Andrea Alù, City College of New York
The goal of the collaboration annual meeting is to provide an overview of the major advances in this first year of our Simons Collaboration, and discuss the use of various forms of symmetries to guide the optimal designs of metamaterials for extreme manipulation of light, radio-waves and mechanical waves. The meeting will focus on symmetry-driven engineered materials and associated extreme wave phenomena.
First Annual Meeting of the Simons Collaboration on Extreme Wave Phenomena Based on Symmetries
Speakers: Andrea Alù, City University of New York, Advanced Science Research Center; Michel Fruchart, University of Chicago; Demetri Christodoulides, University of Central Florida–College of Optics and Photonics; Tsampikos Kottos, Wesleyan University; Robert Kohn, Courant Institute of Mathematical Sciences–New York University; Alfred Douglas Stone, Yale University; Alex Khanikaev, City College of New York; Nader Engheta, University of Pennsylvania.
The first annual meeting of our collaboration hosted 82 attendees, 63 in person and 19 remotely. The meeting went on for two days, featuring eight talks that discussed various problems related to extreme wave phenomena based on symmetries. The attendees enjoyed many lively discussions during breaks and meals as well as throughout the two days of the meeting. We also featured a poster session with 25 posters presented by junior members of our collaboration. Overall, it was an excellent opportunity to meet in person after the first year when the interactions were limited to Zoom by the pandemic, and it was a very productive way to engage the broader scientific community. We received useful feedback and are excited by the research progress that the collaboration funding has been enabling.
The opening talk from Alù discussed recent results from the collaboration in the context of polaritonics, nano-optics, electromagnetics, and acoustics, showcasing how geometrical and temporal broken symmetries enable a wide range of extreme wave phenomena, including topological transitions in 2D materials, exceptional point singularities in wave scattering, sub- diffractive wave propagation and energy transformations. A highlight from this presentation was the experimental demonstration of topological transitions in phononic materials, such as calcite and molybdenum trioxide, through geometrical rotations. Khanikaev’s talk built on these concepts and showcased exciting progress in topological wave physics exploiting acoustic, electromagnetic and polaritonic metamaterials. He demonstrated the extreme control of light and sound waves using two types of engineered systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetries. Of particular interest, in his talk, Khanikaev showed the latest results — realized within this collaboration — on topological polaritons in boron nitride or transition metal dichalcogenides strongly coupled to metasurfaces, in which the topological phase is transferred from light to phonons or excitons due to the involved symmetries.
Kottos’ talk further enhanced the discussions on exceptional points and non-Hermitian physics. In his talk, he discussed the role of loss and its manipulation as a useful design element to enable nonconventional wave phenomena. His recent work has shown the realization of non- Hermitian spectral singularities and demonstrated an exciting experiment on the superior sensing performance in an accelerometer. Significant discussion has followed this talk on the role of noise, nonlinearities, and active elements in achieving this performance. During the discussions, Johnson brought up interesting opportunities in analyzing linewidth broadening at the lasing point, and the noise ramifications for sensing, connected with a powerful theoretical model to deal with these spectral singularities developed within the collaboration. Stone’s talk followed along similar themes and served as an excellent tutorial on the manipulation of poles and zeros and their degeneracies in general non-Hermitian systems, and their role in enabling extreme wave phenomena. He showed important experimental results, developed in collaboration with Alù’s group, on exceptional point zeros at real and complex frequencies, which can lead not only to enhanced but also new opportunities for efficient energy storage and state transfer in quantum systems. He also discussed opportunities emerging in subclasses of complex systems, which may support reflectionless scattering modes at real and complex frequencies. Stone also unveiled his recent explorations connecting these concepts to PT-symmetry and associated quantum mechanics problems, in close interaction with Bender, and to metasurfaces in chaotic systems, in collaboration with Fink.
