathematical modelling in photonics and phononics, and mathematical biomedical imaging. He has published more than two hundred research papers, eight high profile research-oriented books and edited eight books on contemporary issues in applied mathematics. He has advised thirty four PhD students and twenty three postdoctoral researchers. Habib Ammari was awarded with several international prizes.
Seminar 17: Metasurfaces for light shaping: a look into the past to better appreciate the present and future
Speaker: Philippe Lalanne (The Photonics, Numerical and Nanosciences Laboratory, CNRS, France)
Q & A:
Abstract: In integrated circuits, an important prerequisite for success is that every transistor can be driven or read independently, and nanotechnology is used to push the integration limit subject to that essential requirement. In dielectric metasurfaces for wavefront shaping, one aims to imprint spatially varying phases (or amplitudes, polarizations) on an incoming optical beam, and nanotechnology is used to spatially control the phase down to the subwavelength scale, as required for high numerical aperture focusing or imaging, beam steering over large angles, and computer-generated holography. Just like for integrated circuits, it is important that the phase can independently be controlled by adjacent nanostructures (or meta-atoms).
This demanding requirement has marked the history of diffractive optics. I will review this history, evidence some fundamental limitations and introduce recent prospects in my group in relation to disordered metasurfaces.
Biography: Philippe Lalanne is Research Director at CNRS and is an international expert in computational and nanoscale electrodynamics. He was first involved in the group of Pierre Chavel at l’Institut d’Optique at Orsay. In 1995, he spent a sabbatical year with G.M. Morris at the Institute of Optics in Rochester.
With his colleagues, he has launched new modal theories and improved numerical tools for gratings, waveguides and nanoresonators. He has used these tools to provide deep insight into the physical mechanisms involved in key nanoscale optical phenomena and devices, e.g. light confinement in photonic-crystal cavities, the extraordinary optical transmission, light interaction with plasmonic nanoresonators. He has pioneered the development of large-NA metalenses and has designed and demonstrated novel nanostructures with record or completely novel performance in their time.He has supervised 17 PhD candidates and co-supervised 6 PhD candidates. He is an Associate Editor of Optica, a member of the editorial board of Laser & Photonics Reviews, and is director of GDR Ondes, a broad virtual laboratory that gathers the French community working on acoustic and electromagnetic waves. He is a recipient of the Bronze medal of CNRS and the prix Fabry de Gramont of the Société Française d’Optique. He is a fellow of the IOP, OSA and SPIE.
Seminar 16: Mechanics and dynamics of two-dimensional quasiperiodic composites
Speaker : Massimo Ruzzene (University of Colorado Boulder, USA)
Q & A:
Abstract: Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational symmetry. This provides the opportunity to investigate novel classes of quasicrystal inspired elastic composites whose mechanical static and dynamic properties are largely unexplored. This presentation illustrates the performance of continuous elastic quasicrystals composites, here denoted as quasiperiodic (QP) composites, characterized by different rotational symmetry orders which is directly enforced through a design procedure in reciprocal space. Static mechanical properties are investigated as a function of symmetry order and filling fraction. Results indicate that higher order symmetries, such as 8-, 10- and 14-fold, lead to equivalent stiffness characteristics that interpolate those of the constituent materials while maintaining high levels of isotropy for all filling fractions. Thus, QP composites exhibit more uniform strain energy distributions when compared to periodic 4-fold and 6-fold symmetric configurations. Similarly, nearly-isotropic wave propagation is observed over a broader range of frequencies. The spectral dynamic properties are also investigated by enforcing rotational symmetry constraints in a wedge-type unit cell, which allows for the estimation of bandgaps, whose presence is confirmed in frequency response computations. Wave directionality and bandgaps are also estimated through parallel studies conducted on plate structures characterized by QP patterns of surface stubs. These experiments show clear bandgaps, illustrate how wave fronts reflect the rotational symmetry of the domains, and demonstrate that higher order geometries lead to isotropic propagation over a broader range of frequencies. The investigations presented herein open avenues for the general exploration of the properties of quasiperiodic media, with potentials for novel architectured material designs that expand the opportunities provided by periodic media.
