The theory of optical communication lines with a short-scale dispersion management

We investigate, theoretically and numerically, properties of dispersion-managed (DM) solitons in fiber lines with the dispersion compensation period L much shorter than the amplification distance Z _a. We present the path-averaged theory of DM transmission lines with a short-scale management in the case of asymmetric maps. Applying a quasi-identical transformation, we demonstrate that the path-averaged dynamics in such systems can be described by an integrable model in some limits.     

Instability of dispersion-managed solitons in a system with filtering

Unstable behavior of dispersion-managed (DM) solitons in a system with lumped filtering is numerically studied. A variational analysis shows that the system cannot have stable fixed DM soliton solutions when the filter location is improperly chosen. This is because of the unique dynamics of the spectral behavior of DM solitons, which differs from that of standard solitons in fibers with constant dispersion. The instability is confirmed by numerical simulations with and without sliding center frequencies of the filters.     

Soliton formation in hollow-core photonic bandgap fibers

The formation of solitons upon compression of linearly chirped pulses in hollow-core photonic bandgap fibers is investigated numerically. The dependence of soliton duration on the chirp and power of the input pulse and on the dispersion slope of the fiber is investigated, and the validity of an approximate scaling relation is tested. It is concluded that compression of input pulses of several ps duration and sub-MW peak power can lead to a formation of solitons with ∼100 fs duration and multi-megawatt peak powers. The dispersion slope of realistic hollow-core fibers appears to be the main obstacle for forming still shorter solitons.     

Dispersion management for randomly varying optical fibers

An asymptotic theory for optical pulse propagation in a dispersion-managed (DM) fiber with random dispersion is presented. The validity of the theory is verified with direct numerical simulation. The equations that describe the slow evolution of initial pulses have special solutions that, for fibers with moderate noise in the dispersion profile, perform much better than ideal DM solitons optimized for the unperturbed fiber.     

Soliton stability against polarization-mode-dispersion in dispersion-managed systems

We study the dynamics of two-component solitons in a dispersion-managed (DM) system, built as a periodic concatenation of segments of optical fibers with anomalous and normal group-velocity dispersion (GVD). The model includes, in addition to the usual GVD and nonlinear terms, birefringence and polarization-mode-dispersion (PMD), in the form of the polarization scrambling (random rotation of the polarization) taking place at randomly distributed defects. We propose a numerical algorithm for finding optimized DM solitons in such a system, which secure stable transmission over a large distance. The analysis includes effects of the PMD-induced noise, together with the noise due to the spontaneous amplifier emission, and the input-source noise. It is concluded that, if the group-velocity birefringence is not excessively large, the use of the optimized solitons makes it possible to tolerate the PMD effects in the long-haul DM link.     

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described.     

Short optical solitons in fibers

The dynamics of short (of the order of a few wave periods) intense optical pulses and interaction of short optical solitons in fibers are considered within the framework of the third-order nonlinear Schrodinger equation. It is shown that an initial pulse tends to one or a few short solitons plus a linear quasiperiodic wave when the third-order linear dispersion and nonlinear dispersion have parameters of the same sign. The number and parameters of the solitons depend on the magnitudes of initial pulse parameters. Interaction of short optical solitons having different amplitudes is accompanied by radiation of part of the wave field from the area of interaction, by an increase of the soliton with larger amplitude, and a decrease of the soliton with a smaller one. (c) 2000 American Institute of Physics.     

Stability of temporal solitons in uniform and “managed” quadratic nonlinear media with opposite group-velocity dispersions at fundamental and second harmonics

The problem of the stability of solitons in second-harmonic-generating media with normal group-velocity dispersion (GVD) in the second-harmonic (SH) field, which is generic to available χ⁽²⁾ materials, is revisited. Using an iterative numerical scheme to construct stationary soliton solutions, and direct simulations to test their stability, we identify a full soliton-stability range in the space of the system’s parameters, including the coefficient of the group-velocity-mismatch (GVM). The soliton stability is limited by an abrupt onset of growth of tails in the SH component, the relevant stability region being defined as that in which the energy loss to the tail generation is negligible under experimentally relevant conditions. We demonstrate that the stability domain can be readily expanded with the help of two “management” techniques (spatially periodic compensation of destabilizing effects) - the dispersion management (DM) and GVM management. In comparison with their counterparts in optical fibers, DM solitons in the χ⁽²⁾ medium feature very weak intrinsic oscillations.     

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

We report results of the study of solitons in a system of two nonlinear-Schrödinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective “management” scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.     

Analysis of enhanced-power solitons in dispersion-managed optical fibers

We analyze pulse propagation in an optical fiber employing a periodic dispersion map. Second-order averaging is used to determine a general evolution equation valid for both return-to-zero and non-return-to-zero pulses in dispersion-managed systems. The equation is then applied to the case of solitons, and an analytic expression for the power enhancement arising from the dispersion management is obtained.     

飞秒啁啾孤子在线性色散平坦光纤中的相互作用

采用分步傅里叶方法数值研究了在线性色散平坦光纤反常色散区等幅同相孤子脉冲相互作用受高阶色散、拉曼效应、光纤损耗和啁啾参量C等的影响规律。多孤子脉冲在线性和凸形色散平坦光纤中传输100个孤子周期后仍具有孤子特性。在线性色散平坦光纤,多孤子脉冲相互作用受三阶色散影响较严重,三阶色散使各脉冲产生较大的色散波和线性时延;更高阶色散的影响可以忽略;拉曼效应使脉冲产生较大的非线性时延;啁啾加强了脉冲间相互作用;光纤损耗减弱了脉冲间相互作用。     

Subpicosecond pulse compression in nonlinear photonic crystal waveguides based on the formation of high-order optical solitons

We investigate by numerical simulation the compression of subpicosecond pulses in two-dimensional nonlinear photonic crystal (PC) waveguides. The compression originates from the generation of high-order optical solitons through the interplay of the huge group-velocity dispersion and the enhanced self-phase modulation in nonlinear PC waveguides.Both the formation of Bragg grating solitons and gap solitons can lead to efficient pulse compression. The compression factors under different excitation power densities and the optimum length for subpicosecond pulse compression have been determined. As a compressor, the total length of the nonlinear PC waveguide is only ten micrometres and therefore can be easily incorporated into PC integrated circuits.     

