Self-accelerating Wave Research Articles

Density prediction of self-accelerating waves

Density prediction of self-accelerating waves

Self-accelerating wave packets in free space

Self-accelerating wave packets in free space

Unveiling the Link between Airy-like Self-Acceleration and Diametric Drive Acceleration.

We theoretically reveal the link between two types of self-acceleration mechanisms widely emerging in wave dynamics and experimentally demonstrate such a connection via pulse interactions in nonlinear optical fibers. We find that, in order to realize a pulse pair subjected to a diametric drive acceleration, one of the two components can be directly obtained from a self-accelerating Airy-like pulse under appropriate conditions. Such a form of synchronized acceleration cannot be achieved by approaches previously used to generate diametric drive acceleration. Our results generalize the fundamental concept of diametric drive acceleration and may bring about unconventional approaches to control self-accelerating waves.

Tail-free self-accelerating solitons and vortices

Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.

Self-accelerating Airy-Laguerre-Gaussian light bullets in a two-dimensional strongly nonlocal nonlinear medium.

We report a self-accelerating wave packets eigenmode solution of a two-dimensional (2D) nonlocal nonlinear Schrödinger equation (NNLSE) with an Airy-beam time-dependence, and present their spatiotemporal profiles. The behaviours of such Airy-Laguerre-Gaussian light bullets, as propagated in a strongly nonlocal nonlinear medium (SNNM), are investigated both analytically and numerically. We found that the generation, control, and manipulation of the NL spatiotemporal light bullets are affected by the radial mode number and the azimuthal mode number, as well as the modulation depth. Our scheme is quite different from the linear light bullets, in which the wave propagates in a NL medium and is an eigenmode of NLSE.

Self-acceleration in non-Hermitian systems

We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian system. We explore self-accelerating waves with constant intensity and integrable self-accelerating waves. We find that self-accelerating constant intensity waves are possible even when gain and loss are not balanced in the system.

Self-accelerating parabolic cylinder waves in 1-D

We introduce a new self-accelerating wave packet solution of the Schrodinger equation in one dimension. We obtain an exact analytical parabolic cylinder wave for the inverted harmonic potential. We show that truncated parabolic cylinder waves exhibits their accelerating feature.

Self-oscillating beams in a photonic lattice

We study self-acceleration in a parabolic tight-binding lattice and construct a self-accelerating wave packet in k-space. As opposed to accelerating Airy wave packets in free space, self-acceleration occurs in k-space and this leads to self-oscillation in the lattice. We analytically derived a formula for self-acceleration and perform numerical computation to see such an oscillation for the truncated wave.

Self-accelerating matter waves

The free particle Schrödinger equation admits a nontrivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here, we present self-accelerating waves for the Bose–Einstein condensate in a time-dependent harmonic oscillator potential. We show that parity and time reversal symmetries for self-accelerating waves are spontaneously broken.

Incoherent self-accelerating beams

Self-accelerating optical beams form as a direct outcome of interference, initiated by a predesigned initial condition. In a similar fashion, quantum mechanical particles exhibit force-free acceleration as a result of interference effects following proper preparation of the initial Schrodinger wave function. Indeed, interference is at the heart of such wave packets, and hence it is implied that self-accelerating wave packets must be coherent entities. Counter to that, we demonstrate theoretically and experimentally spatially incoherent self-accelerating beams, in both the paraxial and the nonparaxial domains. We show that in principle, the transverse correlation distance can be as short as a single wavelength, while a properly designed initial beam will give rise to shape-preserving acceleration for the same distance as a coherent accelerating beam propagating on the same trajectory. These findings expand the understanding of the relation between coherence and accelerating beams, and may have implications for the design of self-accelerating quantum wave packets with limited quantum coherence.

Semiconductor laser beam bending

This study is about a single-component cylindrical structured lens with a gradient curve that was used for bending laser beams. It operates under atmospheric conditions and bends the laser beam independently of temperature, pressure, polarity, polarization, magnetic field, electric field, radioactivity, and gravity. A single-piece cylindrical lens that can bend laser beams was developed. Lenses are made of transparent, tinted, or colored glass and are used to undermine or absorb the energy of laser beams. This study is not a work of a plasma filamentation, nor is related to a self-accelerating wave packet. Rather, it focuses on bending the laser beam as required. The dimensions of the light-bending curvatures vary depending on the source and the lens. This is an application of laser beam bending. The dimensions of the captured images are 500 $\times $ 700 mm.

Partial Bessel electromagnetic wave

We present the spatially self-bending solutions (the partial Bessel functions) of the Maxwell equations, where the self-bending wave can be produced through launching a group of plane waves that interfere with each other by modulating their initial phases and the emission directions. The self-bending electromagnetic waves accelerating in a circular trajectory preserve the beam shape within a certain propagation distance. Unlike Ariy wave packet, the bending angle of the new self-accelerating wave can be much larger than that of Ariy beam. The Poynting vector of the half Bessel beam shows that the main lobe maintains a propagation-invariant structure and can complete a turn close to 180°. In addition, one pair of half Bessel electromagnetic waves is forbidden to propagate inside a certain area where the designed beam generates the self-shielding region.

Spectral decomposition of the operator p 2–q 2

It is shown that the operator p2–q2 has a continuous spectrum extending from −∞ to +∞. The expansion of an arbitrary function with respect to the eigenfunctions is given. The action of the operators q and p on the eigenfunctions can be written explicitly by means of symbolic formulae. Finally, an alternative method for studying the behaviour of self-accelerating wave packets is given.