Modulation instability of wave packets in a Gires–Tournois interferometer

We study the specific features of the perturbation dynamics of a wave packet in a Gires–Tournois interferometer. We obtain a dispersion relationship that relates the perturbation parameters to the parameters of the structure and pump wave, the analytical expressions for the gain increment of a harmonic perturbation and other important characteristics that determine the dynamics of the modulation instability of the reflected wave. Based on numerical simulation, we plot the dependences of the dispersion and nonlinearity parameters and the gain increment on the spacing between the interferometer mirrors, the angle of incidence of the radiation onto the mirrors, and the radiation intensity.     

Evolution of spin-dependent atomic wave packets in a harmonic potential

We have investigated theoretically the evolution of spin-dependent atomic wave packets in a harmonic magnetic trapping potential. For a Bose-condensed gas, which undergoes a Mott insulator transition and a spin-dependent transport, the atomic wavefunction can be described by an entangled single-atom state. Due to the confinement of the harmonic potential, the density distributions exhibit periodic decay and revival, which is different from the case of free expansion after switching off the combined harmonic and optical lattice potential.     

Influence of flow shear on localized Rayleigh–Taylor and resistive drift wave instabilities

The impact of velocity shear on the localized solutions of Rayleigh–Taylor (RT) and resistive drift wave (DW) instabilities has been investigated. Slab geometry is used, and the plasma density gradient is assumed to have a finite spatial structure. It demonstrates that the velocity shear has quite different effects on these instabilities: while it stabilizes RT instability and causes tilting of the eddies of equipotential contour, it has a very mild impact on the resistive DW instability and simply shifts the eddies with no tilting.     

Three-dimensional tomographic reconstruction of ultrashort free electron wave packets

We present a tomographic technique based on Photoelectron Angular Distributions (PADs) measured by Velocity-Map-Imaging (VMI) to reconstruct the three-dimensional shape of ultrashort free electron wave packets obtained from 1+2 Resonance Enhanced Multi-Photon Ionization (REMPI) of potassium atoms. To this end the laser pulse is rotated about its propagation direction and a set of PADs are recorded at different rotation angles. The tomographic reconstruction technique is described and results for linear and elliptical polarization are presented. Results for linearly polarized light producing cylindrically symmetric electron wave packets confirm the validity of our method whereas elliptically polarized light serves as a prototype for polarization-shaped laser pulses.     

Propagation properties of Airy–Gaussian beams

The propagation of the Airy–Gaussian beams is studied in strongly nonlocal nonlinear media analytically and numerically. The linear momentum of the analytical Airy–Gaussian beam solution of the Snyder–Mitchell model is not conservational, which is the reason that results in the disagreement between the analytical Airy–Gaussian beam solution and the numerical simulations of the nonlocal nonlinear Schr?dinger equation in the case of strong nonlocality. The quasi-Airy–Gaussian soliton in the Gaussian-shaped response material can be obtained when the parameter χ ₀ is large enough, and the patterns of Airy–Gaussian beams are variable periodically in liquid crystal material during propagation.     

Using Lorentz’s theorem for studying the propagation wave packets in a nonlinear medium

We obtain integral relationships expressing the amplitude of wave-packet field on the output surface of a layer via the field amplitude on the input surface, the field on the side surface of the layer, and the integral of the nonlinear currents inside the layer at the previous times in the spectral and spatiotemporal forms. These relationships allow one to perform studies and develop numerical simulation algorithms of propagation and interaction of wave packets which have wide frequency and angular spectra, including calculations of excitation of evanescent waves in the case of sharp focusing or formation of supernarrow filaments. Using the obtained relationships, we propose an algorithm that employs a simple iteration of the first order and allows one to significantly speed up the calculations. The possibility of using the fast Fourier transform to develop algorithms for numerical simulation of the boundary-value problems of nonlinear optics is demonstrated.     

Complex solutions and novel complex wave localized excitations for the(2+1)-dimensional Boiti–Leon–Pempinelli system

With the help of the symbolic computation system Maple, the Riccati equation mapping approach and a linear variable separation approach, a new family of complex solutions for the （2＋ 1）-dimensional Boiti-Leon-Pempinelli system （BLP） is derived. Based on the derived solitary wave solution, some novel complex wave localized excitations are obtained.     