Biography: Massimo Ruzzene is the Slade Professor of Mechanical Engineering and holds a joint appointment in the Smead Aerospace Engineering Sciences Department of CU Boulder. M. Ruzzene currently serves as the Associate Dean for Research of the College of Engineering and Applied Science. He joined CU in the summer of 2019, after serving as the Pratt and Whitney Professor in the Schools of Aerospace and Mechanical Engineering at Georgia Institute of Technology. M. Ruzzene received a PhD in Mechanical Engineering from the Politecnico di Torino (Italy) in 1999. He is author of 2 books, more than 180 journal papers and 250 conference papers. He has participated as a PI or co-PI in various research projects funded by the Air Force Office of Scientific Research (AFOSR), the Army Research Office (ARO), the Office of Naval Research (ONR), NASA, the US Army, US Navy, DARPA, the National Science Foundation (NSF), as well as companies such as Boeing, Eurocopter, Raytheon, Corning and TRW. Most of his current and past research work has focused on solid mechanics, structural dynamics and wave propagation with application to structural health monitoring, metamaterials, and vibration and noise control. M. Ruzzene is a Fellow of ASME and SES, an Associate Fellow of AIAA, and a member of AHS, and ASA. He served as Program Director for the Dynamics, Control and System Diagnostics Program of CMMI at the National Science Foundation between 2014 and 2016.
Seminar 15: Dynamics of waves in continuum honeycomb structures
Speaker : Michael I Weinstein (Dept of Applied Physics and Applied Mathematics, and Dept of Mathematics, Columbia University)
Q & A:
Abstract: We overview results on the dynamics of waves (e.g. Schroedinger and Maxwell equations) in honeycomb structures and their deformations.
We study phenomena which arise from the presence of Dirac (conical) points in the bulk band structure.
These include the existence of robust edge (interface) states, which localize along certain sharp terminations, and along domain walls.
We then discuss recent work on the emergence of pseudo-magnetic fields in non-uniformly deformed honeycomb structures.
We apply these results to predict Landau-like energy levels in photonic crystals, and present numerical confirmation of the theory.
Biography: Michael I. Weinstein works on the mathematical modeling, analysis, and applications of wave phenomena across many areas of physical science. A recent focus has been on PDE (Partial Differential Equations) models which describe optical and quantum waves in novel media such as topological insulators and metamaterials. Such physical media have applications to technologies which could potentially revolutionize robust information transfer in computing and communication systems. Weinstein received a B.S. in Mathematics from Union College, summa cum laude, in 1977 and a Ph.D. in Mathematics from the Courant Institute at NYU in 1982. He is a Professor of Applied Mathematics in the Department of Applied Physics and Applied Mathematics and a Professor of Mathematics in the Department of Mathematics at Columbia University. Weinstein is a Fellow of the American Mathematical Society (AMS) and a Fellow of the Society for Industrial and Applied Mathematics (SIAM). In 2015, he received a Math + X Investigator Award from the Simons Foundation.
Seminar 14: Black-hole waves at corners of a metallic particle
Speaker: Anne-Sophie Bonnet-BenDhia (The Applied Mathematics department of l’ENSTA Paris)
Q & A:
Abstract: In this talk, we consider electromagnetic waves in presence of a metallic inclusion with corners, assuming that the dielectric permittivity has a very small imaginary part, that will be neglected, and a negative real part. Due to the sign-change of the dielectric permittivity, very unusual singular phenomena take place at corners. In particular, for some configurations, a part of the energy may be trapped by the corners: this is the so-called blackhole effect .
In this presentation, we first give a mathematical analysis of this blackhole phenomenon, based on a detailed description of the corner’s singularities, in the 2D case.
This phenomenon leads to numerical instabilities of finite element simulations. The solution that we have found and validated is to introduce a complex scaling at the corners.
Finally, we compute the plasmonic eigenvalues of a 2D subwavelength particle with a corner . While a smooth particle has a discrete sequence of eigenvalues, blackhole waves at the corner lead to the presence of an essential spectrum filling an interval. Numerical results show that the complex scaling deforms this essential spectrum, so as to unveil both embedded eigenvalues and complex plasmonic resonances. The latter are analogous to well-known complex scattering resonances, with the local behaviour at the corner playing the role of the behaviour at infinity.
