arXiv subjects

Z. Qiu

Publications and source records attributed to Z. Qiu.

21 records · Page 2Linked to original sources

arXiv2010

Splitting broad beams into arrays of dissipative spatial solitons by material and virtual gratings

We elaborate two generic methods for producing two-dimensional (2D) spatial soliton arrays (SSAs) in the framework of the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) model. The first approach deals with a broad beam launched into the dissipative nonlinear medium, which is equipped with an imprinted grating of a sufficiently sharp form. The beam splits into a cluster of jets, each subsequently self-trapping into a stable soliton, if the power is sufficient for that. We consider two kinds of sharp gratings -- "raised-cosine" (RC) and Kronig-Penney (KP) lattices -- and two types of the input beams, fundamental and vortical. By selecting appropriate parameters, this method makes it possible to create various types of solitons arrays, such as solid, annular (with single and double rings), and cross-shaped ones. The second method uses a "virtual lattice", in the form of a periodic transverse phase modulation imprinted into the broad beam, which is passed through an appropriate phase mask and then shone into a uniform nonlinear medium. Two different types of the masks are considered, in the form of a "checkerboard" or "tilings". In that case, broad fundamental and vortical beams may also evolve into stable SSAs, if the beam's power and spacing of the virtual phase lattice are large enough. By means of the latter technique, square-shaped, hexagonal, and quasi-crystalline SSAs can be created.

nlin.PS↗

arXiv2009

Ionization in damped time-harmonic fields

We study the asymptotic behavior of the wave function in a simple one dimensional model of ionization by pulses, in which the time-dependent potential is of the form $V(x,t)=-2δ(x)(1-e^{-λt} \cosωt)$, where $δ$ is the Dirac distribution. We find the ionization probability in the limit $t\to\infty$ for all $λ$ and $ω$. The long pulse limit is very singular, and, for $ω=0$, the survival probability is $const λ^{1/3}$, much larger than $O(λ)$, the one in the abrupt transition counterpart, $V(x,t)=δ(x)\mathbf{1}_{\{t\ge 1/λ\}}$ where $\mathbf{1}$ is the Heaviside function.

math-ph↗

arXiv2003

Gravitational Lensing by Dark Matter Caustics

Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first three, the line of sight is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative or zero. In the fourth case the line of sight passes near a cusp. For each we derive the map between the image and source planes. In some cases, a point source has multiple images and experiences infinite magnification when the images merge. Unfortunately, for the dark matter caustics expected in realistic galactic halo models, the angular resolution required to resolve the multiple images is not presently achievable. A more promising approach aims to observe the distortions caused by dark matter caustics in the images of extended sources such as radio jets.

astro-ph↗