2023 Simons Collaboration on Extreme Wave Phenomena Based on Symmetries Annual Meeting

4D Waves: Electromagnetic and water platforms

Emmanuel Fort
ESPCI Paris, University

Nader Engheta,
University of Pennsylvania

In any wave phenomenon, the space and time play central roles. There are certain symmetries and analogies between the spatial dimensions and the temporal dimension, while there are of course some differences. To manipulate and tailor waves, spatial inhomogeneities in material platforms have often been exploited. Diffraction, scattering, and guidance of waves are all examples of how inhomogeneities in material parameters can provide useful wave control. By bringing the 4th dimension of time in material parameters while the wave is present, more degrees of freedom are offered in structuring and sculpting waves. Such “4D waves” offer new concepts and exciting phenomena in wave physics with potential applications in frequency conversion, wave amplification, time-reversal techniques, etc. In this talk, we discuss some of the features of 4D electromagnetic waves (when the material permittivity is changed in time) and 4D water waves (when the parameters such as gravity are effectively altered). We will show some of the similarities and differences between these two types of waves, and we will present how the water wave can offer an interesting playground for testing and observing some of wave features predicted in the 4D electromagnetic waves.
Symmetry engineered topological photonics

Mário G. Silveirinha
University of Lisbon

Alexander B. Khanikaev
City College of New York

In this talk we will outline our recent progress on the use of symmetries to engineer topological phases of electromagnetic waves. We will show how spatial symmetries can be used to generate effective Hamiltonians emulating relativistic-like Dirac physics in optical systems. We will describe how this leads to structured optical modes carrying angular momentum and valley degrees of freedom – two types of the pseudo-spin. We will present theoretical and experimental results that show how synthetic gauge potentials acting on these degrees of freedom can be used for trapping and guiding electromagnetic waves. We also show that synthetic gauge fields can be designed to selectively act on the optical spin-full guided modes to produce single qubit gate operations with quantum information encoded into pseudo-spins. Furthermore, we will extend the topological theory of bands to time-variant photonic crystals with a travelling wave modulation. We will show how by tailoring the anisotropy of materials it may be possible to engineer topological states with a nontrivial angular momentum from a linear momentum bias. Finally, we will discuss the topological origin of a novel non-Hermitian linear electro-optic effect in low-symmetry natural materials. It will be shown that such systems may be the ideal platforms to realize topological lasers with the orbital angular momentum of the laser mode locked to the orientation of the electric bias.
Optimization in hyperbolic space: from airplane boarding to hyperbolic metamaterial lenses

Eitan Bachmat
Ben-Gurion University

Simon Yves
Advanced Science Research Center, City University of New York

We will consider the problem of minimizing airplane boarding time given a group of “fast” passengers (say those without overhead bin luggage). An airline can place the “fast” passengers at the front of the queue, back of the queue or can apply a more sophisticated policy which also takes the row of the passenger into account. We describe the problem in terms of Lorentzian (space-time) geometry and provide constructions of optimal row/queue locations for the “fast” passengers.

Then, we develop a direct analogy between the airplane boarding problem in Lorentzian space and hyperbolic metamaterials by describing “slow” and “fast” passengers by hyperbolic media with different isofrequency contours. Harnessing the optimization results of the airplane boarding study, we manage to fully design a hyperbolic lens with high numerical aperture.

This work highlights the benefits of transdisciplinarity both for optimization problems and enhanced wave propagation control.
Nanophotonics by design: reaching the limits of light–matter interactions

Steven Johnson
Massachusetts Institute of Technology

Owen Miller
Yale University

Nanoscience is developing at a rapid pace, with ever more materials, form factors, and structural degrees of freedom now available. To confront these large design spaces, and leverage them for transformative technologies, new theoretical tools are needed. One approach is “inverse design,” a bottom-up computational optimization technique for discovering non-intuitive, superior designs. We describe novel formulations of problems ranging from multilayer metasurfaces to incoherent wavefront control that enable large-scale inverse design. An emerging complementary approach is “top down,” surveying the landscape and identifying fundamental limits to what is possible. We show that there is a surprising amount of mathematical structure hidden in the typical differential equations of physics, and that this structure enables new connections to modern techniques in convex optimization. The key differential-equation constraints can be transformed to infinite sets of local conservation laws, which have a structure amenable to quadratic and semidefinite programming. This approach can lead to global bounds (“fundamental limits”) for many design problems of interest, and to dramatically new approaches to identifying designs themselves.
Universality of non-Hermitian eigenvalues and eigenstates for reflectionless scattering in classical and quantum wave equations

