2024 Simons Collaboration on Extreme Wave Phenomena Based on Symmetries Annual Meeting

The Simons Collaboration on Extreme Wave Phenomena Based on Symmetries convened leading scientists and rising stars from around the globe at the Simons Foundation on 24–25 October 2024 for the Year 4 Annual Meeting. The 118 onsite and 13 online participants gathered to review new developments stemming from the Simons Collaboration activities. Discussions primed by eight presentations, each featuring two Collaboration PIs or Fellows, and continued during breaks and around twenty-five curated posters; details can be found here. The annual meeting followed a satellite meeting hosted at CUNY’s Advanced Science Research Center on 23 October, featuring eleven presentations around the theme of wave-based analog computing. The collaboration’s PI Professor Nader Engheta kicked off the satellite meeting, presenting an exciting review of areas in which computing with light can have a strong impact, such as imaging, sensing and interesting mathematical operations that can solve large classes of equation types, with applications in inverse design, automation and machine learning. The rapid advancements covered in this talk and pioneered by several collaboration members set the stage for the days that followed. The other ten talks were presented by world leaders in this field, not part of the collaboration. They inspired several discussions that have continued across the three-day event.

At the annual meeting, joint talks from paired key collaboration members highlighted how connections from diverse perspectives foster understanding and scientific advancement within the collaboration. Emmanuel Fort and Andrea Alù compared spatio-temporal symmetry breaking phenomena mapped across the domains of fluids and electromagnetics, with applications like broadband frequency conversion, beam splitting and gain control for communications stemming from the fundamental work. Also highlighted in this talk, surprising transitions between classical and quantum regimes arise in macroscopic systems when dynamics are invoked. Vincenzo Vitelli and Mario Silveirinha mapped across different domains to see exotic effects in systems without time and mirror symmetries. They described the mathematical analogy between active optical and actuated mechanical materials, showing that the topological chiral gain-momentum locking present in electromagnetic materials also arises in suitable mechanical materials with odd elasticity. In fluids with odd viscosity, Vitelli found suppression of intermittency, a significant obstacle to understanding turbulence in general. Nonlinearity plays a key role in such turbulent systems, but recently collaboration members have explored nonlinearities in wave phenomena as a means to shape symmetries.

Tsampikos Kottos conducted stability analyses to describe nonlinear systems of paired resonators controlled by detuning and coupling parameters with non-Hermitian degeneracies on Riemannian eigenvalue surfaces. These parity-time symmetric systems relate to the balanced gain-loss conditions pioneered by Carl Bender in the context of quantum electrodynamical systems, discussed in a later talk. The exceptional point degeneracies are useful to create power limiters and hypersensors. Alex Khanikaev explored other topological states featuring chiral vortices, which can be harnessed to create geometric phase resonators.

Andrew Hofstrand explored nonlinear discrete solitons, or breather waves, on dimerized linear, honeycomb and Kagome lattices, finding in some cases exact solutions for band structure of each lattice. For Kagome lattices a flat band emerged, further described when Michael Weinstein detailed a variational analysis of localized states and stability. He analytically described the non-bipartite graphs and dynamic symmetry class transitions between hexagonal, intermediate and single-site states in solutions of discrete nonlinear Schrodinger equations on Kagome lattices. Robert Kohn described his progress and advances in analytically describing soft modes in periodic mechanical surfaces of rotating squares or parallelograms, Kagome lattices and loaded origami structures, nicely connected with the work of Katia Bertoldi. She has experimentally explored these structures and others like bistable materials to create useful devices that direct and localize mechanical waves, can be deployed in reconfigurable static or dynamic or reconfigurable shapes, or move. Nonlinear optical fiber motivates the talk by Demetrios Christodoulides and Douglas Stone. Christodoulides showed how thermodynamics inspired by multimoded optical fiber could lead to Joule-Thomson optical cooling or thermal engines. Stone developed a comprehensive theory that employs waveshaping techniques to mitigate instabilities in single mode fiber, demonstrating output power over 500W and designing for outputs into the kilowatt range.

Another theme running through the collaboration’s work is driven by large degrees of freedom in typical wave-based systems. This drove Christodoulides and Kottos to develop statistical approaches for highly multimoded systems. Bertoldi combined optimization schemes with neural networks to design complicated mechanical devices. In experimental setups that drive active metasurfaces in separating and directing multiple speaker-listener signals, Mathias Fink and Fabrice Lamoult were limited by complexity of the setup. In response, Steven Johnson used physics-informed end-to-end optimization techniques to find drastically improved cocktail-party effect filters and more. In complicated electromagnetic systems and over a broad range of frequencies, Owen Miller derived bounds on system performance, particularly how bandwidth limitations arise from causality. Often these constraints take the form of very useful generalized sum rules, which Miller applied to several key optical problems.