 A-S Bonnet-BenDhia et al, J. Comput. Phys., vol. 322, pp. 224-247, 2016
 A-S Bonnet-BenDhia et al, https://hal.archives-ouvertes.fr/hal-02923259
Biography: Anne-Sophie Bonnet-Ben Dhia is a former student of the Ecole Normale Supérieure de Jeunes Filles. She received the PhD degree in Applied Mathematics in 1988 and the Habilitation à Diriger les Recherches in 1995 from the University Pierre et Marie Curie. She is presently Directeur de Recherche at CNRS.
She is the head of the research team POEMS (associated to CNRS, INRIA and the Ecole Nationale Supérieure de Techniques Avancées) whose activities are devoted to the mathematical and numerical analysis of wave phenomena. She is a specialist of spectral theory and scattering theory, with a particular interest for waveguides configurations. Her theoretical and numerical contributions apply to various physical domains covering optics and electromagnetism, water waves, acoustics, aeroacoustics and ultrasonics.
Seminar 13: Reflections on constitutive relations for acoustic metamaterials
Speaker : John Willis, FRS (DAMTP, University of Cambridge)
Q & A:
Abstract: I shall introduce a particular methodology for deriving effective constitutive relations for metamaterials including (because I was asked to do so) a brief account of how it evolved. It applies to composite materials (and metamaterials in particular) whose microstructure is random and is based on the calculation of ensemble averages. Periodic media are included as a special case, by regarding the exact location of a chosen point in any one cell as being distributed randomly over a cell fixed in space. Within that general framework, all definitions are exact. In practice, except in the case of periodic media, some approximation is required. The approximations developed here are derived systematically from a stochastic variational principle and can at least be regarded as “honest” even though not exact. Some general observations will be supported by examples which illustrate both the utility and the limitations of any formulation involving effective constitutive relations. In particular, except in the “homogenization” or “long-wavelength” limit, boundary layers present near any interface between random media, or between one random medium and one with uniform properties, seriously compromise the use of effective properties. The variational approach can, however, be applied directly to this configuration and has been employed to obtain one of only two solutions for reflection and transmission of acoustic waves at the boundary of a two-component random medium.
Biography: John Willis is Emeritus Professor of Theoretical Solid Mechanics in the University of Cambridge. He undertook his undergraduate and graduate studies in Mathematics at Imperial College. During his career, he has held the following positions: Assistant Lecturer, Department of Mathematics, Imperial College (1962-64), Research Associate, Courant Institute (1964-65), Senior Assistant/Assistant Director of Research, DAMTP Cambridge (1965-72), Professor of Applied Mathematics, Bath (1972-94 and 2000-01), Professor of Theoretical Solid Mechanics, DAMTP Cambridge (1994-2000 and 2001-07), Professeur de Mécanique, Ecole Polytechnique (part-time, 1998-2004). He was Editor of the Journal of Mechanics and Physics of Solids (1982-2006). Major research interests have included static and dynamic problems for anisotropic media, problems of irradiation damage of materials, structural integrity, effective properties of composite materials (both static and dynamic), mechanics of nonlinear composites, stability of strained-layer semiconductor devices. Recent work has been on strain-gradient plasticity and the dynamics of composites (as applied to acoustic metamaterials). He was elected FRS (1992), Foreign Member, US National Academy of Engineering (2004) and Associé Etranger, Académie des Sciences (2009). Awards include the Timoshenko Medal, ASME (1997), Prager Medal, SES (1998), Euromech Solid Mechanics Prize (2012).
Seminar 12 : Moth wings as metamaterial sound absorbers
Speaker : Marc Holderied (University of Bristol)
Q & A:
Abstract: Providing healthy living and working environments in our ever-noisier world necessitates increasing use of noise control technology. The rapidly expanding field of acoustic metamaterials has led to the emergence of ultrathin subwavelength sound absorbing methods, allowing sound insulation to be thinner and lighter than ever before. We will present our discovery of a natural acoustic metamaterial and show our ongoing work towards bioinspired metamaterial absorbers. Our bioinspiration arises from the 65-million-year acoustic arms race between echolocating bats and their moth prey, which has turned the wing scales of moths into an omnidirectional, ultrathin (1/100 λ) and broadband absorber of ultrasound (peak α = 0.71) that provides acoustic camouflage against bats. Our lithographically produced up-sized scale replicas absorb sound and can resonate at the most important frequencies for human communication. This research paves the way for bioinspired broadband sound absorbers that are thinner and lighter than existing solutions.
