2025 Simons Collaboration on Extreme Wave Phenomena Based on Symmetries Annual Meeting

The fifth annual meeting of the Simons Collaboration on Extreme Wave Phenomena Based on Symmetries hosted 117 onsite and 9 online scientists, engineers and mathematicians from around the world, and featured 25 posters that stimulated lively conversations spanning the broad scope of the collaboration. Most attendees arrived one day earlier to participate in a satellite workshop the day prior at the Advanced Science Research Center at the City University of New York (ASRC CUNY). The workshop comprised a full day of 14 talks from leaders in the fields of metamaterials, photonics, electromagnetics, quantum systems, topology and mathematical analyses related to extreme wave topics.

The Simons Foundation meeting focused on broken temporal symmetries, an area that has rapidly advanced within the Collaboration and found traction in the field of metamaterials. Day 1 of the conference focused on the role of temporal modulation and time symmetry in stabilizing and manipulating wave dynamics. Nader Engheta introduced the concept of “vibrational electromagnetics,” demonstrating how temporally or spatially varying modulations can stabilize several types of electromagnetic systems and circuits. During Q&A, PI Demetrios Christodoulides confirmed that his team’s newly-discovered Lagrangian light waveguides presented at the satellite meeting implement spatially modulated Kapitza materials similar to those proposed theoretically by Engheta. Owen Miller discussed optimal waveshaping with emphasis on focusing, providing insights into spatial and temporal resolution in linear and nonlinear driven systems. He applied a new theoretical approach based on reciprocity to find scaling laws and global optima in studies of superresolution and superoscillations in complex media. Michael Weinstein presented a theory for solitons in crystals with useful flat band structures, highlighting how engineered nonlinearities can stabilize the solitons. Emmanuel Fort explored the effects of time-varying media on water waves, revealing phenomena such as amplification and freezing. One demonstration responded to Engheta’s non-Foster material proposal in the first talk by arbitrarily controlling bubble position in the gravitational equivalent of vibrational electromagnetics, judiciously shaking water waveguides formed of linear and ring-shaped tubes. Vincenzo Vitelli’s talk bridged microscopic and macroscopic scales in a system without common conservation laws and far from equilibrium. He detailed the role of nonreciprocal dynamics in certain biological tissues, where subcellular rotational forces generate large-scale, time dependent circulating cell flows along boundaries. Although the Collaboration’s expertise and experimental platforms are diverse, this was a startling and welcome translation of advanced metamaterial concepts to a messy biological system.

Day 2 continued the exploration of temporal dynamics in engineered systems. Katia Bertoldi presented an inverse design framework for creating flexible mechanical metamaterials with programmed nonlinear responses, enabling functionalities like mechanical sensing and computation within a single structure. In one case, metamaterial robobugs negotiated their way through obstacles courses using multistable mechanical sensing and actuation alone, without any form of electronic processing. Francesco Monticone explored the fundamental role of temporal asymmetries in wave physics stemming from causality, probing limits particularly in the case of spatial and temporal nonlocality. Andrea Alù concluded with a discussion of Floquet metasurfaces, emphasizing how time driven systems can manipulate light-matter interactions to produce nonreciprocal responses and phenomena such as time reflections, and harnessing synthetic rotations to produce striking effects such as Penrose radiation and selective emission. Over the course of three days, the talks illustrated how temporal modulation and other symmetry breaking can lead to novel wave phenomena, from enhanced stability to exotic material properties and dynamic behavior.

We thank the Simons Foundation for providing support for the research and for these vibrant annual meetings that bring together outstanding researchers united to address fundamental scientific challenges. Building on the foundations laid within the Collaboration’s establishment period, we look forward to working together over the course of the next two years to drive advances in extreme wave phenomena based on symmetries.

Andrea Alù
Photonics Initiative, Advanced Science Research Center, City University of New York

Floquet Metasurfaces
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In this talk, I discuss our recent efforts in the context of time-driven wave systems, with a special emphasis on out-of-equilibrium dynamics supporting material and/or electromagnetic resonances structured both in space and time. I will discuss our recent results leveraging time as a degree of freedom in these systems, a tool to manipulate the frequency and momentum response, and enable non-reciprocal and amplification regimes. The combination of strong tailored nonlinearities in metasurfaces and driven systems offers new opportunities for photonic engineering, which in turn enables exotic phenomena, such as time reflections, momentum bandgaps, synthetic rotations and Penrose super-radiance for photons. During the talk, I will discuss the exotic light-matter interactions arising in these systems, and their opportunities for wave physics and photonic technologies.
 

Katia Bertoldi
Harvard University

Programming Tasks in Nonlinear Mechanical Metamaterial from Wave Management to Sensing
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Flexible mechanical metamaterials are a class of structures with unique geometric features engineered to exhibit extraordinary properties in the nonlinear regime. These systems have the potential to drive the next generation of smart materials and devices, enabling functionalities such as shape morphing, programmable nonlinear mechanical behaviors, and energy manipulation. In this talk, I will introduce an inverse-design framework to discover flexible mechanical metamaterials with a target nonlinear dynamic response. We’ll then exploit this framework to integrate programmable mechanical responses, sensing capabilities, and computation within a single synthetic structure, paving the way for a new class of machines that are monolithic, require minimal electronic inputs, and possess advanced functionalities inherently embedded in their architecture.
 

