Dark Soliton of a Growing Bose--Einstein Condensate in an External Trap

The dynamics of dark soliton in a growing Bose-Einstein condensate with an external magnetic trap are investigated by the variational approach based on the renormalized integrals of motion. The stationary states as physical solutions to the describing equation are obtained, and the evolution of the dark soliton is numerically simulated. The numerical results confirm the theoretical analysis and show that the dynamics depend strictly on the initial condition, the gain coefficient and the external potential.     

Abundant exact solutions for a strong dispersion-managed system equation

The generalized nonlinear Schr?dinger equation (NLSE), which governs the dynamics of dispersion-managed (DM) solitons, is considered. A novel transformation is constructed such that the DM fibre system equation with optical loss (gain) is transformed to the standard NLSE under a restricted condition. Abundant new soliton and periodic wave solutions are obtained by using the transformation and the solutions of standard NLSE. Further, we discuss their main properties and the interaction scenario between two neighbouring solitons by using direct computer simulation.     

Optical parametric chirped pulse amplification based on photonic crystal fibre

A compact two-stage optical parametric chirped pulse amplifier based on photonic crystal fibre is demonstrated.A 1064-nm soliton pulse is obtained in a home-made photonic crystal fibre (PCF) with femtosecond pulse pumping and then amplified to 2 mJ in an Nd:YAG regenerative amplifier.After the amplified pulses pass through the LBO crystal,the 532-nm double-frequency light with an energy of 0.8 mJ and a duration of over 100 ps at 10-Hz repetition rate is generated as a pump source in the following two-stage optical parametric amplification (OPA).The 850-nm chirped signal light gain from the stretcher is 1.5×10 4 in the first-stage OPA while it is 120 in the second-stage OPA.The total signal gain of optical parametric chirped pulse amplification (OPCPA) can reach 1.8×10 6.     

Analytical Periodic Wave and Soliton Solutions of the Generalized Nonautonomous Nonlinear Schrdinger Equation in Harmonic and Optical Lattice Potentials

We construct analytical periodic wave and soliton solutions to the generalized nonautonomous nonlinear Schrdinger equation with time-and space-dependent distributed coefficients in harmonic and optical lattice potentials.We utilize the similarity transformation technique to obtain these solutions.Constraints for the dispersion coefficient,the nonlinearity,and the gain(loss) coefficient are presented at the same time.Various shapes of periodic wave and soliton solutions are studied analytically and physically.Stability analysis of the solutions is discussed numerically.     

Chirped optical solitons and stability analysis of the nonlinear Schr?dinger equation with nonlinear chromatic dispersion

The present paper aims to investigate the chirped optical soliton solutions of the nonlinear Schr?dinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index. The exquisite balance between the chromatic dispersion and the nonlinearity associated with the refractive index of a fiber gives rise to optical solitons, which can travel down the fiber for intercontinental distances. The effective technique, namely, the new extended auxiliary equation method is implem...     

Influences of finite gain bandwidth on pulse propagation in parabolic fiber amplifiers with distributed gain profiles

The evolutions of the pulses propagating in decreasing and increasing gain distributed fiber amplifiers with finite gain bandwidths are investigated by simulations with the nonlinear Schr¨odinger equation. The results show that the parabolic pulse propagations in both the decreasing and the increasing gain amplifiers are restricted by the finite gain bandwidth. For a given input pulse, by choosing a small initial gain coefficient and gain variation rate, the whole gain for the pulse amplification limited by the gain bandwidth may be higher, which is helpful for the enhancement of the output linearly chirped pulse energy. Compared to the decreasing gain distributed fiber amplifier, the increasing gain distributed amplifier may be more conducive to suppress the pulse spectral broadening and increase the critical amplifier length for achieving a larger output linearly chirped pulse energy.     

Periodic solitons in dispersion decreasing fibers with a cosine profile

Periodic solitons are studied in dispersion decreasing fibers with a cosine profile. The variable-coefficient nonlinear Schr¨odinger equation, which can be used to describe the propagation of solitons, is investigated analytically. Analytic soliton solutions for this equation are derived with the Hirota’s bilinear method. Using the soliton solutions, we obtain periodic solitons, and analyze the soliton characteristics. Influences of physical parameters on periodic solitons are discussed. The presented results can be used in optical communication systems and fiber lasers.     

