The concept of transformation media has been primarily explored in the monochromatic regime, where device performance can deteriorate when applied to short pulses. Here, we review recent advances in tailoring transient flexural-wave propagation in transformed plates. Using the coordinate-transformation method, we implement practical solutions for a waveshifter, cloak, carpet cloak, and rotator for flexural waves, constructed from alternating thin layers of varying thicknesses within a plate. Time-resolved experiments, supported by full-wave simulations, confirm the effectiveness of these designs in bending, cloaking, and rotating flexural wave pulses while preserving their wavepackets. These results demonstrate how the traditional limitations of dispersion and impedance mismatch in transformed devices can be overcome.

ABSTRACT The bell‐like ringdown of the gravitational field in the final stage of massive black‐hole mergers is now routinely detected on Earth by the latest generation of gravitational‐wave detectors. Its spectrum is interpreted as a sum of damped sinusoidal vibrations of spacetime in the vicinity of the black hole. These so‐called quasinormal modes are the subject of extensive current studies, yet their physical nature remains elusive. Here, we emulate in the laboratory genuine four‐dimensional (3+1)D black‐hole metrics using an effective (2+1)D optical metric defined on a two‐dimensional curved surface that preserves the features of light‐like geodesics. We analytically compute the quasinormal modes of the optical cavity and show that, in addition to conventional whispering‐gallery modes (WGMs) supported near the cavity boundary, a new family of modes is confined around the photon sphere, the unstable region where spacetime curvature traps light in circular orbits. By 3D‐printing non‐Euclidean dye‐doped microcavities, we demonstrate lasing in both WGMs and photon‐sphere modes, with the latter exhibiting spatial profiles in close agreement with analytical predictions. These results place our system within the broader framework of analogue‐gravity experiments, providing a complementary photonic platform to investigate black‐hole photon‐sphere physics under tabletop conditions and inspiring new approaches to microcavity photonics.

The bell-like ringdown of the gravitational field in the last stage of the merging of massive black holes is now routinely detected on earth by the last generation of gravitational wave detectors. Its spectrum is interpreted as a sum of damped sinusoidal vibrations of the spacetime in the vicinity of the black hole. These so-called quasinormal modes are currently the subject of extensive studies, yet, their true nature remains elusive. Here, we emulate, in the laboratory, genuine four-dimension black hole metrics by two-dimensional optical curved surfaces that preserve the features of lightlike geodesics.

The basic physics of lasers is characterized by a second-order continuous phase transition at the critical lasing threshold. Nevertheless, laser bistability with abrupt transitions has been reported in some laser systems, but its underlying mechanism has never been explored. Here we study experimentally and theoretically a novel nonlinearly self-coupled laser system. We show both experimentally and theoretically that this system experiences spontaneous cascading that yields an abrupt mixed-order transition. At the critical point, a long-lived cascading plateau is observed, characterized by a critical branching factor equal to one. When deviating from criticality, the branching factor departs monotonically from one. The critical scaling close to and at the critical point resembles similar phenomena observed recently in other interdependent systems, suggesting a common universal cascading origin for abrupt transitions. Our results shed light on the cascading mechanism of abrupt transitions in laser systems, which can be utilized for future research and applications.

In non-Hermitian photonics, introducing gain and loss offers new degrees of freedom to control optical systems and a unique approach to explore fundamental concepts. Random lasers are a natural class of non-Hermitian open optical systems where spatial confinement, leakage, and non-orthogonality of the modes are further controlled by the degree of scattering. How Anderson localization is impacted by complex potentials, gain and loss and, more generally, nonlinearities has been the subject of numerous theoretical debates, without any conclusive experimental demonstration yet. Indeed, in systems where localized modes have sufficient spatial extension to be observed and investigated, their mutual interaction and coupling to the sample boundaries make it extremely difficult to isolate them spectrally and investigate them alone. Here, the degree of non-Hermiticity of an active scattering medium is controlled by shaping the pump. By imaging the intensity distribution of individual localized lasing modes, we demonstrate experimentally their insensitivity to local pumping; a signature that orthogonality is preserved between modes localized away from the system boundaries, as theoretically established. Demonstration of the one-to-one correspondence between lasing modes and localized states of the passive system opens the route to investigate the robustness of localized states in the presence of nonlinear gain and nonlinear modal interactions. Interestingly, gain saturation and mode competition for gain do not affect the spatial distribution of the modes, demonstrating their orthogonality in an otherwise strongly non-Hermitian system.

