Space-time Wave Research Articles

Behavior of optical parametric amplification of space-time wave packets

The space-time wave packet (STWP) is a type of pulsed optical field, exhibiting distinctive characteristics, including the capacity to propagate without diffraction or dispersion and to have arbitrary group velocities. However, the intensity of the STWP is constrained by the low damage threshold of some indispensable optical elements like the spatial light modulator (SLM). While optical parametric amplification (OPA) has been proposed for amplifying STWPs, spatio-temporal (ST) characteristics of amplified STWPs remain significantly unexplored. In this article, we investigate the effects of OPA on STWPs and examine how key parameters influence the amplification results. Based on the numerical simulation results, we propose two methods to reduce the duration of the amplified STWP and one method to amplify the STWP with higher group velocities. These findings could facilitate the application of STWPs in strong-field optics.

Unruh-deWitt detector in impulsive plane wave spacetimes

Unruh-deWitt detector in impulsive plane wave spacetimes

Abrupt X-to-O-wave structural field transition in presence of anomalous dispersion

All linear, propagation-invariant, paraxial pulsed beams are spatiotemporally X-shaped (conical waves) in the absence of group-velocity dispersion (GVD) or in the presence of normal GVD. It is known, however, that such conical waves become O-shaped in the presence of anomalous GVD, resulting in a field profile that is circularly symmetric in space and time. To date, experiments generating conical waves in which the wavelength of a high-energy pump laser is tuned across the zero-dispersion wavelength of a nonlinear medium have not revealed the expected X-to-O-wave structural field transition. We report here an unambiguous observation of a fixed-central-wavelength X-to-O-wave structural field transition occurring in linear dispersion-free wave packets in the anomalous GVD regime, without needing to change the sign or magnitude of the GVD. Instead, by tuning the group velocity of a space–time wave packet (STWP) across a threshold value that we call the “escape velocity,” we observe an abrupt transition in the STWP from an O-shaped to an X-shaped spatiotemporal profile. This transition is associated with an abrupt change in the associated spatiotemporal spectrum of the STWP: from closed elliptical spatiotemporal spectra below the escape velocity to open hyperbolic spectra above it. These results may furnish new opportunities for engineering the phase-matching conditions in nonlinear and quantum optics.

Energy Backflow in Unidirectional Monochromatic and Space–Time Waves

Energy Backflow in Unidirectional Monochromatic and Space–Time Waves

The Penrose limit of the Weyl double copy

Abstract We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. We also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.

Weyl fermions in a (2+1)-dimensional gravitational wave spacetime

In this study, we work on understanding the behavior of relativistic fermions within the framework of a (2+1)-dimensional gravitational wave environment. Our main objective is to uncover an analytical solution for the massless Dirac equation in this particular scenario. Initially, we derive a set of coupled equations that describe the quantum dynamics of the system under consideration. Subsequently, we embark on finding an analytical solution for the resulting wave equation governing Weyl fermions by utilizing the generators associated with the [Formula: see text] algebra. This approach enables us to determine the relativistic frequency modes of the system. We then delve into examining how the parameters of the gravitational wave spacetime influence the real oscillation modes of Weyl fermions. Our findings highlight the sensitivity of Weyl fermions to the specific gravitational wave spacetime background being considered.

Space-time dispersive symmetric Pearcey-Pearcey wave packets in the fractional Schrödinger equation.

This study presents an investigation into the propagation characteristics of a symmetric Pearcey-Pearcey space-time (SPPST) wave packet in a dispersive medium for the first time, to the best of our knowledge, in an optical system based on the fractional Schrödinger equation. Subsequently, the influence of the dispersion (normal and abnormal dispersion) on the SPPST packet is analyzed comprehensively. By manipulating the parameters of the SPPST wave packet including the parameters of the symmetric Pearcey beam, the value of the chirp, and the dispersion in the medium, it is possible to control its shape, orientation, and propagation dynamics. Simultaneously, the study delves into the effects of the combination of the dispersion and the second-order chirp on the evolution of SPPST wave packets and the associated intensity with these wave packets. Studying self-focusing wave packets with spatiotemporal symmetry provides new theoretical support for the development of quantum optics and optical communication.

