Papers by Fatkhulla Abdullaev
Physica D: Nonlinear Phenomena, 2002
The diffraction of intensive electromagnetic waves by a system of N slits in a non-linear medium ... more The diffraction of intensive electromagnetic waves by a system of N slits in a non-linear medium is studied. The beams, created by the slits, have an arbitrary polarization and are therefore characterized by two orthogonal modes. To describe the dynamics of the modes the set of two coupled non-linear Schrödinger equations (the Manakov system) is used. The dynamics is analyzed on the basis of the corresponding linear 3 × 3 scattering problem. The dependence of the number of emerging solitons and their parameters on both the initial conditions and the separating distance is obtained. The important observation is that beams without initial phase modulations can result in beams propagating on some non-zero angle to the initial wave-vector. The case N = 2 is analyzed in detail. The influence of the initial intensity and polarization on the mode switching, soliton binding and separating is studied. Numerical calculations of the Manakov equations show good agreement with theoretical predictions.
Journal of the Optical Society of America B, 2001
The instability of a plane wave in an optical medium with two-photon absorption is studied. The a... more The instability of a plane wave in an optical medium with two-photon absorption is studied. The analysis is based on the modified nonlinear Schrödinger equation. The linearized equation for the modulation is shown to have an exact solution in terms of confluent hypergeometric functions. It is found that the gain spectrum varies with position. This may result in a change of the wave dynamics and in a decrease of the repetition rate of the pulse train developed from the plane wave. The application of the results to the optical pulse propagation in semiconductor gratings and fiber gratings is discussed.
Springer Proceedings in Physics, 1989
Softcover reprint of the hardcover 1st edition 1989 The use of registered names, trademarks, etc.... more Softcover reprint of the hardcover 1st edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.
NATO Security through Science Series C: Environmental Security, 2009
We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation ... more We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in two-and three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schrödinger equation, sharing with these the propriety of being unstable against small norm (number of atoms) variations. We show that in the presence of the optical lattice the solution separates stable localized solutions (gap-solitons) from decaying ones, characterizing the delocalizing transition occurring in the multidimensional case. The link between these higher dimensional solutions and the ones of one dimensional nonlinear Schrödinger equation with higher order nonlinearities is also discussed.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2012
The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonl... more The existence and stability of three-dimensional (3D) solitons, in cross-combined linear and nonlinear optical lattices, are investigated. In particular, with a starting optical lattice (OL) configuration such that it is linear in the x-direction and nonlinear in the y-direction, we consider the z-direction either unconstrained (quasi-2D OL case) or with another linear OL (full 3D case). We perform this study both analytically and numerically: analytically by a variational approach based on a Gaussian ansatz for the soliton wavefunction and numerically by relaxation methods and direct integrations of the corresponding Gross-Pitaevskii equation. We conclude that, while 3D solitons in the quasi-2D OL case are always unstable, the addition of another linear OL in the z-direction allows us to stabilize 3D solitons both for attractive and repulsive mean interactions. From our results, we suggest the possible use of spatial modulations of the nonlinearity in one of the directions as a tool for the management of stable 3D solitons.
Proceedings of SPIE - The International Society for Optical Engineering, 2001
Springer Proceedings in Physics, 1989
Photonics and Fiber Technology 2016 (ACOFT, BGPP, NP), 2016
Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) in deep optical lattices... more Binary mixtures of quasi one-dimensional Bose-Einstein condensates (BEC) in deep optical lattices and in the presence of periodic rapid modulations of the interspecies scattering length are investigated. In the strong management limit the existence of binary compactons of stationary and quasi-stationary type is demonstrated. The existence of a threshold on the inter-species scattering length in the case of quasi-stationary compactons is shown.
Journal of Physics: Conference Series, 2016
Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states... more Two anti-phase bright solitons in a dipolar Bose-Einstein condensate can form stable bound states, known as soliton molecules. In this paper we study the scattering of a two-soliton molecule by external potential, using the simplest and analytically tractable Gaussian potential barriers and wells, in one spatial dimension. Theoretical model is based on the variational approximation for the nonlocal Gross-Pitaevskii equation (GPE). At sufficiently low velocity of the incident molecule we observe quantum reflection from the potential well. Predictions of the mathematical model are compared with numerical simulations of the GPE, and good qualitative agreement between them is demonstrated.
Physical Review A, 2014
The existence of compacton matter waves in binary mixtures of quasi one-dimensional Bose-Einstein... more The existence of compacton matter waves in binary mixtures of quasi one-dimensional Bose-Einstein condensates in deep optical lattices and in the presence of nonlinearity management, is first demonstrated. For this, we derive an averaged vector discrete nonlinear Schrödinger equation (DNLSE) and show that compacton solutions of different types can exist as stable excitations. Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system and their dependence on the inter-and intra-species scattering lengths, investigated. We show that under proper management conditions, compactons can be very robust excitations that can emerge spontaneously from generic initial conditions. A possible experimental setting for compacton observation is also discussed.
Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the ef... more Dynamics of a matter wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential are analyzed. In numerical experiments we observe the Fermi type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared with the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.
We study localized nonlinear excitations of a dilute Bose-Einstein condensate (BEC) with spinorbi... more We study localized nonlinear excitations of a dilute Bose-Einstein condensate (BEC) with spinorbit coupling in a deep optical lattice (OL). We use Wannier functions to derive a tight-binding model that includes the spin-orbit coupling (SOC) at the discrete level in the form of a generalized discrete nonlinear Schödinger equation. Spectral properties are investigated and the existence and stability of discrete solitons and breathers with different symmetry properties with respect to the OL is demonstrated. We show that the symmetry of the modes can be changed from on-site to inter-site and to asymmetric modes simply by changing the interspecies interaction. Asymmetric modes appear to be novel modes intrinsic of the SOC.
Soviet Physics Journal, 1988
We consider a one-dimensional model of displacive structural phase transitions with "random tempe... more We consider a one-dimensional model of displacive structural phase transitions with "random temperature"-type impurities. The modification to the central peak is calculated. It is shown that random-temperature impurities lead to a divergence in the central peak intensity. We find good agreement between our results and the experimental temperature dependence of the central peak. In the present work we study the dynamics of domain walls in uniaxial ferroelectrics undergoing structural displacive phase transitions.
Technical Physics Letters, 2002
Propagation of dispersion-managed solitons in optic fibers with randomly distributed dispersion i... more Propagation of dispersion-managed solitons in optic fibers with randomly distributed dispersion is studied. It is shown that the effect of the dispersion fluctuations can be described within the framework of a modified nonlinear Schrödinger equation with a frequency-dependent damping term (~ ω 4). The presence of randomly modulated dispersion leads to the damping of optical pulses. The condition for stable pulse propagation is determined based on the corresponding variational equations.
Physics Letters A, 1996
We analyse modulational instability (MI) of electromagnetic waves in a large variety of optical f... more We analyse modulational instability (MI) of electromagnetic waves in a large variety of optical fibers having different refractive-index profiles. For the normal-, anomalous-, and zero-dispersion regimes of the wave propagation, we show that whenever the second-order dispersion competes with higher-order dispersion (HOD), propagation of plane waves leads to a rich variety of dynamical behaviors. Most of the richness comes from the existence of critical behaviors, which include situations in which the HOD suppresses MI in the anomalous dispersion regime, and other situations in which the HOD acts in the opposite way by inducing non-conventional MI processes in the normal-and anomalous-dispersion regimes. We show that non-conventional MI sidebands are more prone to Ramaninduced degradations than ordinary MI sidebands can be.
Physics Letters A, 2000
Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap an... more Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-bodÿ interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D G 2. In case D s 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse.
Physical Review Letters, 2013
We report a diversity of stable gap solitons in a spin-orbit-coupled Bose-Einstein condensate sub... more We report a diversity of stable gap solitons in a spin-orbit-coupled Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is shown that the solitons can be classified by the main physical symmetries they obey, i.e., symmetries with respect to parity (P), time (T), and internal degree of freedom, i.e., spin (C), inversions. The conventional gap and gap-stripe solitons are obtained in lattices with different parameters. It is shown that solitons of the same type but obeying different symmetries can exist in the same lattice at different spatial locations. PT and CPT symmetric solitons have antiferromagnetic structure and are characterized, respectively, by nonzero and zero total magnetizations.
Physical Review A, 2012
We study the existence and stability of solitons in the quadratic nonlinear media with spatially ... more We study the existence and stability of solitons in the quadratic nonlinear media with spatially localized PT-symmetric modulation of the linear refractive index. Families of stable one and two hump solitons are found. The properties of nonlinear modes bifurcating from a linear limit of small fundamental harmonic field are investigated. It is shown that the fundamental branch, bifurcating from the linear mode of the fundamental harmonic is limited in power. The power maximum decreases with the strength of the imaginary part of the refractive index. The modes bifurcating from the linear mode of the second harmonic can exist even above PT symmetry breaking threshold. We found that the fundamental branch bifurcating from the linear limit can undergo a secondary bifurcation colliding with a branch of two-hump soliton solutions. The stability intervals for different values of the propagation constant and gain/loss gradient are obtained. The examples of dynamics and excitations of solitons obtained by numerical simulations are also given.
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Papers by Fatkhulla Abdullaev