Nondispersive Wave Packets Research Articles

Observation of optical de Broglie–Mackinnon wave packets

de Broglie wave packets accompanying moving particles are dispersive and lack an intrinsic length scale solely dictated by the particle mass and velocity. Mackinnon proposed a localized non-dispersive wave packet constructed out of dispersive de Broglie phase waves that possess an intrinsic length scale via an inversion of the roles of particle and observer. So far, the de Broglie–Mackinnon wave packet has remained a theoretical proposal. Here we report the observation of optical de Broglie–Mackinnon wave packets using paraxial space–time-coupled pulsed laser fields in the presence of anomalous group-velocity dispersion. Crucially, the bandwidth of de Broglie–Mackinnon wave packets has an upper limit that is compatible with the wave-packet group velocity and equivalent mass. In contrast to previously observed linear-propagation-invariant wave packets whose spatio-temporal profiles at any axial plane are X-shaped, those for de Broglie–Mackinnon wave packets are uniquely O-shaped (circularly symmetric with respect to space and time). By sculpting their spatio-temporal spectral structure, we produce dispersion-free de Broglie–Mackinnon wave packets in the dispersive medium, observe their circularly symmetric spatio-temporal intensity profiles and closed-trajectory spectra, and tune the field parameters that uniquely determine the wave-packet length scale. de Broglie–Mackinnon wave packets are an extension of matter waves, but have so far remained a theoretical construct. Combining spatio-temporal light fields with anomalous dispersion has now allowed their experimental observation.

Evaluation of the sensitivity of higher order modes cluster (HOMC) guided waves to plate defects

Higher Order Modes Cluster (HOMC) guided waves are non-dispersive wave packets consisting of higher order Lamb wave modes. This paper investigates the effect of frequency and dominant mode(s) of an HOMC guided wave on its sensitivity to plate defects. The propagation of HOMC guided waves in a 10-mm thick mild steel plate is simulated by two-dimensional finite element model. The level of contribution of Lamb wave modes to the wave cluster is analyzed by using a two-dimensional Fast Fourier Transform (2D FFT) at various frequency-thickness products ranging from 15 to 35 MHz-mm. The normal stress profiles of the HOMC guided waves are plotted and used to show the changes in normal stress as a function of frequency-thickness product. The HOMC guided waves interactions with notches of 5%, 10%, 30% and 50% depths relative to the plate thickness are examined at various frequency-thickness products ranging from 15 to 35 MHz-mm. It is observed that the reflected energy from these notches decreases with increase in frequency-thickness product. Experimental measurements are also conducted on a similar plate. The experimental results are in line with simulations and confirm the changes observed in the reflection coefficient of notches at different frequency-thickness products.

Optical nondiffractive and nondispersive dark-wave dynamics in hydrodynamic origin

The primary attention of this work focuses on finding rational and generalized rational solutions for the (2 + 1)-dimensional Kadomtsev–Petviashvili equation that can be used to describe nondispersive and nondiffractive localized wave packet in power law nonlinear media. Specifically, the (2 + 1)-dimensional nonlinear Schrödinger equation with power law nonlinearity is first transformed into the Kadomtsev–Petviashvili equation. Then, through the bilinear form and symbolic computation, we derive two hierarchies of multi-lump solitary waves, composing of three, six, and eight lump waves. The obtained solutions observe a specific ‘circularity structure’ that the lump waves sit at the same circular. In addition, we illustrate that these waves are stable during propagation.

Contribution of Lamb wave modes in the formation of higher order modes cluster (HOMC) guided waves