Exact analytical solutions of three-dimensional Gross-Pitaevskii equation with time-space modulation

By the generalized sub-equation expansion method and symbolic computation,this paper investigates the(3 + 1)dimensional Gross-Pitaevskii equation with time-and space-dependent potential,time-dependent nonlinearity,and gain or loss.As a result,rich exact analytical solutions are obtained,which include bright and dark solitons,Jacobi elliptic function solutions and Weierstrass elliptic function solutions.With computer simulation,the main evolution features of some of these solutions are shown by some figures.Nonlinear dynamics of a soliton pulse is also investigated under the different regimes of soliton management.     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.     

Soliton structures in the (1+1)-dimensional Ginzburg–Landau equation with a parity-time-symmetric potential in ultrafast optics

In this paper, the(1+1)-dimensional variable-coefficient complex Ginzburg–Landau(CGL) equation with a paritytime(PT) symmetric potential U(x) is investigated. Although the CGL equations with a PT-symmetric potential are less reported analytically, the analytic solutions for the CGL equation are obtained with the bilinear method in this paper. Via the derived solutions, some soliton structures are presented with corresponding parameters, and the influences of them are analyzed and studied. The single-soliton structure is numerically verified, and its stability is analyzed against additive and multiplicative noises. In particular, we study the soliton dynamics under the impact of the PT-symmetric potential. Results show that the PT-symmetric potential plays an important role for obtaining soliton structures in ultrafast optics, and we can design fiber lasers and all-optical switches depending on the different amplitudes of soliton-like structures.     

Spatiotemporal evolution of continuous-wave field and dark soliton formation in a microcavity with normal dispersion

Stable dark soliton and dark pulse formation in normally dispersive and red-detuned microcavities are investigated by numerically solving the normalized Lugiato-Lefever equation. The soliton essence is proved by fitting the calculated field intensity profile with the analytical formula of a dark soliton. Meanwhile, we find that a dark soliton can be generated either from the nonlinear evolution of an optical shock wave or narrowing of a locally broad dark pulse with smoother fronts. Explicit analytical expression is obtained to describe the oscillatory fronts of the optical shock wave. Furthermore,from the calculation results, we show that for smaller frequency detunings, e.g., α 3, in addition to the dark soliton formation, a single dark pulse with an oscillatory dip can also arise and propagate stably in the microcavity under proper pump detuning and pump strength combination. The existence region together with various field intensity profiles and the corresponding spectra of single dark pulse are demonstrated.     

Controllable optical superregular breathers in the femtosecond regime

We investigate optical superregular breathers in the femtosecond regime under dispersion management in an inhomogeneous fiber governed by the nonautonomous higher-order nonlinear Schr o¨dinger equation(NLSE). Exact solutions describing the dynamics of superregular breathers are obtained. Furthermore, we discuss the propagation behaviors of controllable superregular breathers, including stabilization and recurrence in an exponential dispersion fiber and a periodic distributed fiber system. Particularly, the nonlinear dynamics of superregular modes evolved from an identical initial small-amplitude modulation is analyzed in detail.     

Controlling the propagation of optical rogue waves in nonlinear graded-index waveguide amplifiers

A unified theory to construct exact optical rogue wave solutions of (1+1)-dimensional nonlinear Schrdinger equation with varying coefficients is proposed. The dynamics of the first-order optical rogue waves in nonlinear graded-index waveguide amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearity are also investigated. Moreover, under the suitable parameter condition, the propagation characteristics of the rogue waves in the nonlinear optical media are discussed. The properties of the optical rogue waves, such as width, amplitude, and position, can be controlled in the nonlinear optical media.     

Study of in-line single-mode optical fiber polarizer

The theoretical calculation method of multilayer metal-clad planar optical waveguide presented by Y. YAMAMOTO is greatly improved and transplant into the optical fiber and a suitable waveguide model of in-line single-mode optical fiber polarizer is set up to study its characteristics, the theorical analyses are in accordance with the experimental re suits. The polarizer whose extinction ratio is more than 30 dB at 0.633μm wavelength with an insertion loss of 0.5 dB is formed by grinding off the cladding on one side of a single-mode fibre and evaporating metal onto the polished durface in our Lab.     