Persistent gravitational wave observables: nonlinearities in (non-)geodesic deviation

AbstractThe usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, ‘persistent’ observables which measure permanent effects on idealized detectors have been introduced, each probing distinct physical effects. These observables can be defined in (regions of) any spacetime where there exists a notion of radiation, such as perturbation theory off of a fixed background, nonlinear plane wave spacetimes, or asymptotically flat spacetimes. Many of the persistent observables defined in the literature have only been considered in asymptotically flat spacetimes, and the perturbative nature of such calculations has occasionally obscured deeper relationships between these observables that hold more generally. The goal of this paper is to show how these more general results arise, and to do so we focus on two observables related to the separation between two, potentially accelerated observers. The first is thecurve deviation, which is a natural generalization of the displacement memory, and also contains what this paper proposes to calldriftmemory (previously called ‘subleading displacement memory’) andballisticmemory. The second is a relative proper time shift that arises between the two observers, either at second order in their initial separation and relative velocity, or in the presence of relative acceleration. The results of this paper are, where appropriate, entirely non-perturbative in the curvature of spacetime, and so could be used beyond leading order in asymptotically flat spacetimes.

Geometric deformation and redshift structure caused by plane gravitational waves

The curved spacetime induced by gravitational waves can give rise to visual effects such as geometric distortions and redshift structures in the observed image. By establishing a mapping from the object's surface coordinates to the observer's screen coordinates, we study these effects in the context of plane gravitational waves. The simulation reveals that the image of an object doesn't merely seem compressed or stretched, but rather appears twisted and wobbled. Furthermore, the redshift structure on the object's surface appears to rotate as a whole. This outcome offers an intuitive depiction of the lensing effect in plane gravitational wave spacetimes.

Temporally and longitudinally tailored dynamic space-time wave packets.

In general, space-time wave packets with correlations between transverse spatial fields and temporal frequency spectra can lead to unique spatiotemporal dynamics, thus enabling control of the instantaneous light properties. However, spatiotemporal dynamics generated in previous approaches manifest themselves at a given propagation distance yet are not arbitrarily tailored longitudinally. Here, we propose and demonstrate a new versatile class of judiciously synthesized wave packets whose spatiotemporal evolution can be arbitrarily engineered to take place at various predesigned distances along the longitudinal propagation path. Spatiotemporal synthesis is achieved by introducing a 2-dimensional spectrum comprising both temporal and longitudinal wavenumbers associated with specific transverse Bessel-Gaussian fields. The resulting spectra are then employed to produce wave packets evolving in both time and axial distance - in full accord with the theoretical analysis. In this respect, various light degrees of freedom can be independently manipulated, such as intensity, polarization, and transverse spatial distribution (e.g., orbital angular momentum). Through a temporal-longitudinal frequency comb spectrum, we simulate the synthesis of the aforementioned wave packet properties, indicating a decrease in relative error compared to the desired phenomena as more spectral components are incorporated. Additionally, we experimentally demonstrate tailorable spatiotemporal fields carrying time- and longitudinal-varying orbital angular momentum, such that the local topological charge evolves every ∼1 ps in the time domain and 10 cm axially. We believe our space-time wave packets can significantly expand the exploration of spatiotemporal dynamics in the longitudinal dimension. Such wave packets might potentially enable novel applications in light-matter interactions and nonlinear optics.

Gravitational wave analogs in spin nematics and cold atoms

Large-scale gravitational phenomena are famously difficult to observe, making parallels in condensed matter physics a valuable resource. Here we show how spin nematic phases, found in magnets and cold atoms, can provide an analog to linearized gravity. In particular, we show that the Goldstone modes of these systems are massless spin-2 bosons, in one-to-one correspondence with quantized gravitational waves in flat spacetime. We identify a spin-1 model supporting these excitations and, using simulation, outline a procedure for their observation in a 23Na spinor condensate. Published by the American Physical Society 2024

Nondiffracting supertoroidal pulses and optical “Kármán vortex streets”

Supertoroidal light pulses, as space-time nonseparable electromagnetic waves, exhibit unique topological properties including skyrmionic configurations, fractal-like singularities, and energy backflow in free space, which however do not survive upon propagation. Here, we introduce the non-diffracting supertoroidal pulses (NDSTPs) with propagation-robust skyrmionic and vortex field configurations that persists over arbitrary propagation distances. Intriguingly, the field structure of NDSTPs has a similarity with the von Kármán vortex street, a pattern of swirling vortices in fluid and gas dynamics with staggered singularities that can stably propagate forward. NDSTPs will be of interest as directed channels for information and energy transfer applications.