Biography: Dr Marc Holderied is a sensory ecologist and bioacoustician with strong links to bio-inspired engineering. He finds bio-inspired acoustic solutions in three areas. Bat avionics: biosonar place recognition, flow perception and obstacle avoidance, in-flight group coordination and bio-inspired radar. Predator-prey acoustics: bat stealth hawking , the acoustic ecology of scorpion-eating bats, and a new insect ear. Echo evolution: Using airborne ultrasound tomography he discovered retroreflectors in bat-pollinated plants, echo shadows of insects, and identified moth fur as enhanced porous sound absorber, and moth scales as broadband resonant metamaterial absorbers. His research regularly features on the BBC (eg ‘Planet Earth II’, ‘Super Senses’). He heads the Behavioural Acoustics and Sensory Biology lab at the University of Bristol. He is a fellow of the German National Academic Foundation and an international consultant on ultrasonic vision for the automotive sector.
Seminar 11 : Multipurpose metamaterials: designing for static, acoustic and elastic properties in a single architecture
Speaker : Chiara Daraio (California Institute of Technology)
Q & A:
Abstract: Mechanical metamaterials are materials with a tailored, architected structure, designed to achieve properties that depart from those found in natural or more “conventional” engineering materials. Common realizations of metamaterials are periodic and derive their properties from an interplay of the constitutive material responses and their architected geometry. Most of these designs to date have been developed to address a single functionality (e.g., for supporting a certain band gap, a low-frequency resonant response, a topological waveguide). However, many engineering applications have to satisfy simultaneously multiple constraints and demand specific static and dynamic responses. Increasing the design complexity allows the realization of materials with desirable effective properties, and added functionalities. In this talk, I will highlight some of our recent work in the design, fabrication and characterization of structured, multipurpose metamaterials and their possible application to engineering problems. For example, materials that can control acoustic and elastic waves simultaneously, which can function as ultimate protectors, or materials that are designed with specific acoustic impedance and load-bearing properties, which can function as acoustic windows, or flexible, resonant metamaterials for haptic interfaces.
Biography: Professor Daraio received her undergraduate degree in Mechanical Engineering from the Universita’ Politecnica delle Marche, Italy (2001). She received her M.S. (2003) and Ph.D. degrees (2006) in Materials Science and Engineering from the University of California, San Diego. She joined the Aeronautics and Applied Physics departments of the California Institute of Technology (Caltech) in fall of 2006 and was promoted to full professor in 2010. From January 2013 to August 2016, she joined the department of Mechanical and Process Engineering at ETH Zürich, with a chair in Mechanics and Materials. She returned to Caltech in August 2016, as a Professor of Mechanical Engineering and Applied Physics. She received a Presidential Early Career Award from President Obama (PECASE) in 2012, was elected as a Sloan Research Fellow in 2011 and received an ONR Young Investigator Award in 2010. She is also a winner of the NSF CAREER award (2009), of the Richard Von Mises Prize (2008) and received the Hetenyi Award from the Society for Experimental Mechanics (2015). She was selected by Popular Science magazine among the “Brilliant 10” (2010). She serves as a Board Editor for Science (AAAS) and as an Associate Editor for the journals Matter (Cell Press), Multifunctional Materials (IOP) and Frontiers in Materials (Frontiers). A complete list of publications and research information can be found at:
Seminar 10 : Theoretical thermotics and thermal metamaterials: A brief review
Speaker : Jiping Huang (Department of Physics, Fudan University, Shanghai, China)
Q & A:
Abstract: Transformation thermotics [1-5] is a kind of theoretical method which is based on the coordinate transformation between two different spaces, which can precisely couple geometric structure parameters into physical quantities such as thermal conductivity. This method makes it possible to artificially tailor the geometric structure to accurately control the flow of heat. Free control of heat flux is always a dream of human beings. For this purpose, thermal metamaterials come to appear [6,7], which just originate from the theory of transformation thermotics. Here, I review the crucial theoretical and experimental research progresses in this field after the birth of transformation thermotics for steady-state thermal conduction in 2008 [1,2]. They mainly include the following novel thermal phenomena or functional metamaterial devices: thermal cloak, thermal concentrator, thermal rotator, macroscopic thermal diode, thermal camouflage, thermal transparency, thermal imitator, thermal golden touch, ultra-low thermal conductivity, thermocrystal, zero-energy consumption and negative-energy consumption in ambient temperature difference, thermal anti-parity-time symmetry, thermal convection cloak/concentrator/camouflage, and daily radiation cooling. I will present the relevant microscopic or macroscopic heat-transfer mechanisms and make some prospects for the future.