Principle of stationary phase for propagating wave packets in the unidimensional scattering problem

We point out some incompatibilities which appear when one applies the stationary phase method for deriving phase times to obtain the spatial localization of wave packets scattered by a unidimensional potential barrier. We concentrate on the above barrier diffusion problem where the wave packet collision implies the possibility of multiple reflected and transmitted wave packets, which, depending on the boundary conditions, can overlap or stand in relative separation in space. We demonstrate that the indiscriminate use of the method for such a particular configuration leads to paradoxical results for which the correct interpretation, confirmed by analytical/numerical calculations, imposes the necessity of the appearance of multiple peaks as a consequence of multiple reflections by the barrier steps. Also at Instituto de Física Gleb Wataghin, UNICAMP, PO Box 6165, 13083-970 Campinas, SP, Brazil.     

Temporal Airy–Talbot effect in linear optical potentials

We investigate the Airy–Talbot effect of an Airy pulse train in time-dependent linear potentials. The parabolic trajectory of self-imaging depends on both the dispersion sign and the linear potential gradient. By imposing linear phase modulations on the pulse train, the Airy–Talbot effects accompanied with positive and negative refractions are realized. For an input composed of stationary Airy pulses, the self-imaging follows straight lines, and the Airy–Talbot distance can be engineered by varying the linear potential gradient. The effect is also achieved in symmetric linear potentials. The study provides opportunities to control the self-imaging of aperiodic optical fields in time dimension.     

Interaction of Airy–Gaussian beams in saturable media

Based on the nonlinear Schr o¨dinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure.     

Wormhole solutions in Gauss–Bonnet–Born–Infeld gravity

A new class of solutions which yields an (n + 1)-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.     

Two-mirror spin–wave neutron interferometer

The characteristics of a spin-wave neutron interferometer comprising two parallel magnetic mirrors located in noncollinear to the magnetizations of the mirrors are investigated. The device can be used to study the properties of the neutron wave packet and measure the time and spatial correlations of material densities in the medium and on the surface. The interferometer’s sensitivity and the observed neutron coherence length are estimated using experimental data. The possible applications of neutron spin-echo spectrometry based on the two-mirror interferometer are discussed.     

Gravastars in modified Gauss–Bonnet gravity

This paper aims to discuss the viable and analytic solution of the spherically symmetric gravastar model under the influence of modification of Gauss–Bonnet gravity, i.e., f(G) gravity, where G is the Gauss–Bonnet curvature term. For this purpose, we evaluate the field equations in corresponding theory and conservation equation with the help of an effective energy–momentum tensor. A mathematical formalism of the gravastar’s three regions, i.e., interior de-Sitter region, thin shell, and the exterior Schwarzschild vacuum region have been discussed. We, then analyze different realistic features, in particular energy, entropy, and length of the shell. The viability of these physical features is then examined through the graphical representations separately. Within the framework of an alternative theory, we have obtained the exact and singularity free model of gravastar.     

Gauss–Bonnet term on vacuum decay

We study the effect of the Gauss–Bonnet term on vacuum decay process in the Coleman–De Luccia formalism. The Gauss–Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss–Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss–Bonnet coefficient.     

More on the dilatonic Einstein–Gauss–Bonnet gravity

Einstein–Gauss–Bonnet gravity coupled to a dynamical dilaton is examined from the viewpoint of Einstein’s equivalence principle. We point out that the usual frame change that applies to the action without curvature correction does not cure the problem of nonminimal couplings by the dynamical nature of a dilaton field. Thus a modification of the Einstein frame is required. It is proposed that the kinetic term of a dilaton should be brought to a canonical form, which completely fixes the additional terms associated with the frame transformation.     

Propagation of an Airy–Gaussian beam in uniaxial crystals

Under the paraxial approximation, the analytical propagation expression of an Airy–Gaussian beam(Ai GB) in uniaxial crystals orthogonal to the optical axis is investigated. The propagation dynamics of the Ai GB is given for different ratios of the extraordinary index to the ordinary refractive index. It has been found that the continuity and the self-bending effect of Ai GB become weaker when the ratio increases. From the figure of the maximum intensity of Ai GB, one can see that the maximum intensity is not monotone decreasing due to the anisotropic effect of the crystals. The intensity distribution of Ai GB in different distribution factors is shown. The Ai GB converges toward a Gaussian beam as the distribution factor increases.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.