Dark Soliton of Polariton Condensates under Nonresonant PT-Symmetric Pumping

A quantum system in complex potentials obeying parity-time(PT) symmetry could exhibit all real spectra,starting out in non-Hermitian quantum mechanics. The key physics behind a PT-symmetric system consists of the balanced gain and loss of the complex potential. We plan to include the nonequilibrium nature(i.e., the intrinsic kinds of gain and loss of a system) to a PT-symmetric many-body quantum system, with an emphasis on the combined effects of non-Hermitian due to nonequilibrium nature and PT symmetry in determining the properties of a system. To this end, we investigate the static and dynamical properties of a dark soliton of a polariton Bose–Einstein condensate under the PT-symmetric non-resonant pumping by solving the drivendissipative Gross–Pitaevskii equation both analytically and numerically. We derive the equation of motion for the center of mass of the dark soliton's center analytically with the help of the Hamiltonian approach. The resulting equation captures how the combination of the open-dissipative character and PT-symmetry affects the properties of the dark soliton; i.e., the soliton relaxes by blending with the background at a finite time. Further numerical solutions are in excellent agreement with the analytical results.     

Generation of Efficient Dispersive Waves in Photonic Crystal Fibers

Based on the generalized nonlinear Schroedinger equation, we investigate efficient dispersive wave （DW） generation in a photonic crystal fiber （POF） by numerical simulation and discuss a way to control DW generation by using an initial input pulse chirp. It is shown that efficient red-shifted DW generation can be obtained in a PCF with negative dispersion slopes. The energy contained in the DWs is considerably decreased for both positively and negatively chirped pulses at the fiber output. This provides us with an opportunity to conveniently and efficiently manipulate the DW generation by controlling the pre-chirp of the soliton. Moreover, we also show that forth- and higher-order dispersion terms play Iittle part in deciding the evolution of DWs.     

Scintillation index of optical wave propagating in turbulent atmosphere

A concise expression of the scintillation index is proposed for a plane optical wave and a spherical optical wave both propagating in a turbulent atmosphere with a zero inner scale and a finite inner scale under an arbitrary fluctuation condition. The expression is based on both the results in the Rytov approximation under a weak fluctuation condition and the numerical results in a strong fluctuation regime. The maximum value of the scintillation index and its corresponding Rytov index are evaluated. These quantities are affected by the ratio of the turbulence inner scale to the Fresnel size.     

Nonautonomous solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrdinger equation with time- and space-modulated coefficients

A class of analytical solitary-wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrdinger equation with time- and space-modulated coefficients and potentials are constructed using the similarity transformation technique. Constraints for the dispersion coefficient, the cubic and quintic nonlinearities, the external potential, and the gain (loss) coefficient are presented at the same time. Various shapes of analytical solitary-wave solutions which have important applications of physical interest are studied in detail, such as the solutions in Feshbach resonance management with harmonic potentials, Faraday-type waves in the optical lattice potentials, and localized solutions supported by the Gaussian-shaped nonlinearity. The stability analysis of the solutions is discussed numerically.     

Investigation of combined Brillouin gain and loss in a birefringent fiber with applications in sensing

The most general model of elliptical birefringence in an optical fiber is extended to describe a transient Bril-louin interaction including both gain and loss. The effects of elliptical birefringence cause a Brillouin spectral shape distortion, which is detrimental for fiber sensing techniques. The model investigates the effects of bire- fringence and the corresponding evolution of spectral distortion effects along the fiber, and also investigates regimes where this distortion is minimal.     

Evolution of dark solitons in the presence of Raman gain and self-steepening effect

Based on the equation satisfied by optical pulse that is a slowly varying function, the higher-order nonlinear Schr o¨dinger equation(NLSE) including Raman gain and self-steepening effect is deduced in detail, and a new Raman gain function is defined. By using the split-step Fourier method, the influence of the combined effect between Raman gain and self-steepening on the propagation characteristic of dark solitons is simulated in the isotropic fiber. The results show that gray solitons can be symmetrically formed by high order dark soliton, however self-steepening effect will inhibit the formation mechanism through the phenomenon that gray solitons are produced only in the trailing edge of the central black soliton. Meanwhile, the Raman gain changes the propagation characteristic of optical soliton and inhibits the self-steepening effect, resulting in the broadening of pulse width and the decreasing of pulse offset.