We demonstrate temperature-controlled spectral tunability of a partially-pumped single-wavelength random laser in a solid-state random laser based on DCM (4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran) doped PMMA (polymethyl methacrylate) dye. By carefully shaping the spatial profile of the pump, we first achieve low-threshold, single-mode random lasing with excellent side lobes rejection. Notably, we show how temperature-induced changes in the refractive index of the PMMA-DCM layer result in a blue-shift of this single lasing mode. Continuous tunability of the lasing wavelength is demonstrated over an 8nm-wide bandwidth.

Overcoming the diffraction limit is crucial for obtaining high-resolution images and observing fine microstructures. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years, how spatial curvature affects the diffraction limit is an attractive and important question. Here we investigate the issue of the diffraction limit and optical resolution on two-dimensional curved space—surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and the resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by the propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control the optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of the nonuniform strong gravitational effect by probing locally the optical resolution.

A two-dimensional (2D) solid-state random laser emitting in the visible is demonstrated, in which optical feedback is provided by a controlled disordered arrangement of air-holes in a dye-doped polymer film. We find an optimal scatterer density for which threshold is minimum and scattering is the strongest. We show that the laser emission can be red-shifted by either decreasing scatterer density or increasing pump area. We show that spatial coherence is easily controlled by varying pump area. Such a 2D random laser provides with a compact on-chip tunable laser source and a unique platform to explore non-Hermitian photonics in the visible

Maxwell's fisheye is a paradigm for an absolute optical instrument with a refractive index deduced from the stereographic projection of a sphere on a plane. We investigate experimentally the dynamics of flexural waves in a thin plate with a thickness varying according to the Maxwell fisheye index profile and a clamped boundary. We demonstrate subwavelength focusing and temporal pulse compression at the image point. This is achieved by introducing a sink emitting a cancelling signal optimally shaped using a time-reversal procedure. Perfect absorption and outward going wave cancellation at the focus point are demonstrated. The time evolution of the kinetic energy stored inside the cavity reveals that the sink absorbs energy out of the plate ten times faster than the natural decay rate.

A steerable parametric loudspeaker array is known for its directivity and narrow beam width. However, it often suffers from the grating lobes due to periodic array distributions. Here we propose the array configuration of hyperuniform disorder, which is short-range random while correlated at large scales, as a promising alternative distribution of acoustic antennas in phased arrays. Angle-resolved measurements reveal that the proposed array suppresses grating lobes and maintains a minimal radiation region in the vicinity of the main lobe for the primary frequency waves. These distinctive emission features benefit the secondary frequency wave in canceling the grating lobes regardless of the frequencies of the primary waves. Besides that, the hyperuniform disordered array is duplicatable, which facilitates extra-large array design without any additional computational efforts.

The disorder induced feedback makes random lasers very susceptible to any changes in the scattering medium. The sensitivity of the lasing modes to perturbations in the disordered systems have been utilized to map the regions of perturbation. A tracking parameter, that takes into account the cumulative effect of changes in the spatial distribution of the lasing modes of the system has been defined to locate the region in which a scatterer is displaced by a few nanometers. We show numerically that the precision of the method increases with the number of modes. The proposed method opens up the possibility of application of random lasers as a tool for monitoring locations of nanoscale displacement which can be useful for single particle detection and monitoring.

Chaos, namely exponential sensitivity to initial conditions, is generally considered a nuisance, inasmuch as it prevents long‐term predictions in physical systems. Here, an easily accessible approach to undo deterministic chaos and tailor ray trajectories in arbitrary 2D optical billiards by introducing spatially varying refractive index therein is presented. A new refractive index landscape is obtained by a conformal mapping, which makes the trajectories of the chaotic billiard fully predictable and the billiard fully integrable. Moreover, trajectory rectification can be pushed a step further by relating chaotic billiards with non‐Euclidean geometries. Two examples are illustrated by projecting billiards built on a sphere as well as the deformed spacetime outside a Schwarzschild black hole, which respectively lead to all periodic orbits and spiraling trajectories remaining away from the boundaries of the transformed 2D billiards/cavities. An implementation of this method is proposed, which enables real‐time control of chaos and can further contribute to a wealth of potential applications in the domain of optical microcavities.

Invisibility cloaks for flexural waves have mostly been examined in a continuous-wave regime, while invisibility is likely to deteriorate for short pulses. Here, we propose the practical realization of a unidirectional invisibility cloak for flexural waves based on an area-preserving coordinate transformation. Time-resolved experiments reveal how the invisibility cloak deviates a pulsed plane wave from its initial trajectory and how the initial wavefront perfectly recombines behind the cloak, leaving the diamond-shaped hole invisible, notwithstanding the appearance of a forerunner. Three-dimensional full-elasticity simulations support our experimental observations.