Fruchart gave an excellent overview of dualities, very well connected to the other talks dealing with symmetry-driven topological concepts. He showed how systems mapped onto themselves by a duality transformation can enhance the symmetries of a Hamiltonian or a dynamical matrix, enabling the design of metamaterials with emergent properties that escape standard group theory analysis. He showed examples in twisted mechanical kagome lattices that supported nontrivial pairs of distinct configurations exhibiting the same vibrational spectrum and related elastic moduli. Their duality-enforced twofold degeneracy can then be harnessed to construct mechanical spins and obtain non-commuting mechanical responses through non- Abelian geometric phases. During the discussions, several opportunities for acoustic and optical metamaterials emerged, and the intriguing connections with topological wave phenomena were discussed. Along related, lines, Kohn discussed the team progress on modeling mechanical metamaterials and capturing their unusual wave phenomena in the context of linear and nonlinear problems. His work with Bertoldi in our collaboration has been unveiling several exciting opportunities for mechanism-based mechanical metamaterials, some showcasing highly nontrivial and new topological wave phenomena.
Christodoulides updated the attendees on his progress on optical thermodynamics, an exciting journey to model chaotic systems. He developed a thermodynamic theory of highly multimoded nonlinear optical systems based on symmetries and the application to predict the nonlinear excitation, dynamic evolution, and optical pressure of multimode systems in terms of statistical mechanics. His results pave the way toward high-power optical sources with controllable orbital angular momenta and, at a more fundamental level, toward shedding light on the physics of other complex multimoded nonlinear bosonic systems that display additional conservation laws that result from their underlying symmetries. The collaboration team has been largely benefiting from these explorations, and during the discussion time, several additional opportunities were brought up. The closing talk of the meeting was given by Engheta, who offered an exciting overview of the duality between space and time in electromagnetics and the opportunities arising from considering tailored space, time, and space-time interfaces. Exploring similarities and differences in space-time analogy, symmetry, and duality in electromagnetic metamaterials, he showcased exciting possibilities and new venues for light-matter interactions. He described these opportunities as four-dimensional (4D) metamaterials, wave-based material-based platforms in which the some of the material parameters vary in time (i.e., temporal inhomogeneities) in addition to (or instead of) varying in space (i.e., spatial inhomogeneities). Such spatiotemporal features can also be merged and combined with the pseudospin-polarized states in electromagnetic metamaterials, and consequently, richer wave-based functional platforms can be achieved. Along similar lines, Alù described topological wave phenomena and parity-time symmetry emerging at time interfaces, and exciting connections between these works started to emerge during the discussion time.
Overall, the meeting featured truly excellent discussions and several new research directions, succeeding at expanding the collaboration’s impact and offering new opportunities for interactions within all collaboration members and the broader scientific community. We look forward to a rich second year of scientific discussions and research progress.
Thursday, October 21
9:30 AM Andrea Alù | Symmetry-driven metamaterials 11:00 AM Michel Fruchart | Dualities for material design 1:00 PM Demetrios Christodoulides | Optical thermodynamics of highly multimoded nonlinear systems 2:30 PM Tsampikos Kottos | Wave-Matter interactions at the Exceptional Point 4:00 PM Robert Kohn | Mechanical metamaterials
Friday, October 22
9:30 AM A. Douglas Stone | Exceptional points in scattering: a general approach 11:00 AM Alexander Khanikaev | Symmetry-engineered pseudospins for topological photonics, acoustic, and polaritonics 1:00 PM Nader Engheta | Spatiotemporal metamaterials
Abstracts and Slides
Symmetry driven meta-materials
In this talk, I discuss our recent research activity in the area of metamaterials, with an emphasis on the opportunities enabled by symmetries and symmetry breaking to induce emerging wave phenomena. I will discuss how geometrical asymmetries, temporal modulation and switching in metamaterials enable a wide range of new phenomena, magnet-free nonreciprocity, topological wave transport, parametric gain, and new forms of polariton waves. During the talk, I will discuss the opportunities and challenges it opens for the next-generation of artificial materials and technologies based on them.
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 NAI, AAAS, IEEE, MRS, OSA, SPIE and APS, and has received several scientific awards, including the Blavatnik National Award for Physical Sciences and Engineering, the AAAFM Heeger Award, the Dan Maydan Prize in Nanoscience, the IEEE Kiyo Tomiyasu Award, the Vannevar Bush Faculty Fellowship from DoD, the ICO Prize in Optics, the NSF Alan T. Waterman award, the OSA Adolph Lomb Medal, and the URSI Issac Koga Gold Medal.