Dynamics, quantum states and Compton scattering in nonlinear gravitational waves

The classical dynamics and the construction of quantum states in a plane wave curved spacetime are examined, paying particular attention to the similarities with the case of an electromagnetic plane wave in flat spacetime. A natural map connecting the dynamics of a particle in the Rosen metric and the motion of a charged particle in an electromagnetic plane wave is unveiled. We then discuss how this map can be translated into the quantum description by exploiting the large number of underlying symmetries. We examine the complete analogy between Volkov solutions and fermion states in the Rosen chart and properly extend this to massive vector bosons. We finally report the squared S-matrix element of Compton scattering in a sandwich plane wave spacetime in the form of a two-dimensional integral.

Beyond particles and planets: Exploring the universe through quantum mechanics, general relativity, and string theory

This paper provides a comprehensive overview of the fundamental principles and implications of quantum mechanics, general relativity, and string theory, focusing on their role in shaping our understanding of the universe. We delve into quantum mechanics through wave-particle duality, quantum entanglement, and the measurement problem, highlighting the probabilistic nature of reality and the challenges of observer-dependent phenomena. In exploring general relativity, we examine the curvature of space-time, black holes, singularities, and gravitational waves, showcasing the theory's impact on our perception of gravity and the cosmos. String theory is discussed as a unifying framework, with emphasis on its basics, the necessity of extra dimensions, and the landscape of possible universes it predicts. This paper aims to bridge complex theoretical concepts with observational evidence and technological advancements, offering insights into the ongoing quest to understand the fabric of the universe

Energy-Space-Time Plateau-Rayleigh Instability, Quantum Phenomenon & the Fundamental Interactions

In general, fluids in motion or at rest tend to minimize their surface area due to their surface tension. It is shown that kinetic energy flow through space-time experience the same Plateau-Rayleigh instability observed in fluid dynamics. Energy, space-time act like fluids, and the space-time reaction to the energy action is the equivalent of an interface tension between energy and space-time. Energy cannot continuously flow through space-time due to an energy-space-time Plateau-Rayleigh instability, space-time compression (contraction) on kinetic energy direction of motion induces an energy wave like motion (a space-time compression wave acting as kinetic energy waveguide), the particle or energy packet must follow when moving through space-time, the reason for the observed wave - particle duality. Quantum phenomenon is simply a consequence of the space-time compression on kinetic energy direction of motion. Kinetic energy and space-time are fluids and energy quanta can reach a critical point when energy quanta can change from linear to circular motion and assume a spherically symmetrical shape (the minimum surface area possible to minimize the tension at the space-time energy interface) and so it condensates as mass energy. It is shown that energy quanta to mass transformation occurs via Plateau–Rayleigh energyspace-time instability and it is governed by an energy-space-time Young-Laplace equation. Electric field lines are described as space contraction energy shock waves induced by a dynamic space-time phase transition at maximum kinetic energy space- time interface tension which is the “charge”. Space-time always reacts to the presence of energy and that reaction is the interface tension at the energy-space-time boundary: gravitational & electric energy fields are consequences of energyspace-time interface tension (at either rest or kinetic energy boundary) also governed by an energy-space-time instability Young-Laplace equation. Gravitational constant G and the fine structure constant ∝ are respectively, the energy interface field’s interaction constants. The Strong force is a consequence of a direct contact between the nucleon's energy-space-time interface tension fields and has no interaction constant. The range and variation in the strength of the Strong force is due to Heisenberg’s uncertainty principle

PT-symmetric PINN for integrable nonlocal equations: Forward and inverse problems.

Since the PT-symmetric nonlocal equations contain the physical information of the PT-symmetric, it is very appropriate to embed the physical information of the PT-symmetric into the loss function of PINN, named PTS-PINN. For general PT-symmetric nonlocal equations, especially those equations involving the derivation of nonlocal terms due to the existence of nonlocal terms, directly using the original PINN method to solve such nonlocal equations will face certain challenges. This problem can be solved by the PTS-PINN method, which can be illustrated in two aspects. First, we treat the nonlocal term of the equation as a new local component so that the equation is coupled at this time. In this way, we successfully avoid differentiating nonlocal terms in neural networks. On the other hand, in order to improve the accuracy, we make a second improvement, which is to embed the physical information of the PT-symmetric into the loss function. Through a series of independent numerical experiments, we evaluate the efficacy of PTS-PINN in tackling the forward and inverse problems for the nonlocal NLS equation, the nonlocal derivative NLS equation, the nonlocal (2+1)-dimensional NLS equation, and the nonlocal three-wave interaction systems. The numerical experiments demonstrate that PTS-PINN has good performance. In particular, PTS-PINN has also demonstrated an extraordinary ability to learn large space-time scale rogue waves for nonlocal equations.

