A collective variable approach for optical solitons in the cubic-quintic complex Ginzburg-Landau equation with third-order dispersion

Considering the theory of electromagnetic, especially from the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fibers is derived, namely a cubic-quintic complex Ginzburg-Landau equation (CQGLE) with third-order dispersion (TOD). Considering this one-dimensional CQGLE, we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance. A fully numerical simulation of the CQGLE finally tests the results of the CV theory. It appears chaotic pulses, attenuate pulses and stable pulses under some parameter values.     

在光纤零群速色散区传输的光孤子波

通过对超短光脉冲在单模光纤中传输方程的分析研究,给出了在零群速色散传输方程的亮,反波解。结果表明,超短光脉中在光纤的零群群速色散仍能以亮,暗孤波的形式传输,且不存在孤子自频移现象。     

Influence of nonlinear dispersion on modulation instability of coherent and partially coherent ultrashort pulses in metamaterials

The combination of dispersive magnetic permeability with nonlinear polarization leads to a series of nonlinear dispersion terms in the propagation equations for ultrashort pulses in metamaterials. Here we present an investigation of modulation instability (MI) of both coherent and partially coherent ultrashort pulses in metamaterials to identify the role of nonlinear dispersion in pulse propagation. The Wigner–Moyal equation for partially coherent ultrashort pulses and the nonlinear dispersion relation for MI in metamaterials are derived. Combining the standard MI theory with the unique properties of the metamaterial, the influence of the controllable first-order nonlinear dispersion, namely self-steepening, and the second-order nonlinear dispersion on both coherent and partially coherent MI, in both negative-index and positive-index regions of the metamaterial for all physically possible cases is analyzed in detail. For the first time to our knowledge, we demonstrate that the role of the second-order nonlinear dispersion in MI is equivalent to that of group-velocity dispersion (GVD) to some extent, and thus due to the role of the second-order nonlinear dispersion, MI may appear in the otherwise impossible cases, such as in the normal GVD regime. PACS 42.25.Kb; 42.65.Sf; 78.20.Ci     

Localization of optical pulses in guided wave structures with only fourth order dispersion

Inspired by the recent realization of pure-quartic solitons (Blanco-Redondo et al. (2016) [1]), in the present work we study the localization of optical pulses in a similar system, i.e., a silicon photonic crystal air-suspended structure with a hexagonal lattice. The propagation of ultrashort pulses in such a system is well described by a generalized nonlinear Schrödinger (NLS) equation, which in certain conditions works with near-zero group-velocity dispersion and third order dispersion. In this case, the NLS equation has only the fourth order dispersion term. In the present model, we introduce a quasiperiodic linear coefficient that is responsible to induce the localization. The existence of Anderson localization has been confirmed by numerical simulations even when the system presents a small defocusing nonlinearity.     

Tuning the frequency of ultrashort laser pulses by a cross-phase-modulation-induced shift in a photonic crystal fiber

Femtosecond pulses of fundamental Cr:forsterite laser radiation are used as a pump field to tune the frequency of copropagating second-harmonic pulses of the same laser through cross-phase modulation in a photonic crystal fiber. Sub-100-kW femtosecond pump pulses coupled into a photonic crystal fiber with an appropriate dispersion profile can shift the central frequency of the probe field by more than 100 nm, suggesting a convenient way to control propagation and spectral transformations of ultrashort laser pulses.     

Influence of the polarization mode dispersion on the propagation of ultrashort optical pulses in single-mode fiber lightguides with very weak linear birefringence and random inhomogeneities

We consider the influence of the polarization mode dispersion, which is stipulated by the presence of random inhomogeneities in single-mode fiber lightguides, on the propagation of ultrashort optical pulses in the fiber communication lines with very weak linear birefringence. Evolution of the envelope of ultrashort optical pulses and their spectra as functions of the length of a single-mode fiber lightguide with very weak linear birefringence and random inhomogeneities are obtained by the method of mathematical simulation. An increase in the pulse duration is shown to be proportional to the square root of the length of a single-mode fiber lightguide. The numerical-simulation results are compared with the results of experimental measurements of the polarization mode dispersion.     

Propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber

We analyze the propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber (PCF) by solving a pair of coupled-mode equations that include all the significant linear and nonlinear terms. In particular, we highlight the fact that the coupling coefficient dispersion can cause significant pulse distortion over a short length of a two-core PCF. We also study all-optical switching and multi-frequency generation and obtain a reasonable agreement with recent experimental data.     

负曲率空芯光纤对飞秒超短脉冲光的压缩研究

为了实现对飞秒激光器产生的超短脉冲的进一步压缩,对近年来出现的一种新型负曲率空芯光纤展开了研究,并基于该光纤对800 nm飞秒激光进行了压缩实验。首先介绍了一种圆形玻璃管包层结构的负曲率空芯光纤,通过有限元方法对光纤的损耗特性进行计算,并与实验测试结果进行对比。然后利用广义非线性薛定谔方程对脉冲在光纤中的传输进行了模拟仿真。最后利用该光纤进行了超短脉冲压缩实验,将脉冲宽度为160 fs的钛宝石飞秒激光耦合进一段充高压氩气的圆形玻璃管包层结构的负曲率空芯光纤,通过光纤内反常色散和自相位调制的共同作用,得到84 fs的输出,实现脉冲的压缩,实验结果与仿真计算一致。这种新型的负曲率空芯光纤损伤阈值高、色散、非线性系数小且灵活可调,非常适用于超快领域研究。     

Blue light and infrared continuum generation by soliton fission in a microstructured fiber

The nonlinear propagation of ultrashort pulses in a microstructured fiber is experimentally investigated. By working around 800 nm, in the anomalous dispersion region, clear evidence of pulse break-up and soliton propagation is obtained. This is consistent with the recently suggested mechanism of spectral broadening based upon the fission of higher order solitons into red-shifted fundamental solitons and blue-shifted dispersion waves. When 190-fs pulses at high input intensities are used, the output spectrum is made of a broad infrared supercontinuum coexisting with a sharp and very intense blue peak that takes up to 24% of the input power. We tentatively propose an explanation of this effect by invoking pulse-trapping phenomena controlled by the group-velocity matching of infrared and visible pulses. PACS 42.65.Tg; 42.81.Dp     

Breathers and Rogue Waves Derived from an Extended Multi-dimensional N-Coupled Higher-Order Nonlinear Schrödinger Equation in Optical Communication Systems

In this paper, an extended multi-dimensional N-coupled higher-order nonlinear Schrödinger equation (NCHNLSE), which can describe the propagation of the ultrashort pulses in wavelength division multiplexing (WDM) systems, is investigated. By the bilinear method, we construct the breather solutions for the extended (1+1), (2+1) and (3+1)-dimensional N-CHNLSE. The rogue waves are derived as a limiting form of breathers with the aid of symbolic computation. The effect of group velocity dispersion (GVD), third-order dispersion (TOD) and nonlinearity on breathers and rogue waves solutions are discussed in the optical communication systems.     

Combined optical solitary waves of the Fokas—Lenells equation

In this work, we investigate the Fokas–Lenells equation describing the propagation of ultrashort pulses in optical fibers when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrö dinger equation are retained. In addition to group velocity dispersion and Kerr nonlinearity, the model involves both spatio-temporal dispersion and self-steepening terms. A class of exact combined solitary wave solutions of this equation is constructed for the first time, by adopting the complex envelope function ansatz. The influences of spatio-temporal dispersion on the characteristics of combined solitary waves is also discussed.     