Generation of domain-wall solitons in an anomalous dispersion fiber ring laser

We report experimental observations performed using a net anomalous dispersion Er-doped fiber ring laser without polarization-selective elements, highlighting the domain-wall solitary pulses generated under the incoherent polarization coupling. By adjusting the pump power and the polarization state appropriately, bright and dark solitons can stably co-exist in the cavity, both centered at 1562.16 nm with a 3-dB spectral width of ～ 0.15 nm and a repetition rate of 3.83 MHz. Moreover, the 0.8 mm long thulium-doped fiber (TDF) facilitated the mode-locking and self-starting of the laser. This is the first demonstration of a laser being used to generate bright and dark solitons synchronously while using TDF as the saturable absorber (SA). Except possessing the all-fiber structure, the laser exhibits good stability, which may have a significant influence on improvement of the pulse-laser design, and may broaden practical applications in optical sensing, optical communication, and soliton multiplexed systems.     

光纤中基于拉曼放大与脉冲压缩的超短光孤子产生

提出一种在单模光纤负群速色散枢由弱脉冲产生高强度超短光孤子的新方法。     

Dispersion-managed solitons in fibre systems and lasers

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a variety of physical problems and engineering applications. The mathematical concept of dispersion managed solitons already has made an impact on the development of fibre communications, optical signal processing and laser science. We overview here the field of the dispersion managed solitons starting from mathematical theories of Hamiltonian and dissipative systems and then discuss recent advances in practical implementation of this concept in fibre-optics and lasers.     

色散补偿光纤通信系统中孤子之间的相互作用

采用变分原理与位力定理研究了非线性光通信系统色散补偿方案中,相邻孤子之间的相互作用对孤子传输特性的影响。结果表明:在相位匹配与等幅孤子注入时,在普通单模光纤中这两个孤子先相互吸引,而后又相互排斥,显现周期性碰撞的变化规律,形成束缚孤子态,而在色散补偿光纤中传输的孤子之间不发生碰撞;对相位不匹配与等幅孤子注入,孤子之间发生分离;对相位匹配和不等幅孤子注入,在色散补偿光纤中传输的孤子,如果初始间隔φ0越小,应注入较大的初始幅值差η0,以利于孤子的传输。     

非均匀光纤中暗孤子传输特性研究

由于变系数非线性Schrödinger方程的增益、色散和非线性项都是变化的, 根据方程这一特点可以研究光脉冲在非均匀光纤中的传输特性. 本文利用Hirota方法, 得到非线性Schrödinger方程的解析暗孤子解. 然后根据暗孤子解对暗孤子的传输特性进行讨论, 并且分析各个物理参量对暗孤子传输的影响. 经研究发现, 通过调节光纤的损耗、色散和非线性效应都能有效的控制暗孤子的传输, 从而提高非均匀光纤中的光脉冲传输质量. 此外, 本文还得到了所求解方程的解析双暗孤子解, 最后对两个暗孤子相互作用进行了探讨. 本文得到的结论有利于研究非均匀光纤中的孤子控制技术.     

A scheme for pre-shaping of dispersion-managed solitons

We demonstrate efficacy of shaping Gaussian pulses into dispersion-managed (DM) solitons by dint of a device which includes two fibers with the same group-velocity-dispersion (GVD) coefficients as in the DM system, a frequency-domain filter, and an amplifier. The shaping of a given input pulse is optimized by adjusting values of four free parameters of the cell, viz., lengths of the two fibers, filtering coefficient, and amplification gain, with the objective to achieve the best fit of the transformed pulse to the (numerically found) DM soliton, including systems with the third-order GVD, and with three-step DM maps. Launching reshaped pulses into the DM system, we demonstrate, in direct simulations, their complete stability over indefinitely long propagation distances. We examine sensitivity of the reshaping to deviations of the control parameters from their optimum values, a noteworthy results being very weak dependence on variations of the filtering strength. The dependence of the four control parameters on the width and chirp of the Gaussian input signal is also studied in detail.     

在远离光子晶体光纤零色散波长的正常色散区入射飞秒脉冲产生四波混频及孤子效应的实验研究

在远离光子晶体光纤零色散波长的正常色散区入射飞秒脉冲,实验产生了一对由四波混频引起的信号波带和闲频波带,及一对由脉冲内拉曼散射和非孤子辐射引起的孤子和色散波带,并观察到功率饱和现象.利用有限元法理论模拟了光纤的色散和非线性特性,用四波混频的相位匹配条件模拟了光纤在满足相位匹配条件下所产生的信号波带和闲频波带出现的可能位置,并与实验结果符合得很好.结果表明:即使在光子晶体光纤的正常色散区抽运激光脉冲亦可以产生四波混频和孤子效应;研究发现四波混频的产生是由四阶色散参量引起的;并进一步从理论上解释了孤子及色散波的产生原因.     

Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion

We determine the power dependence of dispersion-managed solitons on map strength and average dispersion, using a combination of numerical simulations and the variational approach. In particular, we investigate the behavior near zero dispersion and identify the region of existence of dispersion-managed solitons in the average normal-dispersion regime.