A. Douglas Stone
Yale University

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

Reflectionless resonant scattering of waves has been studied since the beginning of modern physics, in the context of both classical wave equations (electromagnetic, optical, acoustic) and Schrödinger’s equation, yet no general framework had been developed to determine when such solutions exist and how to construct them for arbitrary linear scattering problems with and without symmetry. Recently we have developed such a framework, by posing reflectionless scattering as an eigenvalue problem which is intrinsically non-Hermitian, and leads to a discrete complex spectrum of frequencies (in the classical case) and of energies (in the quantum case), with associated eigenfunctions. Steady-state reflectionless scattering is only possible for any linear system when some or all of these eigenvalues are real, at the corresponding frequencies or energies, and only when the corresponding coherent eigenfunction is incident. Such steady-state solutions are termed Reflectionless Scattering Modes (RSMs), solutions off the real axis are termed R-zeros, and are accessible with transient excitation. Degeneracy of R-zeros creates a new kind of exceptional point, associated with broadband reflectionless scattering. Without any spatial symmetry of the scattering structure, the R-zero spectrum is generically complex and no steady-state reflectionless solutions exist; however typically the tuning of one continuous structural parameter can create a reflectionless solution without restoring symmetry. We illustrate this for the case of a multichannel chaotic cavity, under multichannel excitation, both theoretically and experimentally. When the system has a discrete symmetry, such as parity, RSMs may or may not exist, and concepts based on Parity-Time symmetry can describe the physics of the RSM/R-zero spectrum. Interestingly, the theory predicts a possible PT phase transition in the RSM spectrum without introducing imaginary terms in the potential or susceptibility. We report on such a case, the single-particle Schrödinger equation in a parity symmetric upside-down potential; this phenomenon should be measurable in cold-atom condensate experiments. We also report on functionalization of RSMs for routing of microwave signals, and transient excitation of R-zeros and R-zero EPs.
Extreme wave mechanics: strong non-linearities, non-reciprocity and dualities

Katia Bertoldi
Harvard University

Vincenzo Vitelli
University of Chicago

We present an overview of recent advances by the collaboration on linear and non-linear waves in mechanical metamaterials emphasizing the role of mechanisms, material geometry and symmetry breaking. We first present a systematic procedure to generate families of Hamiltonians endowed with generalized hidden symmetries, called dualities and provide a universal description of Hamiltonian families near self-dual points and associated non-abelian phenomenology. We apply our findings to recent experiments on wave propagation in mechanical metamaterials and discuss potential extensions to other physical domains. Next, we discuss linear and non-linear waves in continuum mechanics with non-reciprocal (i.e. odd) constitutive relations and provide a generalization to odd electromagnetic media.
Symmetries and symmetry-breaking induced by nonlinear processes

Demetri Christodoulides
University of Southern California

Tsampikos Kottos
Wesleyan University

In this presentation we will highlight the interplay between nonlinear wave interactions and the underlying symmetries and violations which can be leveraged to develop a novel theoretical framework capable of describing the utterly convoluted dynamics in complex systems. This approach can lead to universal models that can be used for understanding and predicting the response of highly multimode nonlinear optical sources based on overarching principles of statistical mechanics. In addition, this same methodology can be deployed to enhance the sensitivity and asymmetric transport phenomena in nonlinear environments where spatio-temporal symmetries can be violated in a self-induced fashion. The implications of these formalisms in various bosonic settings will be discussed.
Harnessing symmetry classes for extreme wave phenomena

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

In this talk, I will review our Simons Collaboration’s synergistic progress in framing a universal platform to enable extreme wave phenomena based on symmetries. I will discuss how our team has been enabling new forms of topological order based on broken geometrical and temporal symmetries, time- and space-time metamaterials based on time-reversal symmetry breaking, tailored wave propagation in complex wave systems relying on unfolding symmetries, and duality phenomena associated with hidden symmetries. Of particular relevance is the emergence of new wave phenomena enabled by combining these symmetry classes into a unified paradigm, and their universality across various physics domains and frequency ranges. During the talk, I will discuss the current progress of our team on these topics, the impact from basic physics to relevant technologies, and an outlook for this exciting field of research and the community being formed around these concepts.