2022 Simons Collaboration on Extreme Wave Phenomena Based on Symmetries Annual Meeting

Speakers: Andrea Alù, City University of New York; Mario Silveirinha, University of Lisbon; Mathias Fink, ESPCI Paris; Katia Bertoldi, Harvard University; Nader Engheta, University of Pennsylvania; Michael Weinstein, Columbia University; Massimo Ruzzene, University of Colorado; Steven Johnson, Massachusetts Institute of Technology.

The second annual review meeting of the Simons Collaboration on Extreme Wave Phenomena Based on Symmetries took place on October 20-21, 2022, at the Simons Foundation in New York City. Over 112 attendees participated in this lively event, engaging a broad community of scientists, physicists, engineers and mathematicians working in related fields from around the world. Fifty of these researchers arrived a day earlier to attend a vigorous and packed satellite workshop, held at the City University of New York Advanced Science Research Center, featuring a dozen relevant talks from annual meeting attendees. This workshop, and the 25 posters displayed by junior scientists during the Annual Meeting, laid a stimulating backdrop to the meeting, and were referenced throughout the annual review presentations and ongoing discussions. The structure of the meeting supported productive informal interactions among the team and the invited attendees from the broader community, resulting in several potential new directions for research. In particular, the topics of time metamaterials realizable over various physical platforms, and of singularities in the complex frequency plane, were particularly compelling and drove extensive discussions and opportunities for investigations within the Collaboration and beyond.

Presentations during the annual review highlighted exciting interdisciplinary work aimed at unveiling the role of symmetries to control extreme optical, acoustical, thermal, mechanical and radio-frequency wave-matter interactions. The Collaboration team showcased a wide range of expertise, advancing opportunities stemming from the synergy of physicists, mathematicians and engineers working on the same problems from different angles. Their approaches involved new physics theories, advanced computational methods, design strategies, mathematical tools, and experimental validations, spawning interesting discussions. A broad theme in the presentations involved new models that describe extreme wave phenomena. Several presentations offered different perspectives on the role of dynamical symmetries and time interfaces, a theme emerging within the Collaboration that is exciting for its fundamental nature, rapid development and potential impact, which been driving new directions in physics, math and engineering since the start of the Collaboration.

Alù kicked off the meeting presentations with new results in all four of the Collaboration symmetry areas, i.e., geometrical, dynamical, unfolding and duality symmetries. As a highlight of his presentation, his team experimentally demonstrated dualities with hidden symmetry in mechanical structures, validating Vitelli’s theoretical discovery presented at last year’s Annual Meeting. The two groups are now writing a joint paper on this demonstration. Following Alù’s discoveries of extreme polaritonic phenomena driven by broken geometrical symmetries in natural crystals presented in the Year 1 Annual Meeting, his team also translated the theory to tunable mechanical structures, paired metasurfaces that break geometric symmetries to obtain maximum shear effects in metamaterials. Alù and guest speaker Ruzzene explored mechanical Moiré effects in interleaved single layer Lego surfaces by exploiting unfolding symmetries, demonstrating transitions between several exotic waveforms. In the context of mechanical metamaterials, Bertoldi discussed the effects of broken geometric symmetry in nonlinear mechanical porous, origami and kirigami metamaterials. She showcased mesmerizing videos of experiments demonstrating wave routing and focusing for applications in signal processing, soft logic circuits, energy absorption, cloaking and harvesting.

A flurry of discussion was inspired by theoretical and experimental results involving time interfaces realized by abrupt changes in time of a medium’s properties. Alù’s team used a radio-frequency waveguide platform based on modulated impedances to observe the temporal equivalent of a Fabry-Perot resonator, as well as broadband time reversed electromagnetic signals, or time-mirrors originally observed by Fink in water waves. Fink built on the time-reversal theme, noting that modern spaces are complex scattering environments for electromagnetic waves. Time-mirrored passive but reconfigurable arrays could be very effective at optimizing and focusing reflected wavefronts, possibly with widespread application in narrow and broadband communications. Ruzzene found that periodic modulations lead to tunable narrowband reflections, and impulsive changes to frequency compression. Engheta discussed ‘4D’ platforms merging space and time boundary conditions, also highlighting frequency modulation, compressive chirps and potential for unusual signal processing. Silveirinha and Ruzzene have been exploring topological aspects of space-time metamaterials. Indeed, in his talk Ruzzene showed that adiabatic stiffness modulations in a mechanical array drive localized edge state transitions to bulk boundary states, whereas Silveirinha provided a general proof through thermal fluctuations of the charge relation between edge and bulk states. Equilibrium may not be possible for some space-time systems with unidirectional energy transport. However, Silveirinha demonstrated thought-provoking uses of his theory to tailor complex topological phases, synthesizing example gyrotropic and Haldane systems.

Another strong theme across the meeting was recent breakthroughs driven by the Collaboration in theory, modeling and computational techniques. In addition to collaborators’ work described above, Weinstein derived the common discrete tight binding model from continuum Hamiltonians in magnetic and non-magnetic systems, with formulas for all cases of flat dispersion bands. He showed that flat bands always exist for zigzag type boundaries in graphene, but never for armchair terminations. This is particularly important in the context of the Collaboration work, since it maps the topological wave phenomena in the context of a rigorous mathematical theory. Johnson applied first physics principles to build an efficient computational model ideally suited to realize optimal responses for the challenging case of distributed electromagnetic emitters that both radiate and confine waves. Bertoldi harnessed learning networks to achieve routing and localization of mechanical waves in optimal forms.

The meeting as a whole was stimulating and productive, with a growing community around the Collaboration and exciting opportunities to expand the reach and impact of our activities. We look forward in the coming year to pursuing new and synergistic directions growing from meeting interactions and the team’s rapid progress, particularly in time-based metamaterials and dualities. We are grateful to the Simons Foundation for providing this opportunity to make scientific impact and engage in exciting discussions with a broad community of junior and senior scientists. We also thank the support staff, especially Emily Klein, Meghan Fazzi and Jason Sposa, who ran a seamless event.

Non-periodic design discovery for optimal dynamic responses in mechanical metamaterials
Katia Bertoldi
John A. Paulson School of Engineering and Applied Sciences – Harvard University

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Resonances for distributed emission
Steven G. Johnson
MIT Applied Math, MIT Physics

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