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Generation of dark solitons in erbium-doped fiber laser based on black phosphorus nanoparticles
摘要： We demonstrate the generation of dark solitons (DSs) in erbium-doped fiber (EDF) laser based on black phosphorus nanoparticles (BPNPs) for the first time. The side-polished fiber deposited with BPNPs is embedded into the laser to enhance the birefringence and nonlinearity of the laser cavity. In the paper, the saturable absorption property of BPNPs with an optical modulation depth of 5.7% and a saturable intensity of 21.7 MW/cm2 are experimentally illustrated. After inserting the BPNPs saturable absorber (SA) into EDF laser, the DSs with repetition rate of 14.68 MHz are obtained at a pump power of 90 mW. Our results prove that the BPNPs are the promising candidate materials for generating DSs in EDF laser.
关键词： Side-polished fiber,Dark solitons,Black phosphorus nanoparticles
更新于2025-11-28 14:24:03
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Darka??dark and brighta??dark solitons for a (2+1)-dimensional variable-coefficient nonlinear Schr??dinger system in a graded-index waveguide
摘要： In this letter, we study a (2 + 1)-dimensional variable-coefficient nonlinear Schr?dinger system, which describes an optical beam inside the two-dimensional graded-index waveguide with polarization effects. Through the Kadomtsev–Petviashvili hierarchy reduction, the N dark–dark soliton and N bright-dark soliton solutions in terms of the Gramian are obtained, where N is a positive integer. We analyze the interaction and propagation of the dark–dark solitons graphically. With the different values of the diffraction coefficient β(t), periodic-, cubic- and parabolic-shaped dark–dark solitons are derived. With the different values of the gain/loss coefficient γ(t), periodic- and arctangent-profile background waves are obtained. Moreover, we discuss the effects from the dimensionless beam width w(t), β(t) and γ(t) on the solitons and background waves: Shapes of the solitons are affected by w(t) and β(t), while profiles of the background waves are affected by w(t) and γ(t).
关键词： (2 + 1)-dimensional variable-coefficient nonlinear Schr?dinger system,bright–dark solitons,graded-index waveguide,dark–dark solitons,Kadomtsev–Petviashvili hierarchy reduction
更新于2025-09-23 15:19:57
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Bright–dark soliton dynamics and interaction for the variable coefficient three-coupled nonlinear Schr?dinger equations
摘要： Under investigation in this paper is the variable coefficient three-coupled nonlinear Schr?dinger (CNLS) equations, which govern the dynamics of solitonic excitations along three-spine α-helical protein with inhomogeneous effect. Via the Hirota method and symbolic computation, the exact two-bright-one-dark (TBD) and one-bright-two-dark (BTD) soliton solutions are constructed analytically. The propagation properties are discussed for TBD and BTD solitons when the variable coefficient is a hyperbolic secant function. Figures are plotted to reveal the following interactions of TBD and BTD two solitons: (1) Evolution without interactions of double-parabola-shaped solitons, of double-S-shaped solitons and of parabola-S-shaped solitons; (2) Evolution with periodic interaction of double-parabola-shaped solitons and of parabola-S-shaped solitons; (3) Collision of double-S-shaped solitons and of parabola-S-shaped solitons.
关键词： bright–dark solitons,Hirota bilinear method.,interaction,Three-coupled variable-coefficient nonlinear Schr?dinger equations
更新于2025-09-16 10:30:52
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Bright-dark solitons for a coupled nonlinear Schr?dinger system with variable coefficients in an inhomogeneous optical fiber
摘要： Optical fiber communication becomes one of the main pillars of modern communication. In this paper, we study a coupled nonlinear schr¨odinger system with variable coefficients, which can describe the simultaneous propagation of the M-field components in an inhomogeneous optical fiber, where M is a positive integer. When M=2, the N-bright-dark soliton solutions in terms of the Grammian can be obtained via the Kadomtsev-Petviashvili hierarchy reduction, where N is a positive integer. With the asymptotic analysis and graphic analysis, we find that the amplitudes of one-bright-dark solitons and the background in the dark components exhibit the periodic oscillations. Without the amplification/absorption effect, elastic interaction between the two-bright-dark solitons which keep both the amplitudes and the wave backgrounds invariant is demonstrated. Particularly, we find inelastic interaction between the two-bright-dark solitons, which possess the V-shape profiles in the zero background components and the Y-shape profiles in the periodic oscillating background components. The bound-state soliton under that inelastic condition is also shown. Besides, we present the bound-state bright-dark solitons with varying amplitudes. Furthermore, the analysis of the N-bright-dark soliton solutions are extended to those with M>2, and as an example, inelastic interaction of the solitons with the case of M=4 is presented.