 C. Z. Fan, Y. Gao, and J. P. Huang, Shaped graded materials with an apparent negative thermal conductivity, Applied Physics Letters 92, 251907 (2008).
 T. Y. Chen, C. N. Weng, and J. S. Chen, Cloak for curvilinearly anisotropic media in conduction, Applied Physics Letters 93, 114103 (2008).
 J. Y. Li, Y. Gao, and J. P. Huang, A bifunctional cloak using transformation media, Journal of Applied Physics 108, 074504 (2010).
 G. X. Yu, Y. F. Lin, G. Q. Zhang, Z. Yu, L. L. Yu, and J. Su, Design of square-shaped heat flux cloaks and concentrators using method of coordinate transformation, Frontiers of Physics 6, 70 (2011).
 S. Guenneau, C. Amra, and D. Veynante, Transformation thermodynamics: cloaking and concentrating heat flux, Optics Express 20, 8207 (2012).
 M. Maldovan, Sound and heat revolutions in phononics, Nature 503, 209 (2013). M. Wegener, Metamaterials beyond optics, Science 342, 939–940 (2013).
Biography: Jiping Huang is a professor in the Department of Physics, Fudan University, from 2005-now. He is Vice-Dean of Department of Physics, Fudan University, from 2007-2009 and from 2020-now. He was a Humboldt Research Fellow in Max Planck Institute for Polymer Research from 2004-2005. His research interests: theoretical thermotics (transformation thermotics and extended theory) and thermal metamaterials. Inspired by transformation optics, he proposed the theory of transformation thermotics for steady-state thermal conduction [Appl. Phys. Lett. 92, 251907 (2008)], and predicted the concepts of thermal cloak and apparently negative thermal conductivity (thermal rotator). His work has triggered the upsurge of theoretical and experimental design of artificial structures to control heat transfer, and promoted the formation of a hot research direction, thermal metamaterials. His pioneering contribution has been recognized by peers. In this direction, he has published the first book on thermal metamaterials, namely, “Theoretical Thermotics: Transformation Thermotics and Extended Theories for Thermal Metamaterials (Springer, 2020)”, together with tens of journal papers in Phys. Rev. Lett., Phys. Rev. E, Phys. Rev. Appl., Appl. Phys. Lett., and Int. J. Heat & Mass Transfer.
Seminar 9 : Localisation of light in ordered time dependent systems
Speaker : Sir John Pendry, FRS (Imperial College London)
Q & A:
Abstract: Electromagnetic waves in periodically ordered materials are delocalised into Bloch states, just like electrons in ordered solids. Recently interest has grown in systems ordered in both space and time the simplest example of which might be a permittivity with a 1D grating,
We stress that this is not a moving medium but a modulation of the medium’s properties phased in time. Hence the velocity of propagation, cg = W/g can take any value -∞< cg<+∞ and is not constrained by relativity. Here too light can propagate in extended Bloch states but there is a range of values ,
for which the Bloch picture fails. In this so called luminal region any incident radiation will be localised in a series of wells defined by the grating and travelling at the velocity of the grating. We present analytical solutions to this model and in particular explore the localised/delocalised transition which has an exponent of 1/2. Light incident on a grating with cgin the luminal range is compressed and amplified by a novel mechanism into a series of ever more localised pulses which emerge from the far side of the grating as shown in the figure below. For values of cg outside the luminal region a plane electromagnetic wave enters the grating as a linear combination of Bloch waves which oscillate in amplitude as they propagate. Approaching the critical velocity the oscillation period and amplitude diverge. The same exponent controls the diverging period as controls the exponential growth inside the luminal regime: a familiar result from localisation in disordered systems.
 Oliner, A. A., and A. Hessel, IRE Transactions on Microwave Theory and Techniques 9 337-343. (1961).