Localized source above a time-modulated dielectric half-space: Green's function theory

In this paper, we explore the two-dimensional Green's function problem above an instantaneous time-modulated dielectric half-space. In particular, we focus on studying the excitation dynamic with modulation that is carried out near the critical angle and the total internal reflection regime, where an impinging spectrum of waves expects the so-called lateral wave excitation on the interface. We start by analyzing the reflection of a plane wave, with detailed attention given to the difference between two cases: a slow quasistatic modulation versus a relatively fast modulation that leads to substantial excitation of intermodulation frequencies. Next, we provide a space-time representation to the space-domain Green's function, and later, we move to evaluate the spectral integral both in a brute-force numerically exact manner and using integration along the steepest descent path and the branch cuts, which unravel the distinction between different wave phenomena associated with the excitation problem. Thus, we identify different wave species that can be associated with reflected rays and waves that resemble the known head wave in the classical problem of stationary stratified media. We examine the unique time-dependent behavior of each wave species that arises as a consequence of the interface between the time-harmonics of the reflected space-time plane wave spectrum. Lastly, we demonstrate the broader validity of our analytical predictions, also in the case of a dispersive and finite time-modulated medium. To that end, we use a full-wave simulation of a source above a finite time-modulated thick layer that is implemented using a time-varying wire medium. These full-wave results are compared with our current analytical model with effective (homogenized) parameters of the time-modulated wire medium taken from . Published by the American Physical Society 2024

Propagation-Invariant Space-Time Plasmonic Pulse in Subwavelength MIM Waveguide.

The metal-insulator-metal (MIM) plasmonic waveguide has been highly anticipated for confining and guiding surface plasmon polaritons (SPPs) on the subwavelength scale. However, perennial drawbacks such as a short propagation length and an unbounded transverse field have set limits on the use of the MIM waveguide in various applications. Herein, diffraction- and dispersion-free MIM modes are synthesized by using space-time wave packets (STWPs) and are therefore referred to as space-time MIM (ST-MIM) waveguide modes. Compared to a Gaussian pulse of the same duration and spectral bandwidth, the ST-MIM demonstrates enhanced propagation lengths of about 2.4 times for the symmetric mode and about 6.3 times for the antisymmetric mode. In the simulations, the ST-MIMs are confined in all transverse dimensions, thereby overriding the diffraction limits. In addition, the group velocities of the ST-MIMs can be arbitrarily designed, which makes it possible to synchronize the pulse propagation speeds of the symmetric and antisymmetric MIM modes.

Exciting space-time surface plasmon polaritons by irradiating a nanoslit structure.

Space-time (ST) wave packets are propagation-invariant pulsed optical beams that travel freely in dielectrics at a tunable group velocity without diffraction or dispersion. Because ST wave packets maintain these characteristics even when only one transverse dimension is considered, they can realize surface-bound waves (e.g., surface plasmon polaritons at a metal-dielectric interface, which we call ST-SPPs) that have the same unique characteristics as their freely propagating counterparts. However, because the spatiotemporal spectral structure of ST-SPPs is key to their propagation invariance on the metal surface, their excitation methodology must be considered carefully. Using finite-difference time-domain simulations, we show that an appropriately synthesized ST wave packet in free space can be coupled to an ST-SPP via a single nanoscale slit inscribed in the metal surface. Our calculations confirm that this excitation methodology yields surface-bound ST-SPPs that are localized in all dimensions (and can thus be considered as plasmonic "bullets"), which travel rigidly at the metal-dielectric interface without diffraction or dispersion at a tunable group velocity.

Self-dual fields on self-dual backgrounds and the double copy

We explore the double copy for self-dual gauge and gravitational fields on self-dual background spacetimes. We consider backgrounds associated with solutions of the second Plebanski equation and describe results with different gauge-fixing conditions. Finally we discuss the kinematic and w-algebras and the double copy, identifying modified Poisson structures and kinematic structure constants in the presence of the self-dual background. The self-dual plane wave and Eguchi-Hanson spacetimes are studied as examples and their respective w-algebras derived. Published by the American Physical Society 2024