Mixed-type solitons for the coupled higher-order nonlinear Schrödinger equations in multi-mode and birefringent fibers

Abstract

In this paper, coupled higher-order nonlinear Schrödinger equations are studied for the ultrashort pulse propagation in such optical media as the multi-mode fibers and birefringent fibers. Through the Hirota method and symbolic computation, analytic mixed-type one- and two-soliton solutions are derived, and three sets of conditions for the non-singular solutions are given as well. Via the one-soliton solutions obtained, critical condition for the black and gray solitons is obtained analytically. Asymptotic analysis is carried out on the two-soliton solutions to derive the condition for the inelastic interaction. Evolution of the bound vector solitons, elastic and inelastic interactions between the two vector solitons are also investigated graphically. Moreover, after the inelastic interaction, the two bright solitons are observed to disappear, while the two dark ones form the new bound soliton.     

Parallel transmission of solitons without interactions

Soliton interactions affect the pulse quality and capacity of communication systems. In this paper, parallel transmission of solitons without interactions are investigated to improve the pulse quality and capacity. Analytic two-soliton solutions for the variable coefficient nonlinear Schrödinger equation are obtained.The exponential profile of optical fibers is suggested to derive the parallel transmission of solitons, and influences of corresponding parameters are analyzed.     

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers

In this letter, under investigation is a nonlinear Schrödinger equation with varying dispersion, nonlinearity and loss for the propagation of ultra-short optical pulses in the normal dispersion regime of optical fibers. By virtue of the modified Hirota's method and symbolic computation, the analytic two-soliton solution is explicitly obtained. Both the bright and dark solitons are observed in the normal dispersion regime of optical fibers with dispersion management. An asymptotic analysis to verify the elastic collision between solitons is performed and the stability of the soliton solutions is investigated. Besides, a new bright solitonic generator for generating high-power and narrow bandwidth pulses is advised. Furthermore, possible applicable soliton control techniques which might be used for the design of optical switch and dispersion-managed systems are proposed.     

Soliton interactions in dispersion-decreasing fibers with the exponential dispersion profile

In this paper, soliton interactions in dispersion-decreasing fibers with the exponential dispersion profile will be investigated. Analytic two-soliton solutions will be obtained with Hirota’s method. With the different dispersion profile of dispersion-decreasing fibers, the propagation characteristics of solitons will be exhibited, and some soliton properties will be adjusted. Results presented in this paper could be used in soliton control in the dispersion-decreasing fibers.     

Dirac electrons of a split-gate Hall bar

In this work we study several unusual properties of Klein tunneling through the abrupt and flat barriers of a split-gate Hall bar system of graphene. We show that Klein tunneling of Dirac electrons can be rather strong in such a system, and that a significant electron density can be present under the barrier. It can be shown that the probability wavefunctions for large angular momenta are identical to the probability wavefunctions of the same angular momenta in the absence of the potential barrier, i.e., it is as if the barrier does not exist and the Klein tunneling is complete. This is a unique effect in a magnetic field. We propose that STM measurements may be used to detect the presence of such a density. We have also investigated drift velocity of electrons as the center of probability wavefunction varies from outside to inside of the flat potential barrier, and find a significant deviation from the semiclassical result.     

Symbolic computation on soliton dynamics and Bäcklund transformation for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity

In this paper, we study the generalized coupled nonlinear Schrödinger equations with the cubic-quintic nonlinearity and arbitrary coupling parameters which describe the effects of the quintic nonlinearity on the ultrashort optical soliton pulse propagation in the non-Kerr media. Dark–dark N- and bright–dark two-soliton solutions are derived with symbolic computation. The bilinear Bäcklund transformation and the corresponding one-soliton solution are also given. Interactions of the dark–dark solitons including the repulsive and coherent interactions are investigated analytically and graphically, which are different from those in previous studies. The relationship between the amplitude and the velocity of the dark soliton is studied, especially the soliton with the small amplitude catches up with the one with the large amplitude. Head-on and overtaking interactions of dark–dark solitons are presented. Interactions between a stationary dark soliton and another dark one are shown. The asymptotic analysis shows that the interaction of dark–dark two solitons is elastic. The periodic attraction and repulsion of the bright–dark two solitons in the bound state are also analyzed, which are in accordance with those in the bright–dark vector soliton studies but different from the asymmetric and symmetric stationary bound states of Manakov bright–dark solitons.     