University of Chicago
Dualities for material design
Dualities are mathematical mappings that reveal links between apparently unrelated systems in virtually every branch of physics. Systems mapped onto themselves by a duality transformation are called self-dual and exhibit remarkable properties, as exemplified by the scale invariance of an Ising magnet at the critical point. In this talk, we will see that dualities can enhance the symmetries of a Hamiltonian or a dynamical matrix, enabling the design of metamaterials with emergent properties that escape a standard group theory analysis. As a first illustration, we consider twisted kagome lattices, reconfigurable mechanical structures that change shape by means of a collapse mechanism. Pairs of distinct configurations along the mechanism exhibit the same vibrational spectrum and related elastic moduli. These puzzling properties arise from a duality between pairs of configurations on either side of a mechanical critical point. The critical point corresponds to a self-dual structure with isotropic elasticity (even in the absence of spatial symmetries) and a two-fold degenerate spectrum over the entire Brillouin zone. The duality-enforced two-fold degeneracy can then be harnessed to construct mechanical spins and obtain non-commuting mechanical responses through non-Abelian geometric phases. We then develop a systematic way to construct families of Hamiltonians endowed with a given duality and to provide a universal description of Hamiltonians families near self-dual points. Our results, based on group-theoretical considerations, apply to all linear systems (photonic, diffusive, mechanical, etc.), provided no (non-linear) constraints exist on the parameters. To go beyond unconstrained parameter spaces, we reformulate the existence of a duality as a minimization problem which is amenable to standard optimization and numerical continuation algorithms. Combined with existing procedures to physically implement coupled-resonator Hamiltonians, our approach enables on demand design of optical, mechanical, thermal, or electronic metamaterials with dualities.
Michel Fruchart is a Kadanoff Rice Fellow post-doctoral fellow working in Vitelli’s group at the University of Chicago. He obtained his PhD in theoretical physics from the Ecole Normale Superieure in Lyon.
University of Central Florida
Optical thermodynamics of highly multimoded nonlinear systems
The prospect of judiciously using symmetries has been actively pursued in recent years as a means to control the flow of light. In this talk, a thermodynamic theory of highly multimoded nonlinear optical systems will be presented. We will show that the orbital angular momentum (OAM) of a light field can be thermalized in a nonlinear cylindrical multimode optical waveguide. Upon thermal equilibrium we find that the maximization of the optical entropy leads to a generalized Rayleigh-Jeans distribution that governs the power modal occupancies with respect to the discrete OAM charge numbers. This distribution is characterized by a temperature that is by nature different from that associated with the longitudinal electromagnetic momentum flow of the optical field. Counterintuitively and in contrast to previous results, we demonstrate that even under positive temperatures, the ground state of the fiber is not always the most populated in terms of power. Instead, because of OAM, the thermalization processes may favor higher order modes. These results may pave the way towards high power optical sources with controllable orbital angular momenta, and at a more fundamental level, could shed light on the physics of other complex multimoded nonlinear bosonic systems that display additional conservation laws that result from their underlying symmetries.
Demetrios Christodoulides is the Cobb Family Endowed Chair and Pegasus Professor of Optics at CREOL-the College of Optics and Photonics of the University of Central Florida. He received his Ph.D. degree from Johns Hopkins University in 1986 and he subsequently joined Bellcore as a post-doctoral fellow. Between 1988 and 2002 he was with the faculty of the Department of Electrical Engineering at Lehigh University. His research interests include linear and nonlinear optical beam interactions, synthetic optical materials, optical solitons, and quantum electronics. He has authored and co-authored more than 430 papers. He is a Fellow of the Optical Society of America and the American Physical Society. He is the recipient of the 2011 Wood Prize and 2018 Max Born Award of OSA.
Robert V. Kohn
New York University
Mechanism-based mechanical metamaterials are designer materials that experience microscale buckling in response to mechanical deformation. A rapidly-growing literature is emerging concerning the design and use of such materials. Their analysis challenges our understanding of the relationship between microscopic and macroscopic behavior in geometrically nonlinear mechanical systems. This talk will mainly focus on a particular example: the Kagome metamaterial. A key issue is whether its macroscopic behavior is adequately modeled by elastic energy minimization (even though its energy landscape is very nonconvex, with many local minima). I’ll discuss theoretical work with Xuenan Li, which has determined the consequences of this model; and I’ll discuss ongoing numerical work with Katia Bertoldi, Bolei Deng, and Xuenan Li, which is exploring the adequacy of the model.