关键词： Kadomtsev-Petviashvili hierarchy reduction,bright-dark solitons,Coupled nonlinear Schr¨odinger system with variable coefficients,an inhomogeneous optical fiber
更新于2025-09-16 10:30:52
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Interactions between M-typed dark solitons in nonlinear optics
摘要： Solitons are used in such field as nonlinear optics. In this manuscript, interactions between M-typed dark solitons are investigated analytically in the decreasing dispersion fiber. With symbolic computation, interactions between them are simulated via the analytic two-soliton solution. Relevant interaction characteristics of them are analyzed. Method of weakening soliton interaction is suggested.
关键词： Analytic solution,Dark solitons,Nonlinear optics,Decreasing dispersion fiber
更新于2025-09-16 10:30:52
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Nonlinear Fiber Optics || Optical solitons
摘要： A fascinating manifestation of the fiber nonlinearity occurs through optical solitons, formed as a result of the interplay between the dispersive and nonlinear effects. The word soliton refers to special kinds of wave packets that can propagate undistorted over long distances. Solitons have been discovered in many branches of physics. This chapter focuses on pulse propagation inside optical fibers in the regime in which both the group-velocity dispersion (GVD) and self-phase modulation (SPM) are equally important and must be considered simultaneously. It is organized as follows. Section 5.1 considers the phenomenon of modulation instability and shows that propagation of a continuous-wave (CW) beam inside optical fibers is inherently unstable and may convert the CW beam into pulse train under appropriate conditions. The inverse-scattering method is discussed in Section 5.2 together with the soliton solutions. The properties of the fundamental and higher-order solitons are also discussed in this section. Section 5.3 is devoted to other kinds of solitons, with emphasis on dark solitons. Section 5.4 considers the effects of external perturbations on solitons. Perturbations discussed include fiber losses, amplification of solitons, and noise introduced by optical amplifiers. Higher-order nonlinear effects such as self-steepening and intrapulse Raman scattering are the focus of Sections 5.5 and 5.6.
关键词： modulation instability,optical amplifiers,dark solitons,intrapulse Raman scattering,inverse-scattering method,self-steepening,group-velocity dispersion,fiber nonlinearity,self-phase modulation,fiber losses,optical solitons
更新于2025-09-12 10:27:22
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Bilinear Forms and Dark-Dark Solitons for the Coupled Cubic-Quintic Nonlinear Schr?dinger Equations with Variable Coefficients in a Twin-Core Optical Fiber or Non-Kerr Medium
摘要： Twin-core optical ?bers are applied in such ?elds as the optical sensing and optical communication, and propagation of the pulses, Gauss beams and laser beams in the non-Kerr media is reported. Studied in this paper are the coupled cubic-quintic nonlinear Schr¨odinger equations with variable coe?cients, which describe the e?ects of quintic nonlinearity for the ultrashort optical pulse propagation in a twin-core optical ?ber or non-Kerr medium. Based on the integrable conditions, bilinear forms are derived, and dark-dark soliton solutions can be constructed in terms of the Gramian via the Kadomtsev-Petviashvili hierarchy reduction. Propagation and interaction of the dark-dark solitons are presented and discussed through the graphic analysis. With di?erent values of the delayed nonlinear response e?ect b(z), where z represents direction of the propagation, the linear- and parabolic-shaped one dark-dark soltions can be derived. Interactions between the parabolic- and periodic-shaped two dark-dark solitons are presented with b(z) as the linear and periodic functions, respectively. Directions of velocities of the two dark-dark solitons vary with z and the amplitudes of the solitons remain unchanged can be observed. Interactions between the two dark-dark solitons of di?erent types are displayed, and we observe that the velocity of one soliton is zero and direction of the velocity of the other soliton vary with z. We ?nd that those interactions are elastic.
关键词： Kadomtsev-Petviashvili hierarchy reduction,coupled cubic-quintic nonlinear Schr¨odinger equations,optical ?ber,dark-dark solitons
更新于2025-09-12 10:27:22