We report tunable random lasing in 2D and 1D solid-state polymer-based dye-doped random lasers. In 2D configuration, we show that the laser emission can be red-shifted by either decreasing scatterer density or increasing pump area. In 1D system, we demonstrate temperature-controlled spectral tunability of a partially-pumped single-wavelength random laser.

Light propagation on a two-dimensional curved surface embedded in a three-dimensional space has attracted increasing attention as an analog model of four-dimensional curved spacetime in laboratory. Despite recent developments in modern cosmology on the dynamics and evolution of the universe, investigation of nonlinear dynamics of light in non-Euclidean geometry is still scarce and remains challenging. Here, we study classical and wave chaotic dynamics on a family of surfaces of revolution by considering its equivalent conformally transformed flat billiard, with nonuniform distribution of refractive index. This equivalence is established by showing how these two systems have the same equations and the same dynamics. By exploring the Poincaré surface of section, the Lyapunov exponent and the statistics of eigenmodes and eigenfrequency spectrum in the transformed inhomogeneous table billiard, we find that the degree of chaos is fully controlled by a single geometric parameter of the curved surface. A simple interpretation of our findings in transformed billiards, the "fictitious force", allows to extend our prediction to other class of curved surfaces. This powerful analogy between two a prior unrelated systems not only brings forward a novel approach to control the degree of chaos, but also provides potentialities for further studies and applications in various fields, such as billiards design, optical fibers, or laser microcavities.

If disorder-induced Anderson localized states have been observed experimentally in optics, their study remains challenging leaving a number of open questions unsolved. Among them, the impact on Anderson localization of non-Hermiticity, optical gain and loss, and more generally, nonlinearities has been the subject of numerous theoretical debates, without yet any conclusive experimental demonstration. Indeed, in systems where localized modes have reasonable spatial extension to be observed and investigated, their mutual interaction and coupling to the sample boundaries make it extremely difficult to isolate them spectrally and investigate them alone. Recently, we successfully exhibited localized lasing modes individually in an active disordered medium, using pump-shaping optimization technique. However, a one-to-one identification of the lasing modes with the eigenmodes of the passive system was not possible, as the impact of non-Hermiticity and nonlinear gain on these localized states was unknown. Here, we apply the pump-shaping method to fully control the non-Hermiticity of an active scattering medium. Direct imaging of the light distribution within the random laser allows us to demonstrate unequivocally that the localized lasing modes are indeed the modes of the passive system. This opens the way to investigate the robustness of localized states in the presence of nonlinear gain and nonlinear modal interactions. We show that, surprisingly, gain saturation and mode competition for gain does not affect the spatial distribution of the modes.

We report temperature-induced, narrow linewidth wavelength-tunable random lasing in 1D solid-state random laser. First, random laser is operated in a single-mode regime using the iterative pump optimization method. After that temperature-induced change in the refractive index of the PMMA-DCM layer leads to wavelength tunability.

We shows, how real time spatial shaping of pump profile imposed on a strongly scattering gain medium can be used to achieve single mode lasing at pre-selected target wavelength. Simultaneously, near field imaging of the sample surface from the top allow us to record field distribution of the localized modes. We show that slope efficiency of Ander-son localized lasing mode enhanced by one order magnitude under selective pumping.

In non-Hermitian settings, the particular position at which two eigenstates coalesce in the complex plane under a variation of a physical parameter is called an exceptional point. An open disordered system is a special class of non-Hermitian system, where the degree of scattering directly controls the confinement of the modes. Herein a non-perturbative theory is proposed which describes the evolution of modes when the permittivity distribution of a 2D open dielectric system is modified, thereby facilitating to steer individual eigenstates to such a non-Hermitian degeneracy. The method is used to predict the position of such an exceptional point between two Anderson-localized states in a disordered scattering medium. We observe that the accuracy of the prediction depends on the number of localized states accounted for. Such an exceptional point is experimentally accessible in practically relevant disordered photonic systems.

Chaos is generally considered a nuisance, inasmuch as it prevents long-term predictions in physical systems. Here, we present an easily accessible approach to undo deterministic chaos in arbitrary two-dimensional optical chaotic billiards, by introducing spatially varying refractive index therein. The landscape of refractive index is obtained by a conformal transformation from an integrable billiard. Our study shows that this approach is robust to small fluctuations. We show further that trajectory rectification can be realized by relating chaotic billiards with non-Euclidean billiards. Finally, we illustrate the universality of this approach by extending our investigations to arbitrarily deformed optical billiards. This work not only contributes in controlling chaos, but provides a novel pathway to the design of billiards and microcavities with desired properties and functionalities.