Robert V. Kohn is a Silver Professor of Mathematics at NYU’s Courant Institute of Mathematical Sciences. He works in nonlinear PDE and the calculus of variations, often focusing on challenges from physics and materials science. His recognitions have included SIAM’s Ralph E. Kleinman Prize, the AMS’s Leroy P. Steele Prize for Seminal Contribution, and membership in the American Academy of Arts and Sciences. He is both a Fellow of the AMS and a SIAM Fellow.
Wave-Matter Interactions at the Exceptional Point
The manipulation and management of wave propagation using artificial structures with tailored geometric symmetries has always been an exciting subject, often challenging the creativity of the researchers and exciting the imagination of the public. There is an alternate viewpoint that is emerging, and its focus is to manipulate the loss within the propagating medium and via a judicious design of the impedance profile to implement dynamical symmetries in the wave structures. The surprising element of this approach is that it elevates the loss — an element which until recently was considered anathema — to a useful design element whose manipulation can lead to the realization of devices with nonconventional properties and novel functionalities. At the core of many of these results is the existence of non-Hermitian spectral singularities in the frequency spectrum of these structures known as an exceptional point (EP). At an EP, the wave matter interaction is enhanced, leading to unexpected wave-transport features. This talk will highlight some recent results on wave-matter interaction at an EP, paying particular attention to specific applications like hypersensitive sensors, reconfigurable nano-indenters and enhanced energy harvesting from ambient noise sources.
A. Douglas Stone
Exceptional points in scattering: a general approach
Scattering in electromagnetics, acoustics and quantum mechanics is a natural setting in which to study non-hermitian physics and extreme wave phenomena, since one is studying an open system in which discrete complex frequency solutions (“modes”) arise. Discrete solutions in turn lead to the possibility of non-hermitian degeneracy and exceptional points (EPs), where interesting phenomena such as enhanced sensitivity to perturbations, intrinsic chirality and asymmetric state transfer occur. The most well-studied discrete solutions in wave scattering are the resonances, which correspond to purely outgoing waves, however despite their complex frequencies, they are typically studied at real frequency, where they lead to enhanced scattering strength and long dwell times in the scattering structure. There have been many studies of the phenomena associated with resonances tuned to an exceptional point at complex frequency.
Recently it has been shown that there exist a large family of discrete complex frequency solutions in scattering theory distinct from the resonances, which physically correspond to either perfect absorption or perfect impedance-matching of the input waves, for a specific adapted spatial wavefront. We refer to such solutions as Reflection Zeros (R-zeros) when they occur at complex frequency, and Reflectionless Scattering Modes (RSMs), when they occur at real frequency (which generically requires structural parameter tuning). RSMs can be accessed with a continuous wave excitation and R-zeros with a specific form of pulsed excitation. With parameter variation RSMs and R-zeros can be tuned to EPs. The physical phenomena associated with this new kind of EP are broadband impedance-matching in the frequency domain and a larger and tailorable set of pulsed solutions in the time domain. Two very recent experiments will be reviewed which have confirmed this behavior for the first time. A fundamental connection between RSMs and PT-symmetric unstable real potentials will be discussed, time permitting.
A. Douglas Stone is Carl A. Morse professor of Applied Physics and Physics at Yale University, where he has been a faculty member since 1986. He has served as Chair of Applied Physics, Director of the Division of Physical Sciences, and currently as Deputy Director of the Yale Quantum Institute. He has a PhD in condensed matter theory from MIT (1983), and is one of the founders of the field of mesoscopic electron/wave physics. His main research specialty is wave equations in complex, chaotic and disordered media, and for the past twenty years his focus has been on optics, photonics and laser physics. He is a Fellow of APS and OSA and in 2015 was a co-recipient of the Willis Lamb Award for Laser Science and Quantum Optics.
