Search

We present hybrid OpenMP/MPI (Open Multi-Processing/Message Passing Interface) parallelized versions of earlier published C programs (D. Vudragovic et al., Comput. Phys. Commun. 183, 2021 (2012)) for calculating both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation in three spatial dimensions. The GP equation describes the properties of dilute Bose-Einstein condensates at ultra-cold temperatures. Hybrid versions of programs use the same algorithms as the C ones, involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method, but consider only a fully-anisotropic three-dimensional GP equation, where algorithmic complexity for large grid sizes necessitates parallelization in order to reduce execution time and/or memory requirements per node. Since distributed memory approach is required to address the latter, we combine MPI programing paradigm with existing OpenMP codes, thus creating fully flexible parallelism within a combined distributed/shared memory model, suitable for different modern computer architectures. The two presented C/OpenMP/MPI programs for real- and imaginary-time propagation are optimized and accompanied by a customizable makefile. We present typical scalability results for the provided OpenMP/MPI codes and demonstrate almost linear speedup until inter-process communication time starts to dominate over calculation time per iteration. Such a scalability study is necessary for large grid sizes in order to determine optimal number of MPI nodes and OpenMP threads per node., Comment: 8 pages, 4 figures; to download the programs, click other formats and download the source

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schr\"odinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D beam deflects along the trajectories $z=\pm2(x-x_0)$, which are independent of the chirp. In the case of 2D Gaussian beam, the propagation is also deflected, but the trajectories align along the diffraction cone $z=2\sqrt{x^2+y^2}$ and the direction is determined by the chirp. Both 1D and 2D Gaussian beams are diffractionless and display uniform propagation. The nondiffracting property discovered in this model applies to other beams as well. Based on the nondiffracting and splitting properties, we introduce the Talbot effect of diffractionless beams in FSE., Comment: 10 pages, 4 figures

By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrodinger equation, the modulation instability (MI) of its n = 1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked-step with the n = 1 mode. This fundamental insight, the enslavement of all higher modes to the n = 1 mode, explains the formation of a triangular-shaped spectrum which generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher order MI with more than one initial unstable modes, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of "super-recurrence", where the FPU period is much longer than that of a single unstable mode., Comment: 23 pages, 12 figures

We construct rogue waves (RWs) in a coupled two-mode system with the self-focusing nonlinearity of the Manakov type (equal SPM and XPM coefficients), spatially modulated coefficients, and a specially designed external potential. The system may be realized in nonlinear optics and Bose-Einstein condensates. By means of a similarity transformation, we establish a connection between solutions of the coupled Manakov system with spatially-variable coefficients and the basic Manakov model with constant coefficients. Exact solutions in the form of two-component Peregrine and dromion waves are obtained. The RW dynamics is analyzed for different choices of parameters in the underlying parameter space. Different classes of RW solutions are categorized by means of a naturally introduced control parameter which takes integer values., Comment: 9 pages, 5 figures

In an atomic vapor, a honeycomb lattice can be constructed by utilizing the three-beam interference method. In the method, the interference of the three beams splits the dressed energy level periodically, forming a periodic refractive index modulation with the honeycomb profile. The energy band topology of the honeycomb lattice can be modulated by frequency detunings, thereby affecting the appearance (and disappearance) of Dirac points and cones in the momentum space. This effect can be usefully exploited for the generation and manipulation of topological insulators., Comment: 8 pages, 5 figures

Dynamics of wavepackets in fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in fractional Schr\"odinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional (1D, 2D) input chirped Gaussian beams is not harmonic. In 1D, the beam propagates along a zigzag trajectory in the real space, which corresponds to a modulated anharmonic oscillation in the momentum space. In 2D, the input Gaussian beam evolves into a breathing ring structure in both real and momentum spaces, which forms a filamented funnel-like aperiodic structure. The beams remain localized in propagation, but with increasing distance display increasingly irregular behavior, unless both the linear chirp and the transverse displacement of the incident beam are zero., Comment: 7 pages, 5 figures, Phys. Rev. Lett., in press

We demonstrate the dual accelerating Airy-Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy-Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. It results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy-Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction., Comment: 7 pages, 3 figures

Mid-infrared spectral broadening is of great scientific and technological interest, which till date is mainly achieved using non-silica glass fibers, primarily made of tellurite, fluoride and chalcogenide glasses. We investigate broadband mid-infrared supercontinuum generation at very low power in semiconductor multiple quantum well (MQW) systems facilitated by electromagnetically induced transparency. 100 femto-seconds pulses of peak power close to a Watt have been launched in the electromagnetically induced transparency window of a 30 period 1.374 {\mu}m long MQW system. Broadband supercontinuum spectra, attributed to self phase modulation and modulation instability, is achievable at the end of the MQW system. The central part of the spectra is dominated by several dips and the far infra-red part of the spectra is more broadened in comparison to the infra-red portion. Key advantage of the proposed scheme is that the supercontinuum source could be easily integrated with other semiconductor devices., Comment: 21 pages, 5 figures