It has been a very powerful event, as testified by many comments from attendees across the three days and after the event. It has been exciting to see the team’s body of work and community growing around the collaboration themes. It is especially good to see early career scientists who started in postdoctoral roles on the project now serving as faculty attending and presenting their work in this meeting. We appreciate the foundation’s continued support to make these fundamental collaborative breakthroughs possible and for hosting this lively event.

Alexander Khanikaev
University of Central Florida

Tsampikos Kottos
Wesleyan University

Topologically Resilient Wave-Matter Systems: From Symmetry Engineered Modes to Nonlinear Interactions

View Khanikaev’s Slides (PDF)
View Kottos’s Slides (PDF)

In recent years, there has been an increased activity in tailoring symmetries that enforce nontrivial topological features of targeted modes in complex wave systems. The aim is to enhance wave-matter interaction that in turn is harvested for a variety of applications ranging from predesigned chiral vortex states and geometrical phase resonators to noise- hypersensitive sensors and limiters, which all exhibit topological resilience. In many of these cases, nonlinearities give rise to many mode interactions leading to complex dynamics where statistical mechanics tools are employed to decipher the underlying collective phenomena. In this talk, we will present various examples which exemplify such enhanced wave-matter interactions in a diverse range of systems ranging from photonics and polaritonics to acoustics and RF. In all cases, the underlying symmetries (and their violation) enforces a complex topology of engineered modes providing topological robustness and novel functionalities.
 

Mathias Fink
ESPCI ParisTech

Fabrice Lemoult
ESPCI Paris, Université PSL, CNRS

Steven G. Johnson
Massachusetts Institute of Technology

Wave Control by Designable and Reconfigurable Scattering Surfaces

View Lemoult’s and Johnson’s Slides (PDF)

The control of waves by thin designable scattering surfaces, from micron-scale optical metasurfaces to reconfigurable intelligent/active surfaces for microwave and acoustic waves, has been studied for a wide range of applications in communications, imaging and sensing. Designing the geometry and phase/amplitude response of such surfaces, composed of hundreds or even millions of passive or active scattering elements, becomes more and more difficult at broader bandwidths, in more challenging environments (e.g. with dynamic scattering bodies), and for more ambitious applications (e.g. involving complex inference and signal processing tasks).

In this talk, we will discuss both experimental and theoretical advances in the design and implementation of such surfaces. On the theoretical side, this includes large-scale and topology optimization of multi-resonant metasurfaces for broadband applications in imaging, filtering and sensing, even co-optimized end-to-end with post-processing analysis of the raw sensor readings. On the experimental side, this includes electrically controllable spatio-temporal active surfaces for multi-user broadband communication (e.g. communicating conversations or music between 2×2 speakers in a complex environment), controlled by hill-climbing optimization or double time-reversal techniques.
 

Demetri Christodoulides
University of Southern California

A. Douglas Stone
Yale University

Nonlinear Multimode Wave Systems in and out of Dynamical Equilibrium

View Christodoulides’ and Stone’s Slides (PDF)
View Stone’s Slides (PDF)

The past few years have witnessed a resurgence of interest in multimode structures, predominantly driven by the ever-increasing demand for higher information capacities, leading to renewed experimental and theoretical interest in the effects of non-linearities in such structures. Due to the complexity of describing the many degrees of freedom involved in such systems a statistical or thermodynamic approach was natural for describing such systems in dynamical equilibrium. This theoretical approach has shown that the mode occupancies in such nonlinear multimode systems follow a universal behavior that always tends to maximize an appropriately defined system entropy at steady-state. This thermodynamic response takes place irrespective of the type of nonlinearities involved and can be utilized to either heat or cool an optical multimode system. Conversely, when such a system is not in dynamical equilibrium, as for example in the case of multimode fiber lasers, non-linear instabilities arise which disrupt the amplification process and limit the ability to generate high power directed energy. A novel approach to mitigate these instabilities is to use wavefront shaping of the input (seed) signal so as to reduce the growth rate of the unwanted nonlinear scattering processes, hence increasing the power level that can be reached with stable amplification. The theory developed to calculate the effect of wavefront shaping predicts that optimal multimode input seeds can achieve substantial increases in the instability threshold, as has been confirmed by recent experiments.
 

Vincenzo Vitelli
University of Chicago

Mário G. Silveirinha
University of Lisbon

Parity Breaking Waves: From Band Topology to Turbulence

View Vitelli’s Slides (PDF)
View Silveirinha’s Slides (PDF)

Parity breaking waves arise in media ranging from optical to mechanical where mirror-symmetry and time-reversal symmetry are simultaneously broken. In this talk, we survey universal properties that emerge across different physical platforms ranging from non-trivial effects in topological band theory to odd wave turbulence.