Symmetry-engineered pseudospins for topological photonics, acoustic, and polaritonics
In recent years, synthetic degrees of freedom have significantly expanded the landscape of classical physics by enabling the emulation of relativistic and topological phenomena. Dirac and Weyl physics and a broad range of topological phases of matter have been successfully realized in artificial photonic and mechanical materials, facilitating an unprecedented control over propagation and scattering of waves. While vector fields naturally offer additional degrees of freedom for emulating such phenomena, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by more subtle material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. In the first scenario, we show that evanescent sound waves bound to the perforated films possess transverse angular momentum locked to their propagation direction that enables highly directional excitation in acoustic metasurfaces. As a second scenario, we demonstrate that the lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum of the modes, enabling control of sound propagation both in the bulk and along the edges. We experimentally confirm that, by spinning the source field, we can directionally excite bulk states in both systems. Based on these principles, we also demonstrate the possibility of steering edge states in topological kagome lattices at will. Our results open a new degree of control of acoustic radiation and propagation, which has so far been possible only for vector and spinor fields, light and electrons, in particular. The proposed systems demonstrate great potential for directional emission and reception of acoustic waves, offering new design approaches for directional acoustic transducers. Combined with the possibility of trapping and directionally guiding acoustic waves along topological boundaries, our results open unprecedented capabilities to engineer acoustic devices and systems.
Dr. Khanikaev received PhD degree in Physics from the M. V. Lomonosov Moscow State University in 2003. After graduation Dr. Khanikaev spent five years at the Department of Electrical and Electronic Engineering, Toyohashi University of Technology, Japan, as a postdoctoral scholar and then as a senior researcher, where he worked on the topics of magnetic photonic crystals and plasmonic nanostructures. From 2009 Dr. Khanikaev held a position of a research scientist at the Department of Physics at the University of Texas at Austin and contributed to the fields of infrared photonics and plasmonic metamaterials, biosensing, and graphene photonics. In 2012 he pioneered the concept of photonic topological insulators. In 2013 Dr. Khanikaev joined the City University of New York as the faculty member. Dr. Khanikaev’s group research focus is on design and experimental studies of photonic and acoustic metamaterials. One of the major research directions is nonreciprocity, topological properties, and light-matter interactions in novel and engineered materials. Dr. Khanikaev presently is a Full Professor at the Gove School of Engineering of City College and at the Graduate Center of CUNY. He is a Fellow of the Optical Society of America and a recipient of the NSF Special Creativity Award (2021).
University of Pennsylvania
In electrodynamics, the “space” and the “time” exhibit certain symmetry and duality. While these two variables in electromagnetics are mathematically analogous in many aspects, their functionalities clearly have obvious differences. Exploring similarities and differences in space-time analogy, symmetry and duality in electromagnetic metamaterials provide exciting possibilities and new venues for light-matter interaction. Spatiotemporal metamaterials, which are also coined as “four-dimensional (4D)” metamaterials, are wave-based material-based platforms in which the some of the material parameters can vary with time (i.e., temporal inhomogeneities) in addition to (or instead of) varying in space (i.e., spatial inhomogeneities). The additional degrees of freedom and spatiotemporal symmetries offered by such 4D structures lead to exciting wave phenomena. Such spatiotemporal features can also be merged and combined with the pseudospin-polarized states in electromagnetic structures, and consequently richer wave-based functional platforms can be achieved. In this presentation, I will present some of our most recent results on these topics.
Nader Engheta is the H. Nedwill Ramsey Professor at the University of Pennsylvania. He received his PhD from Caltech. His current research activities span a broad range of areas including photonics, metamaterials, electrodynamics, microwaves, nano-optics, graphene photonics, imaging and sensing inspired by eyes of animal species, microwave and optical antennas, and physics and engineering of fields and waves. He is the recipient of several awards including the Isaac Newton Medal and Prize from the Institute of Physics (UK), Max Born Award from the Optical Society, Ellis Island Medal of Honor, IEEE Pioneer Award in Nanotechnology, William Streifer Scientific Achievement Awards from the IEEE Photonics society, SPIE Gold Medal, Balthasar van der Pol Gold Medal from the International Union of Radio Science (URSI), IEEE Electromagnetics Award, and more. He is the Fellow of nine technical international organizations, i.e., IEEE, OSA, APS, SPIE, MRS, URSI, AAAS, IOP and NAI.