Fabrication and Characterization of YBa2Cu3O7 − x Thin Film Step Junctions on MgO Substrates

We have investigated the tunneling properties of proximity-effect superconductor-normal-superconductor junctions based on high-temperature superconductor YBCO thin films and normal Ag layer. The systematic analysis of the properties of the films and the fabrication process which leads to a good-quality junctions is discussed in detail. The properties of the tunneling barrier are investigated by dc and rf measurements: the dc properties reveal that our junctions fully behave as expected from the de Gennes model. Regular Shapiro steps in the current–voltage characteristics are obtained as a result of microwave irradiation, indicating reliable rf properties of the junctions.     

Exact quasi-soliton solutions and soliton interaction for the inhomogeneous coupled nonlinear Schrödinger equations

We consider the inhomogeneous (1+1)-dimensional coupled nonlinear Schrödinger equations from the integrability point of view. This system has potential applications in inhomogeneous birefringent fiber media or in optical communication links with variable parameters. The exact analytical multisoliton solutions are obtained by employing the simple, straightforward Darboux transformation based on the obtained 3 × 3 Lax pair. Some main propagation and interaction properties of the one- and two-soliton solutions are discussed simultaneously. Also, the interaction between two neighboring combined solitary waves is numerically discussed. Excellent agreement with analytical results are found in the case of no collision. Moreover, the stability of these solutions are discussed in detail numerically with respect to a finite perturbation.     

Tunneling of Graphene Massive Dirac Fermions Through a Double Barrier

We study the tunneling of Dirac fermions in graphene through a double barrier potential. This is allowing the carriers to have an effective mass inside the barrier as generated by a lattice miss-match with the boron nitride substrate. The consequences of this gap opening on the transmission are investigated and the realization of resonant tunneling conditions is analyzed.     

Soliton collisions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system for an erbium-doped optical fiber

In this paper, we construct soliton solutions for a generalized variable-coefficient coupled Hirota–Maxwell–Bloch system, which can describe the ultrashort optical pulse propagation in a nonlinear, dispersive fiber doped with two-level resonant atoms. Under certain transformations and constraints, one- and two-soliton solutions are obtained via the Hirota method and symbolic computation, and soliton collisions are graphically presented and analyzed. One soliton is shown to maintain its amplitude and shape during the propagation. Soliton collision is elastic, while bright two-peak solitons and dark two-peak solitons are also observed. We discuss the influence of the coefficients for the group velocity, group-velocity dispersion (GVD), self-phase modulation, distribution of the dopant, and Stark shift on the soliton propagation and collision features, with those coefficients are set as some constants and functions, respectively. We find the group velocity and self-phase modulation can change the solitons’ amplitudes and widths, and the solitons become curved when the GVD and distribution of the dopant are chosen as some functions. When the Stark shift is chosen as a certain constant, the two peaks of bright two-peak solitons and dark two-peak solitons are not parallel. In addition, we observe the periodic collision of the two solitons.     

Semi-analytical method for designing finite sets of discriminated solitons and soliton molecules in fibres

An infinite number of solitons, as well as soliton molecules belonging different families, are allowed to propagate stably along a given dispersion-managed optical fibre. In this paper, we propose a semi-analytical method to systematically find a finite number of solitons and two-soliton molecules. Determined solitons and soliton molecules present a greatest power gap between them, to make them sufficiently distinct symbols for encoding several bits of information per symbol in a multilevel modulation format in fibre-optic transmission systems. Furthermore, for illustrative purposes, we discuss the possibility of encoding three bits per symbol.     

聚乙炔同质p^＋—n结的电流传输机理

我们在碘重掺杂聚乙炔(CH)_x基片上,用离子注入法掺钠,形成p~+-(CH)_x/n-(CH)_x结,并测得其电流-电压特性曲线。用P~+区孤子能带中的电子与n区导带底附近的电子,通过结的势垒产生隧道贯穿,形成隧道贯穿电流的模型,导出了结电流随偏置电压和温度变化的关系式,所得结果与实验相符。     

Transport Properties for Triangular Barriers in Graphene Nanoribbon

We theoretically study the electronic transport properties of Dirac fermions through one and double triangular barriers in graphene nanoribbon. Using the transfer matrix method, we determine the transmission, conductance and Fano factor. They are obtained to be various parameters dependent such as well width, barrier height and barrier width. Therefore, different discussions are given and comparison with the previous significant works is done. In particular, it is shown that at Dirac point the Dirac fermions always own a minimum conductance associated with a maximum Fano factor and change their behaviors in an oscillatory way (irregularly periodical tunneling peaks) when the potential of applied voltage is increased.     