In recent years, Higher Order Modes Cluster (HOMC) guided waves have been considered for ultrasonic testing of plates and pipes. HOMC guided waves consist of higher order Lamb wave modes that travel together as a single nondispersive wave packet. The objective of this paper is to investigate the effect of frequency-thickness value on the contribution of Lamb wave modes in an HOMC guided wave. This is an important issue that has not been thoroughly investigated before. The contribution of each Lamb wave mode in an HOMC guided wave is studied by using a two-dimensional finite element model. The level of contribution of various Lamb wave modes to the wave cluster is verified by using a 2D FFT analysis. The results show that by increasing the frequency-thickness value, the order of contributing modes in the HOMC wave packet increases. The number of modes that comprise a cluster also increases up to a specific frequency-thickness value and then it starts to decrease. Plotting of the cross-sectional displacement patterns along the HOMC guided wave paths confirms the shifting of dominant modes from lower to higher order modes with increase of frequency-thickness value. Experimental measurements conducted on a mild steel plate are used to verify the finite element simulations. The experimental results are found to be in good agreement with simulations and confirm the changes observed in the level of contribution of Lamb wave modes in a wave cluster by changing the frequency-thickness value.

Bridge expansion after coalescence of two droplets in air: Inertial regime

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane, or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number (Oh), the dynamics of the bridge differs a lot. For Oh ≈1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge center. The expansion is thus caused by the capillary pressure that drives the fluid toward the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of nondispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result in the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow rate that enters the bridge and thus determines its radial expansion.

Nondispersing Wave Packets in Lattice Floquet Systems.

We show that in a one-dimensional translationally invariant tight binding chain, nondispersing wave packets can in general be realized as Floquet eigenstates-or linear combinations thereof-using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their "round-trip" time) locks in at rational ratios sT/r of the driving period T, where s, r are coprime integers. Wave packets of different s/r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r=1) or over a long time (s/r≠1). Discrete time translation symmetry is manifestly broken for s≠1, reminiscent of integer and fractional Floquet time crystals. We further demonstrate how to reverse engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.

Non-dispersive wavepackets generated in layered structures by a scanning laser source

In this article, we describe the use of a continuous-wave laser scanning method to generate non-dispersive surface acoustic wavepackets, which propagate along the sample surface without any waveform change. To achieve this goal, a coated linear elastic film on a non-linear substrate allows for careful balancing of dispersion and non-linearity effects. The scanning speed of the laser source and the thickness of the coated film were parametrically investigated to determine the optimal scanning speed for the generation of ultrasound for a given thickness of the coated film. In the first step, four different combinations of scanning speeds and the thickness of the coated film are presented to illustrate the generation of the narrowband ultrasound. The purpose of the scanning laser source is to effectively generate large amplitude ultrasound that takes the material into the nonlinear range. Further optimization through a careful matching combination of the scanning speed and the thickness of the coated film, whereby the dispersion effect was compensated entirely by the non-linearity effect, was used to generate non-dispersive ultrasonic wavepackets, which subsequently propagate with little distortion. The main findings of the simulations indicate that non-dispersive surface acoustic wavepackets for coated systems can be generated via the scanning laser source approach for specific values of scanning speed and thickness of the coated film.

Nondispersive wave packets in planar helium

Two-electron wave packets found in driven planar helium follow a classical periodic orbit without spreading and are localized in nonlinear resonance islands of the classical phase space. The general mechanism that produces these nondispersive wave packets is the near-resonant coupling between highly correlated, asymmetric, and doubly excited states of the atom with an external periodic electromagnetic field. We provide a full characterization of these two-electron nondispersive wave packets found in the Floquet spectrum of driven planar helium. This includes the characteristic energy spectrum, relatively long lifetimes, and the identification of the resonance states of helium that are responsible for their formation. This is achieved with the help of an efficient quantum treatment of driven planar helium which combines Floquet theory, complex rotation, and the representation of the Hamiltonian in a set of four coupled harmonic oscillators.

Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves

We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

Entanglement measures in doubly excited states and nondispersive wave packets in planar helium

We calculate the amount of entanglement for bound and doubly excited singlet states below the second, third and fourth ionization thresholds in planar helium. Furthermore, we investigate the dynamics of entanglement in nondispersive two-electron wave packets generated by the resonant coupling of frozen planet states of helium. We show that it is possible to obtain a two-electron nondispersive wave packet for which the time-average entanglement is greater than for each of the unperturbed coupled states.