Biography: John Pendry is a condensed matter theorist and has worked at Imperial College since 1981. He has worked extensively on electronic and structural properties of surfaces developing the theory of low energy diffraction and of electronic surface states. More recently he turned his attention to photonic materials this interest led to his present research into the remarkable electromagnetic properties of materials where the normal response to electromagnetic fields is reversed, leading to negative values for the refractive index. In collaboration with scientists at Marconi he designed a series of metamaterials, completely novel materials with properties not found in nature. These designs were subsequently the basis for new concepts with radical consequences, such as the first material with a negative refractive index, the concept of a perfect lens, and a prototype cloaking device, which have both caught the imagination of the world’s media.
Seminar 8 : Topological metamaterials for robust signal and energy manipulation
Speaker : Romain Fleury (Swiss Federal Institute of Technology in Lausanne, EPFL, Switzerland)
Q & A:
Abstract: Topological metamaterials are artificially engineered structures that confer to the waves that propagate through them a property, for example the presence of a given mode, that is robust to continuous modifications of the metamaterial, such as geometrical deformations, local defects, or irregularities in the wave path. In this talk, I will first explore how robust topological modes can be leveraged as building blocks to engineer resilient scattering responses1,2. Such topological scattering, which enables filtering signals without stringent requirements on the system’s geometry3, is experimentally demonstrated with acoustic waves. We will then discuss the relevance of topology to robust energy concentration or manipulation, in particular using second order topological wave insulators leveraging non-linearity4, or combining topological concepts with classical metamaterial effects such as near-zero-index supercoupling5. Altogether, this talk demonstrates that the field of topology is now sufficiently mature to move from purely physics-driven explorations towards exciting application-oriented developments6.
- Topological analog signal processing, Nat. Commun., vol. 10, no. 1, pp. 1–10, Dec. 2019.
- Topological Fano Resonances, Phys. Rev. Lett., vol. 122, no. 1, p. 014301, Jan. 2019.
- Disorder‐Induced Signal Filtering with Topological Metamaterials, Adv. Mater., vol. 32, no. 28, p. 2001034, Jul. 2020.
- Nonlinear Second-Order Topological Insulators, Phys. Rev. Lett., vol. 123, no. 5, p. 053902, Aug. 2019.
- Zero-Index Weyl Metamaterials, Phys. Rev. Lett., vol. 125, no. 5, p. 054301, Jul. 2020.
- Active times for acoustic metamaterials, Reviews in Physics, vol. 4. Elsevier B.V., p. 100031, 01-Nov-2019.
Biography: Romain Fleury is a professor in the School of Engineering at EPFL, the Swiss Federal Institute of Technology in Lausanne, where he leads the Laboratory of Wave Engineering. His research directions include wave-based information processing leveraging disorder, topology, non-Hermiticity, and non-reciprocity, acoustic imaging techniques, and technological applications of locally-resonant metamaterials. He is the 2017 F.V. Hunt fellow of the Acoustical Society of America, an MSCA fellow, and a Campus France Prestige fellow. He has received an Eccellenza award from the Swiss National Science Foundation, a STI Polysphere teaching award from EPFL students, and the best teacher award from the Institute of Electrical Engineering at EPFL.
Seminar 7: Acoustic metamaterials with digitally virtualized resonance
Speaker: Jensen Li (The Hong Kong University of Science and Technology)
Q & A:
Abstract: We present a platform in constructing acoustic metamaterials with digital electronics feedback, which allows us to realize arbitrary resonating response, as if they are acoustic metamaterials with physical resonance, but now with more engineering degrees of freedom. In the first part of this webinar, we will introduce the essential steps to virtualize an impulse response of acoustic metamaterial to a digital signal processing code, demonstrating hugely tunable resonating frequency, strength and linewidth. It also allows arbitrary specifications of bulk modulus, density and Willis parameters with controllable bandwidth. In the second part, we will investigate impact of these arbitrary material parameters to explore active time-varying systems. Specifically, high efficiency on frequency conversion is experimentally demonstrated by tailor-made time-varying response function. Its application with material gain and loss being alternating in time is also investigated.
Biography: Jensen Li is currently a professor in the Department of Physics at Hong Kong University of Science and Technology. His research directions include optical metasurfaces, non-Hermitian systems, transformation optics and acoustic metamaterials. He has published more than 80 peer-reviewed articles and his research group in Hong Kong and previously in UK has been supported by research grants from EU and Hong Kong RGC. Currently, he is leading a collaborative research project on “Non-Hermitian Systems in Optics and Acoustics” across several universities in Hong Kong.