Propagation of solitary waves in inhomogeneous erbium-doped fibers with third-order dispersion,self-steepening and gain/loss

We propose a generalized inhomogeneous Hirota–Maxwell–Bloch system which explains ultrashort optical pulse propagation in an inhomogeneous nonlinear, dispersive fiber doped with two-level resonant atoms. For this system, higher order effects like third-order dispersion and self-steepening are considered, which are assumed to be inhomogeneous together with group velocity dispersion and self-phase modulation. We have obtained a general solitary wave solution by using Lax pair and Bäcklund transformation techniques. We have analyzed various solitary wave forms like snaking solitons, classic solitons and compressed pulses by controlling the physical parameters and inhomogeneous functions.     

Features of Transport in Ultrathin Gold Nanowire Structures

The origin of the interface formation appearing due to the realization of contacts to ultrathin gold nanowire devices is revealed. Such interfaces play an important role in transport mechanisms in nanowire structures and can determine the electrical and operating parameters of a nanodevice. Based on experimental results, the specific electrical properties of bundles of ultrathin gold nanowires fabricated by wet chemical synthesis and subsequently assembled and contacted with gold electrodes are reported. It is demonstrated that these properties are strongly affected by the monolayers of organic molecules inevitably present on the surface of the nanowires due to synthetic conditions. In particular, such layers form a potential barrier to tunneling of the electrons from contacts to the nanowires. The electric transport behavior of the investigated nanowire structures in the temperature range from 500 mK to 300 K obeys the model of thermal fluctuation‐induced tunneling conduction through the nanowire‐metal electrode molecular junction. Application of this model allows calculation of the parameters of the molecular potential barrier. The formation of such a molecular barrier is verified by scanning tunneling microscope (STM) and transmission electron microscope (TEM) measurements performed using a supporting graphene layer. These findings are important for designing novel nanodevices for molecular electronics on the basis of ultrathin nanowires.     

Superconducting tunneling without the tunneling Hamiltonian

The theory of superconducting tunneling is extended to treat superconducting junctions with arbitrarily thin, but structureless tunnel barriers. An exact expression for the tunneling current is obtained, using standard, many-body, nonequilibrium Green's function techniques, assuming Fermi distributions in each electrode. The tunneling current result agrees with the recent theory of Blonder, Tinkham, and Klapwijk, but extends their results to treat strong coupling superconductors, proximity effect tunneling, and the effects of tunneling angle. Results for the Josephson critical current in S' INS (superconductor S', insulator I, metal N, superconductor S) junctions, where NS is a proximity effect double layer, are presented for barrier thicknesses ranging from zero to barrier thicknesses for which the tunneling Hamiltonian approach is correct, and for varying N metal thicknesses. Results forI-V curves are presented for normal metal (M)-INS junctions for a similar range of barrier thicknesses and N metal thicknesses. It is shown that the tunneling currentI is the sum of a supercurrentI _SUP carried solely by Cooper pairs through S, and a quasiparticle currentI _QP carried solely by quasiparticles. The influence of leakage on phonon structure observed on tunneling into strong coupling superconductors is described. The nonoscillating portion of the Josephson current is plotted as a function of voltage for the S' INS junction in the tunneling Hamiltonian limit.     

Superconducting tunneling without the tunneling Hamiltonian. II. Subgap harmonic structure

The theory of superconducting tunneling without the tunneling Hamiltonian is extended to treat superconductor/insulator/superconductor junctions in which the transmission coefficient of the insulating barrier approaches unity. The solution for the current in such junctions is obtained by solving the problem of a particle hopping in a one-dimensional lattice of sites, with forward and reverse transfer integrals that depend on the site. The results are applied to the problem of subgap harmonic structure in superconducting tunneling. The time-dependent current at finite voltage through a junction exhibiting subgap structure is found to have terms that oscillate at all integer multiples of the Josephson frequency,n(2eV/). The amplitudes of these new, and as yet unmeasured, ac current contributions as a function of voltage are predicted.     

Fabrication and Characteristics of Self-Aligned Dual-Gate Single-Electron Transistors

Single-electron transistors that have electrical tunneling barriers are fabricated, and Coulomb oscillation peaks and negative differential transconductance are observed at room temperature (300 K). Operation characteristics and multioscillation peaks are further investigated at low temperature (80 K). The period of Coulomb oscillation is 2.3 V due to an ultrasmall control gate capacitance, and oscillation peaks are shifted through the side gate bias, which is explained by the derived stability plot for dual-gate structures. Even with the side gates electrically floating, the device still operates as a single-electron transistor since the p-n junction barrier plays a role of tunneling barrier. In addition, by changing the bias condition, double dots are formed along the channel and peak splitting is observed.     

Search for Spin Filtering by Electron Tunneling Through Ferromagnetic EuS Barriers in PbS

Perpendicular transport through single- and double-barrier eterostructures made up of ferromagnetic EuS layers embedded into a PbS matrix was investigated. Both resonant tunneling and probably spin filtering through EuS barrier were observed.