Nader Engheta
University of Pennsylvania

Spatiotemporal Modulation for Stability in Space and Time
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In 1951, Nobel laureate Pyotr Kapitza developed the theory and the mathematical foundation behind the stability of the inverted pendulum. That launched the fields of vibrational mechanics and vibrational resonance. Inspired by these phenomena, we have been exploring how this concept can play a role in electromagnetic wave interaction with metamaterials, particularly the temporal and spatiotemporal structures, thus coining the term “vibrational electromagnetics.” We have investigated theoretically several scenarios in which judiciously selected temporal or spatial modulation can provide stability in otherwise unstable systems. A case study is for the electrical circuits involving non-Foster elements (i.e., a negative element), which are usually unstable, but with the proper temporal modulation of another circuit element with a positive value, we can make this circuit stable. Another scenario can be considered when this concept is extended to its dual scenario in space, i.e., for a monochromatic wave undergoing exponentially evanescent behavior; we have shown that the proper arrangements of thin material layers can transform such wave evanescence into wave propagation. We have also explored other cases that can benefit from such Kapitza-inspired modulation. These include the manipulation of diffusion in inhomogeneous media, temporal illusion in which spatiotemporal variation of permittivity can provide wave effects similar to wave interaction with time-invariant but different permittivity distributions, control of magnetic dipoles in the presence of time-varying magnetic fields, etc. In this talk, I present the results of some of our ongoing work in this area and forecast future research directions.
 

Emmanuel Fort
PSL University

Freezing and Amplification of Water Waves in a Time-Varying Medium
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Water waves provide a particularly versatile platform for exploring time-varying media, since they allow extremely fast and large-amplitude modulations through vertical acceleration that effectively changes gravity. This flexibility enables the study of a broad range of dynamical regimes, from parametric amplification in the spirit of Faraday excitation to high-frequency Kapitza-like modulation that reshapes dispersion and resonances. Temporally ordered and disordered media can also be realized, leading to transient localization of energy and exponential amplification. Moreover, temporal interfaces can be engineered to induce abrupt changes, including regimes reminiscent of non-Foster media associated with effective negative gravity, opening new ways to control propagation. These effects can ultimately induce the slowing down or freezing of wave packets. I will present a selection of such phenomena, highlighting the potential of water waves as a laboratory for the extreme physics of waves in time-modulated media.
 

Owen Miller
Yale University

Sharp Features in Spatial and Temporal Wave-Shaping
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In this talk, I will revisit basic questions in resolution, super-resolution, and optimal wavefront shaping in space and time. First, I will discuss free-space wave focusing in two and three space dimensions, where proper formulation of the focusing optimization yields global optima and new scaling laws. This connects naturally to phase-conjugation and time-reversal approaches for focusing waves in/through complex media, where I will describe a novel theoretical approach to phase-conjugate/time-reversed field solutions, simplifying and generalizing previous theory. I will characterize a number of features of phase-conjugate and time-reversal field excitations, including focusing properties and optimality/non-optimality in linear spatiotemporal systems. Applying this framework to nonlinear driven systems offers new insights about nonlinear time-reversal and partial-time-reversal symmetries. Finally, I will connect these wavefronts to emerging device architectures in photonic inference, where creating spatially (and temporally) sharp features can be surprisingly important.
 

Francesco Monticone
Cornell University

Extreme Wave Effects Based on Temporal (a)Symmetries

Temporal symmetries (such as time-reversal and time-translation) and asymmetries (including the one-sided nature of the temporal impulse response, i.e., causality) play a fundamental role in the response of natural and engineered materials, as well as in the general behavior of wave physics phenomena. In this talk, I will discuss recent efforts aimed at probing fundamental limits and extreme effects in electromagnetics and photonics based on these concepts, as well as new investigations on the interplay of spatio-temporal inhomogeneity and spatio-temporal nonlocality.
 

Vincenzo Vitelli
University of Chicago

Extreme Mechanics of Tissues

Chiral processes that lack mirror symmetry pervade nature from enantioselective molecular interactions to fundamental particles. An outstanding challenge consists in bridging the multiple scales between microscopic and macroscopic chirality. Here, we combine theory, experiments and modern inference algorithms to study a paradigmatic example of dynamic chirality transfer across scales: the generation of tissue-scale flows from subcellular forces. The distinctive properties of our microscopic graph model and the corresponding odd viscoelasticity are (i) inhomogeneous cell proliferation and (ii) nonreciprocal dynamics that cannot be expressed as an energy gradient. To overcome the general challenge of inferring microscopic model parameters from noisy high-dimensional data, we develop a nudged automatic differentiation algorithm (NADA) that can handle large fluctuations in cell positions observed in single snapshots. This data-calibrated microscopic model quantitatively captures proliferation-driven tissue flows observed at large scales in our experiments. Beyond chirality, our inference algorithm can be used to extract interpretable graph models from limited amounts of noisy data of cellular systems such as networks of convection cells and flowing foams.
 

Michael Weinstein
Columbia University

Stability Theory of Flat Band Solitons in Nonlinear Wave Systems

There is significant interest in the dynamics of waves in naturally occurring and engineered crystalline media that exhibit a flat or nearly flat spectral band in their band structure. A consequence of such spectra is the existence of localized, non-transporting, and non-dispersing wavepackets or quasi-particles, a property which enhances interactions in condensed matter, and nonlinear effects in photonics and other physical settings. It is therefore of interest to study the types of stable or long-lived excitations in non-linear wave models, whose underlying linear spectrum has a flat band. In this lecture, I’ll describe a stability theory of “minimal compact solitons” (MCS states) of the discrete nonlinear Schrödinger equation on a multi-lattices which support a flat band. We apply these results to MCS states of the diamond, Kagome, and checkerboard lattices. In lattices where MCS states are unstable, we demonstrate how to engineer the nonlinearity to stabilize small-amplitude MCS states. This is joint work with Cheng Shi (Columbia University), Panayotis Kevrekidis (University of Massachusetts Amherst), and Ross Parker (IDA-CCRP).