An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported ring and are therefore universal. Closed analytical expressions for the resulting universal shapes are provided, including the one-to-one relations between the pressure and tension at which these emerge. The analytical predictions agree with numerical continuation results to within numerical accuracy, for a large range of parameter values, up to the point of self-contact.

While non-Hermitian systems are normally constructed through incoherent coupling to a larger environment, recent works have shown that under certain conditions coherent couplings can be used to similar effect. We show that this new paradigm enables the behavior associated with the $PT$-symmetric phase of a non-Hermitian subsystem to control the containing Hermitian system through the coherent couplings. This is achieved in parametric nonlinear wave mixing where simultaneous second harmonic generation replaces the role of loss to induce non-Hermitian behavior that persists through a full exchange of power within the Hermitian system. These findings suggest a new approach for the engineering of dynamics where energy recovery and sustainability are of importance that could be of significance for photonics and laser science.

Coalescence and breakup of drops are classic problems in fluid physics that often involve self-similarity and singularity formation. While the coalescence of suspended drops is axisymmetric, the coalescence of drops on a substrate is inherently three-dimensional. Yet, studies so far have only considered this problem in two dimensions. In this Letter, we use interferometry to reveal the three-dimensional shape of the interface as two drops coalescence on a substrate. We unify the known scaling laws in this problem within the thin-film approximation and find a three-dimensional self-similarity that enables us to describe the anisotropic shape of the dynamic interface with a universal curve.

Existing methods for the creation of subwavelength resonators use either structures with negative permittivity, by exploiting subwavelength plasmonic resonances, or dielectric structures with a high refractive index, which reduce the wavelength. Here, we provide an alternative to these two methods based on a modification of the modes of dielectric resonators by means of an active medium. On the example of the dielectric active layer of size substantially smaller than a half-wavelength of light, we demonstrate that there is a gain at exceeding of which the change in phase due to the reflection at the layer boundaries compensates the change in phase due to propagation over the layer. Above this value of the gain, an unconventional mode forms, in which the phase shift after a round-trip of the light is zero. We show that this mode can be exploited to create a laser, the size of which is much smaller than the wavelength of the generated light and scales inversely with the square of absolute value of the refractive index in the active medium. Our results pave the way to creation of dielectric lasers of subwavelength size.

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with few modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break down and the Chern topology becomes ill defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be noninteger notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large $\mathbf{k}$.

Underwater bubbles display an acoustic resonance frequency close to spherical ones. In order to obtain a resonance significantly deviating from the spherical case, we stabilize bubbles in toroidal frames, resulting in bubbles which can be slender while still compact. For thin tori the resonance frequency increases greatly. Between a pair of bubble rings, we can achieve a flat acoustic pressure field for a critical distance between rings, a condition reminiscent of Helmholtz coils in magnetostatics. This opens the possibility to shape the acoustic field using long tunnels of rings.

We propose surface modulation of the equilibrium charge density as a technique to control and enhance, via an external static potential, the free electron nonlinear response of heavily doped semiconductors. Within a hydrodynamic perturbative approach, we predict a 2 order of magnitude boost of free electron third-harmonic generation.

We address the formation of topological states in twisted circular waveguide arrays and find that twisting leads to important differences of the fundamental properties of new vortex solitons with opposite topological charges that arise in the nonlinear regime. We find that such system features the rare property that clockwise and counterclockwise vortex states are nonequivalent. Focusing on arrays with ${\mathcal{C}}_{6v}$ discrete rotation symmetry, we find that a longitudinal twist stabilizes the vortex solitons with the lowest topological charges $m=\pm 1$, which are always unstable in untwisted arrays with the same symmetry. Twisting also leads to the appearance of instability domains for otherwise stable solitons with $m=\pm 2$ and generates vortex modes with topological charges $m=\pm 3$ that are forbidden in untwisted arrays. By and large, we establish a rigorous relation between the discrete rotation symmetry of the array, its twist direction, and the possible soliton topological charges.

We consider the fundamental roles of frequency versus phase in parameter estimation, specifically in the Sagnac effect. We describe a novel, ultrasensitive gyroscope based on the extremely steep frequency-dependent gain of a liquid crystal light valve. We provide compelling experimental evidence that the Doppler shift is fundamental in the Sagnac effect giving clarity to a long-debated question. We experimentally show orders of magnitude improvement in sensitivity relative to the standard quantum limit of a gyroscope based on phase estimation.

We prove analytically and show numerically that the dynamics of the Fermi-Pasta-Ulam-Tsingou chain is characterized by a transient Burgers turbulence regime on a wide range of time and energy scales. This regime is present at long wavelengths and energy per particle small enough that equipartition is not reached on a fast timescale. In this range, we prove that the driving mechanism to thermalization is the formation of a shock that can be predicted using a pair of generalized Burgers equations. We perform a perturbative calculation at small energy per particle, proving that the energy spectrum of the chain $E_k$ decays as a power law, $E_k\sim k^{-\zeta (t)}$, on an extensive range of wave numbers $k$. We predict that $\zeta (t)$ takes first the value $8/3$ at the Burgers shock time, and then reaches a value close to 2 within two shock times. The value of the exponent $\zeta =2$ persists for several shock times before the system eventually relaxes to equipartition. During this wide time window, an exponential cutoff in the spectrum is observed at large $k$, in agreement with previous results. Such a scenario turns out to be universal, i.e., independent of the parameters characterizing the system and of the initial condition, once time is measured in units of the shock time.

Suspensions of DNA macromolecules (0.8 wppm, 60 kbp), modeled as finitely extensible nonlinear elastic dumbbells coupled to the Newtonian fluid, show drag reduction up to 27% at friction Reynolds number 180, saturating at the previously unachieved Weissenberg number $\simeq {10}^4$. At a large Weissenberg number, the drag reduction is entirely induced by the fully stretched polymers, as confirmed by the extensional viscosity field. The polymer extension is strongly non-Gaussian, in contrast to the assumptions of classical viscoelastic models.

We demonstrate that soft-clamped silicon nitride strings with a large aspect ratio can be operated at mK temperatures. The quality factors ($Q$) of two measured devices show consistent dependency on the cryostat temperature, with soft-clamped mechanical modes reaching $Q>{10}^9$ at roughly 46 mK. For low optical readout power, $Q$ is found to saturate, indicating good thermalization between the sample and the stage it is mounted on. Our best device exhibits a calculated force sensitivity of $9.6\mathrm{zN}/\sqrt{\mathrm{Hz}}$ and a thermal decoherence time of 0.38 s, which bode well for future applications such as nanomechanical force sensing.

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated stochastic process change its EV distribution? We explore this question for correlated random variables modeled via Langevin dynamics for a particle in a potential field. For potentials growing at infinity faster than linearly and for long measurement times, we find that the EV distribution of the discretely sampled process diverges from that of the full continuous dataset and converges to that of independent and identically distributed random variables drawn from the process’s equilibrium measure. However, for processes with sublinear potentials, the long-time limit is the EV statistics of the continuously sampled data. We treat processes whose equilibrium measures belong to the three EV attractors: Gumbel, Fréchet, and Weibull. Our Letter shows that the EV statistics can be extremely sensitive to the sampling rate of the data.