Seminar 6: Elastic metasurfaces
Speaker : Richard Craster (Imperial College London, Imperial-CNRS Abraham de Moivre IRL)
Abstract: Elastic waves guided along surfaces dominate applications in geophysics, ultrasonic inspection, mechanical vibration, and surface acoustic wave devices; precise manipulation of surface Rayleigh waves and their coupling with polarized body waves presents a challenge that offers to unlock the flexibility in wave transport required for efficient energy harvesting and vibration mitigation devices. In this talk I will describe various designs of elastic metasurfaces, based around a graded array of rod resonators attached to an elastic substrate that, together with critical insight from Umklapp scattering in phonon-electron systems, allow us to leverage the transfer of crystal momentum; we mode-convert Rayleigh surface waves into bulk waves that form tunable beams. Experiments, theory and simulation verify that these tailored Umklapp mechanisms play a key role in coupling surface Rayleigh waves to reversed bulk shear and compressional waves independently, thereby creating passive self-phased arrays allowing for tunable redirection and wave focusing within the bulk medium. We have also looked recently at piezoelectric coupling and the use of these devices in energy harvesting and, if time allows, I will discuss this too.
Biography: Richard Craster is the Dean of the Faculty of Natural Sciences at Imperial College and formerly Head of Department of Mathematics at Imperial College a role he held for six years (2011-2017). He is also Director of the CNRS-Imperial “Abraham de Moivre” International Research Laboratory in Mathematics. He has been at Imperial College as an academic since 1998 apart from holding a distinguished professorship in Alberta, Canada, 2008-2010 returning to become Head of the Mathematics Department at Imperial. In addition to being a Professor of Applied Mathematics he is also a member of the Mechanical Engineering Department at Imperial.
His research lies in the field of applied mathematics in particular wave mechanics, metamaterials, fluid mechanics and elasticity. He is the co-editor of one of first books on Acoustic Metamaterials, PI of an EPSRC Programme grant on the Mathematical fundamentals of Metamaterials, co-organiser of the UK Acoustics Network (www.acoustics.ac.uk), and recently co-editor of the volume on Elastic Metamaterials for the Handbook of Metamaterials.
Seminar 5: Metamaterials, shear bands and invisibility
Speaker: Davide Bigoni (University of Trento)
Q & A:
Abstract: Architected materials are preconized to yield extreme mechanical properties such as foldability, channeled response, and surface effects. These features are expected to lead to the production of artificial materials of unchallenged mechanical properties, in other words, metamaterials. Homogenization theory and Floquet-Bloch techniques will be applied to grids of elastic rods, subject to various conditions, including axial pre-stress, to demonstrate strain localization, wave channeling, total reflection, and negative refraction. Finally, invisibility through cloaking of voids in a flexurally vibrating plate will be presented.
Biography: Davide Bigoni is a mechanician working in solid and structural mechanics and material modeling, wave propagation, fracture mechanics. His approach to research is the employment of a broad vision of mechanics, with a combination of mathematical modelling, numerical simulation, and experimental validation. From 2001 Davide Bigoni holds a professor position at the University of Trento, where he is leading a group of excellent researchers in the field of Solid and Structural Mechanics. He has authored or co-authored more than 100 journal papers. He was elected in 2009 Euromech Fellow (of the European Mechanics Society), has received in 2014 the Doctor Honoris Causa degree at the Ovidius University of Constanta and in 2016 the Panetti and Ferrari Award for Applied Mechanics (from Accademia delle Scienze di Torino). He has been awarded an ERC advanced grant in 2013. He is co-editor of the Journal of Mechanics of Materials and Structures and associate Editor of Mechanics Research Communications and in the editorial board of 8 international journals.
Seminar 4: Broken Symmetries in Acoustic and Mechanical Metamaterials
Speaker: Andrea Alù (City University of New York)
Q & A:
Abstract: In this seminar, I will discuss our recent activity in acoustics and mechanics, showing how suitably tailored broken symmetries in meta-atoms and their arrangements open exciting venues for new technology. I will focus in particular on the opportunities offered by time modulation and switching, reciprocal and non-reciprocal Willis coupling, and topological order in metamaterials, which provide unique opportunities for exotic acoustic and mechanical responses. Physical insights into the underlying phenomena, and new devices based on these concepts will be presented.