Kagome光纤超快非线性光学研究进展

Kagome光纤(简称KGF)是一种不依赖带隙导光的新型空芯微结构光纤,其结构设计灵活、损伤阈值高、损耗低(高透区损耗可低至~40 dB/km)、支持宽带传输(&;amp;lt;500 nm),并可通过纤芯改变所充气体及调节气压实现光纤色散、非线性效应的有效调制,在强场物理、超快激光技术等领域研究中优势突出。基于KGF在超快光学中的重要意义,该文对近年来国际上关于KGF在非线性光学变频及超短脉冲压缩等领域的研究成果进行介绍,并对关键性应用技术进行简要分析,最后对其发展前景进行展望。     

Ultrashort optical pulses in carbon nanotubes and graphene with periodic impurities

The dispersion law for electrons has been derived by the Green’s function method using the Anderson periodic model, which has been proposed to describe the electron subsystem in carbon nanotubes and graphene with impurities. The combined dynamics of electrons and an electromagnetic field has been considered in the low-temperature limit, and the effective equation describing the propagation of ultrashort optical pulses has been obtained. The solutions to this equation as functions of the parameters of the problem have been presented.     

Modulational instability and space-time dynamics in nonlinear parabolic-index optical fibers

Beam propagation in multimode graded-index parabolic optical fibers in the presence of group-velocity dispersion and Kerr nonlinearity is theoretically investigated. It is shown that a modulational instability arising from the periodic spatial focusing of the beam takes place regardless of the sign of fiber dispersion, leading to a highly nonlinear space-time dynamics and the generation of ultrashort optical pulses.     

Role of dispersion in multiple-collapse dynamics

The multiple-collapse dynamics of ultrashort pulses along the propagation direction are investigated under conditions of both normal and anomalous group-velocity dispersion (GVD). In the anomalous-GVD regime we find that collapse events can occur at locations in the medium many diffraction lengths beyond the initial collapse point, in contrast with the normal-GVD regime in which multiple collapse occurs within a diffraction length. Numerical simulations of a modified nonlinear envelope equation are found to be in good qualitative agreement with the observed lengths of the filaments.     

Soliton self-frequency shift decelerated by self-steepening

Self-steepening of ultrashort light pulses is shown to reduce the soliton self-frequency shift (SSFS) induced by the Raman effect in an optical fiber. We derive an analytical expression for the SSFS that conserves the number of photons and allows the SSFS to be calculated for arbitrary frequency profiles of fiber dispersion and Raman gain without a numerical solution of the pulse evolution equation. The accuracy of this analytical approach to SSFS calculation is tested by numerical simulations based on the generalized nonlinear Schr?dinger equation.     

Numerical Analysis of Induced Phase Modulation between Two Ultrashort Pulses in Silica Fiber by the Extended Finite-Difference Time-Domain Method

We have analyzed the induced phase modulation (IPM) for ultrashort (74 fs) two-pulse propagation in a silica fiber by the extended finite-difference time-domain (FDTD) method, considering all exact Sellmeier-fitting values and nonlinear polarization P_NL involving the Raman response function. We show that nonlinear polarization causes several phenomena in spectral characteristics of propagated pulses, such as self-phase modulation (SPM), self-steepening, Raman response and IPM, by the extended FDTD method. To the best of our knowledge, this is the first IPM calculation by the extended FDTD method for the simultaneous propagation of two ultrashort (74 fs) laser pulses in a silica fiber.     

Generation of long broadband pulses with a figure-eight fiber laser

In this paper we performed the experimental and numerical study of a passively mode-locked fiber laser that generates packets of sub-picosecond pulses instead of individual pulses. The proposed configuration is a figure-eight fiber laser scheme, which includes a Nonlinear Optical Loop Mirror with polarization asymmetry inserted into a ring cavity. No experimental evidence of self-starting mode locking operation of the laser was observed; however, for proper adjustments of the wave retarders included in the setup, a mechanical stimulation triggers the onset of mode locking. The autocorrelation of the generated pulses shows a narrow sub-picosecond peak riding a large sub-nanosecond pedestal whose intensity is half that of the peak, and the optical spectrum is smooth and wide. We show that contrary to conventional ultrashort pulses, these pulses do not vanish rapidly after propagation through a long dispersive fiber, which makes then attractive for super-continuum generation as well as for applications in metrology. Finally, we study the pulse formation in the laser and present arguments based on experimental data and numerical simulations that the observed pulses are actually sets of a large number of solitons.