The affective factors on the uncertainty in the collisions of the soliton solutions of the double field sine-Gordon system

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in 1+1 dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will be shown numerically, during collisions between solitons, there will be an uncertainty which originates from the amount of the maximum amplitude and arbitrary initial phases of the trapped wave packets.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Coupling of frozen planet states of helium to its bound states:towards the preparation of two-electron nondispersive wave packets

SynopsisFrozen planet states of helium give rise to two-electron nondispersive wave packets. A study of the coupling of frozen planet states of helium to its bound states suggests a two photon process to populate such states. This is a first step in order to construct such wave packets.

Wave-mechanical model for chemistry

The strength and defects of wave mechanics as a theory of chemistry are critically examined. Without the secondary assumption of wave–particle duality, the seminal equation describes matter waves and leaves the concept of point particles undefined. To bring the formalism into line with the theory of special relativity, it is shown to require reformulation in hypercomplex algebra that imparts a new meaning to electron spin as a holistic spinor, eliminating serious current misconceptions in the process. Reformulation in the curved space–time of general relativity requires the recognition of nonlinear effects that invalidate the practice of linear combination of atomic orbitals, ubiquitous in quantum chemistry, and redefines the electron as a nondispersive wave packet, or soliton.

On quantization of nondispersive wave packets

Nondispersive wave packets are widely used in optics and acoustics. We found it interesting that such packets could be also a subject of quantum field theory. Canonical commutation relations for the nondispersive wave packets are constructed.

Creating and Transporting Trojan Wave Packets

Nondispersive localized Trojan wave packets with n(i) ~ 305 moving in near-circular Bohr-like orbits are created and transported to localized near-circular Trojan states of higher n, n(f) ~ 600, by driving with a linearly polarized sinusoidal electric field whose period is slowly increased. The protocol is remarkably efficient with over 80% of the initial atoms being transferred to the higher n states, a result confirmed by classical trajectory Monte Carlo simulations.

Wave-Particle Duality in Nonlinear Klein-Gordon Equation

In this paper, I present a nonlinear potential for the Klein-Gordon equation which leads to localized, non-dispersive wave-packets with remarkable properties. These properties include the deBroglie’s wavelength-momentum and the Einstein’s energy-momentum-rest mass relations and a relativistic total energy which coincides with the mass parameter times the velocity of light squared, also equal to the Planck’s constant times the frequency in the rest frame of the wave-packet. Energy and momentum, therefore, can be transported by soliton-like wave-packets with well-defined energy and momentum, without the implementation of the canonical quantum procedure.

Slow non-dispersing wavepackets

We show that in plasmonic or metamaterial slab waveguides, it is possible to generate slow non-dispersing wavepackets which undergo neither spatial diffraction nor temporal spreading with no nonlinear effects by forming a type of hybrid wavepacket between slow-light waveguide modes and diffraction-free Airy wavepackets. Three mechanisms are involved in their slowness: the slow-light feature of waveguide modes, the initial launching speed of hybrid wavepackets, and their acceleration along the time domain in a moving frame.

Fictitious-time wave-packet dynamics. I. Nondispersive wave packets in the quantum Coulomb problem

Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a four-dimensional harmonic oscillator, subject to a constraint. This regularization makes use of a fictitious time variable, but arbitrary Gaussian wave packets in that time variable in general violate that constraint. The set of ``restricted Gaussian wave packets'' consistent with the constraint is constructed and shown to provide a complete basis for the expansion of states in the original three-dimensional coordinate space. Using that expansion arbitrary localized Gaussian wave packets of the hydrogen atom can be propagated analytically and exhibit a nondispersive periodic behavior as functions of the fictitious time. Restricted wave packets with and without well-defined angular momentum quantum numbers are constructed. They will be used as trial functions in time-dependent variational computations for the hydrogen atom in static external fields in the subsequent paper [T. Fab\ifmmode \check{c}\else \v{c}\fi{}i\ifmmode \check{c}\else \v{c}\fi{}, J. Main, and G. Wunner, Phys. Rev. A 79, 043417 (2009)].

Creation of nondispersive Bohr-like wave packets

We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high-$n$ $(n\ensuremath{\sim}300)$ Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.