Biography: Andrea Alù is the Founding Director and Einstein Professor at the Photonics Initiative, CUNY Advanced Science Research Center. He received his Laurea (2001) and PhD (2007) from the University of Roma Tre, Italy, and, after a postdoc at the University of Pennsylvania, he joined the faculty of the University of Texas at Austin in 2009, where he was the Temple Foundation Endowed Professor until Jan. 2018. Dr. Alù is a Fellow of AAAS, IEEE, OSA, SPIE and APS, a Simons Investigator, a Highly Cited Researcher, a DoD Vannevar Bush Faculty Fellow, and has received several scientific awards, including the IEEE Kiyo Tomiyasu Award (2019), the ICO Prize in Optics (2016), the NSF Alan T. Waterman award (2015), the OSA Adolph Lomb Medal (2013), and the URSI Issac Koga Gold Medal (2011).
Seminar 3: 3D chiral mechanical metamaterials
Speaker: Martin Wegener (Karlsruhe Institute of Technology)
Q & A:
Abstract: Calling an object or a metamaterial handed or “chiral” requires it to exhibit (i) broken space-inversion symmetry, (ii) no mirror planes, and (iii) no rotation-reflection symmetries. The absence of these symmetries allows for certain effective material behaviour that would otherwise be forbidden by symmetry. Here, we review our recent progress on three-dimensional (3D) chiral mechanical metamaterials in the linear elastic regime. This includes tailored characteristic length scales of push-to-twist conversion behaviour, ultrasound experiments on acoustical activity with transient nanometer-precision displacement-detection, the mapping of this dynamic behaviour (as well as of the static behaviour) onto effective-medium descriptions beyond Cauchy elasticity, and the possibility of isotropic acoustical activity in rationally designed 3D chiral quasi-crystalline mechanical metamaterials.
Biography: Martin Wegener is professor of physics at Institute of Applied Physics at Karlsruhe Institute of Technology (KIT) and Scientific Director of Institute of Nanotechnology at KIT. He has published more than 300 papers in peer-reviewed journals, with more than 33,000 citations and a Hirsch index of h=86 according to google scholar.
Seminar 2: Bio-inspired hierarchical metamaterials
Speaker : Marco Miniaci (Institute of Electronics, Microelectronics and Nanotechnology of Lille)
Q & A:
Abstract: Nature has engineered complex designs to achieve advanced properties and functionalities over hundreds of thousands of years. For instance, a hierarchical organization over multiple length scales allows enhanced quasistatic mechanical properties (such as high specific strength, stiffness, and toughness). While largely investigated in the quasistatic domain, the role of hierarchy in the dynamic behaviour of metamaterials remains largely unexplored. In this webinar a numerical and experimental investigation of the influence of bio-inspired hierarchical organization on the wave dispersion diagram in metamaterials with self-similar structures at various spatial scales is presented. The advantages (and limitations) that the hierarchical architectures provide for the dynamic performance with respect to conventional metamaterials will be discussed.
Biography: Marco Miniaci is a researcher at the French National Scientific Research Center (CNRS) within the UMR 8520 — IEMN (Institute of Electronics, Microelectronics and Nanotechnology) of Lille. He specializes in wave dynamics, periodic structures and metamaterials. His actual research activity mainly concerns topological protection in patterned elastic waveguides and bio-inspired hierarchical elastic metamaterials.
Seminar 1: Topological mode steering across wave physics
Speaker: Mehul Makwana (Imperial College London)
Abstract: Steering waves around sharp bends and splitting their energy between different channels, in a robust and lossless manner, is of interest across many areas of engineering and physics. The seminal work of Mekis et. al [Phys. Rev. Lett. 18, 3787, 1996] in photonic crystals using cavity waveguides to perform this is now used widely in devices. A very active area of current research involves trying to use ideas originating in quantum mechanics, and from topological insulators, for similar purposes, but with the added potential of broadband performance, and enhanced robustness. In this presentation, I will relay the main principles of topological modes in classical wave systems and elucidate their benefits and shortcomings. Theoretical, computation and experimental results will be used to highlight a particular class of these insulators that contain passive elements and are solely reliant upon geometrical properties of the structured media.
Biography: Mehul Makwana is an EPSRC Research Associate in Mathematical Physics at Imperial College London and a Scientific Consultant to Multiwave Technologies AG. He has experience in in the mathematical modelling of wave phenomena, in particular, that of structured media in elasticity and phononics.