We will explore how the geometry of electronic bands and odd viscosity in materials lacking mirror symmetry can result in distinctive forms of electronic transport and unusual optical responses characterized by chiral gain and nonreciprocity. Specifically, we will demonstrate how surface plasmons at the boundary of a chiral-gain medium are controlled by a unique “gain-momentum locking” effect with a topological origin. These phenomena are particularly promising for the generation of light possessing well-defined orbital angular momentum.

In turbulent fluids with odd viscosity, these parity breaking waves, break the multiple scale invariances of the Navier-Stokes equations. Building on this insight, we construct a two-channel helical shell model that reproduces the basic phenomenology including the suppression of anomalous scaling. Our findings illustrate how a fully developed direct cascade that is entirely self-similar can emerge below a tunable length scale, paving the way for designing turbulent flows with adjustable levels of intermittency.
 

Carl Bender
Washington University

Owen Miller
Yale University

Physics Off the Real Axis: Complex-Plane Constraints on Quantum and Classical Field

View Bender’s Slides (PDF)
View Miller’s Slides (PDF)

Schrodinger’s and Maxwell’s equations are local differential equations and boundary conditions are required to determine their solutions uniquely. Depending on the choice of boundary conditions, and their location in the complex plane, a quantum Hamiltonian may describe several different physically observable phases, each exhibiting its own characteristic global symmetry. In electromagnetism, conditions at complex-plane “boundaries” are often fixed by basic material considerations, leading to strong constraints on allowable scattering “T” matrices.
 

Katia Bertoldi
Harvard University

Robert Kohn
New York University

Mechanism-Based Mechanical Metamaterials

View Bertoldi’s Slides (PDF)
View Kohn’s Slides (PDF)

From robots and engines to bikes and watches, mechanisms consisting of rigid bodies interconnected by joints or links are essential components in many mechanical systems. Among these systems are mechanical metamaterials ñ structures with unconventional properties emerging from their internal architecture. Notable examples are origami and the rotating-square mechanism, which consist of rigid units linked by freely-pivoting hinges. These mechanisms have played a pivotal role in the development of mechanical metamaterials with negative Poisson’s ratio, programmable non-linear response and highly-nonlinear dynamic response. The macroscopic properties of such systems are interesting, because there are often “soft modes” obtained by modulating the mechanism. While various examples have been considered in the past, a systematic understanding is just beginning to emerge. It combines ideas from homogenization and the calculus of variations with details specific to (geometrically) nonlinear elasticity. We will discuss this emerging understanding by reviewing some of its successes and some of the questions that remain open.
 

Michael Weinstein
Columbia University

Andrew Hofstrand
New York Institute of Technology

Nonlinear Waves on Lattices

Wave equations on discrete lattices have been explored extensively since they arise as approximations to continuum waves in certain energy regimes, e.g. tight binding approximations, or as useful effective models of metamaterials, formed from a coupled lattice of discrete elements (e.g. electrical circuits, mass-spring systems). First, we present results and work in progress — analytical/asymptotic and numerical — on the global behavior of families of discrete breathers. Our study bridges the anti-continuum and continuum regimes; families of breathers arise from the discrete nonlinear dynamics of an isolated cell and, as the intercell coupling is increased, deform and eventually terminate as weakly nonlinear wavepackets in the phonon spectrum, where they are described by a homogenized / effect mass theory. We then take a variational perspective on discrete problems. For a class of models (discrete nonlinear Schrödinger equations), we study the symmetry class and stability properties of “nonlinear ground states.” While for continuum problems, there is much known about the symmetry class of optimizers, much less is understood for general lattices. In our studies, we focus on 1d SSH, 2d honeycomb and 2d Kagome lattices. This talk is based on collaborations with Panayotis Kevrekidis, Ross Parker and Cheng Shi.
 

Andrea Alù
City University of New York

Emmanuel Fort
PSL Research University

Tailoring Waves with the Time Dimension

View Fort’s and Alù’s Slides (PDF)

In this joint talk, we discuss our collaborative effort to tailor waves based on broken symmetries in time and space-time. Dr. Fort is a pioneer in leveraging abrupt transitions in time and their periodic occurrences to manipulate water waves, and Dr. Alù has recently demonstrated powerful opportunities to leverage time interfaces and their combinations in the context of radio-frequency devices. Within the Simons Collaboration on Extreme Wave Phenomena Driven by Broken Symmetries, these opportunities can be leveraged and combined in unique ways to map exotic wave phenomena emerging at time interfaces and time crystals, from one physical domain to the other. In the talk, we will discuss synergies and opportunities stemming from this Collaboration on this exciting research topic.