Propagation of ultrafast pulses in the anomalous-dispersion regime of silicon-on-insulator strip nanowaveguides

The dynamic evolution of ultrafast high-intensity pulses with a 100 fs half-width at 1/e intensity point based on the silicon-on-insulator (SOI) strip nanowaveguides is considered and investigated numerically under the condition of anomalous group-velocity dispersion (GVD) regime. For ultrafast high-intensity pulses propagating in millimeter-long SOI nanowaveguides, the interplay between the dispersion and nonlinear effects such as the two-photon absorption, free-carrier absorption, free-carrier dispersion, and self-phase modulation has to be taken into account, which results in the significant optical wave breaking phenomenon that occurs near the pulse leading edge for an unchirped Gaussian pulse in the anomalous GVD regime. However, when the input Gaussian pulse with linear up-chirp is introduced, the position of the optical wave breaking shifts from the leading pulse edge to its trailing edge along the several millimeters-long SOI nanowaveguides.     

Solitary waves, steepening and initial collapse in the Maxwell–Lorentz system

We present a numerical study of Maxwell’s equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion relation reveals various asymptotic regimes such as Schrödinger and KdV branches. Existence of soliton-type solutions in the Schrödinger regime and light bullets containing few optical cycles together with dark solitons are illustrated numerically. Envelope collapse regimes of the Schrödinger equation are compared to the full system and an arrest mechanism is clearly identified when the spectral width of the initial pulse broadens beyond the applicability of the asymptotic behavior. We show that beyond a certain threshold the carrier wave steepens into an infinite gradient similarly to the canonical Majda–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities.     

Dispersion characteristics of coupled-resonator optical waveguides

A tight-binding optical waveguide formed by proximity coupling of nearest-neighbor resonators, e.g., a coupled-resonator optical waveguide (CROW), has distinct wave and pulse propagation characteristics compared with a conventional waveguide, and several applications in photonic devices have been proposed recently. But analysis of the dispersion, and in particular the group-velocity dispersion, in such a waveguide requires particular attention: the waveguide displays two distinct regimes of operation, depending on the position of the wave packet in the dispersion relationship.     

Derivation of a wave equation for pulse propagation beyond a slowly varying envelope approximation

An iterative method is used to derive an accurate weve equation that governs ultrashort pulse propagation in a single mode fibre. In the derivation, the slowly varying evelope approximation (SVEA) is not required. Therefore, the wave equation can be used to describe the propagation of an ultrashort pulse of a few optical cycles. It is found that, compared with the wave equation obtained by making an SVEA, an accurate wave equation has the same coefficients of the linear dispersion terms and different coefficients of the high-order time derivatives of the non-linear terms.     

Dark-in-the-Bright solitary wave solution of higher-order nonlinear Schrödinger equation with non-Kerr terms

We present new type of Dark-in-the-Bright solution also called dipole soliton for the higher order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and subject to constraint relation among the parameters in optical context. This equation could be a model equation of pulse propagation beyond ultrashort range in optical communication systems. The solitary wave solution is composed of the product of bright and dark solitary waves. This type of pulse shape to be formed both the group velocity dispersion and third-order dispersion must be compensated. We also investigated the stability of the solitary wave solution under some initial perturbation on the parametric conditions. We have shown that the shape of pulse remains unchanged up to 20 normalized lengths even under some very small violation in parametric conditions.     

Passive nonlinear reshaping towards parabolic pulses in the steady-state regime in optical fibers

The passive nonlinear reshaping in normally dispersive optical fibers in the steady-state regime is studied numerically. It is found that normal dispersion and self-phase modulation are able to provide pulse reshaping towards a parabolic pulse profile at the distances exceeding the optical wave breaking length. However, as compared to the similariton formation in active fibers the resulted pulse shape in passive fibers is strongly depended on the initial pulse parameters and nonlinear and dispersive fiber properties as well. The influence of initial pulse shape, initial chirp, third-order dispersion and loss on the parabolic pulse formation is studied consistently, and estimation of practical conditions which are needed for parabolic pulses formation in a passive fiber is provided.     

具有几个光振荡周期长度的飞秒激光脉冲在线性色散介质中的传输

给出了描写具有几个光振荡周期长度的飞秒激光脉冲在线性色散介质中传输方程的解。对脉冲的传输特性进行了数值摸拟 ,分别考察了来源于电子和晶格的正常和反常群速色散对脉冲展宽和脉冲形状畸变的影响。     

Optical fibre-grating pulse compression

Numerical simulation is used to consider non-linear pulse propagation in fibres and subsequent pulse compression in a dispersive delay line. It is shown that for small initial pulse powers the conventional non-linear Schrödinger equation (NSE) is quite accurate to describe the process of pulse propagation in fibres. In this case initially symmetrical pulses undergo squaring and spectral broadening in fibres, and frequency chirp is linearized over most of the pulse, while shapes of the pulse, spectrum and frequency chirp remain symmetrical at the output of the fibre. There is a certain optimum fibre lengthZ _opt which is determined by the initial pulse parameters and fibre characteristics for pulse compression in the dispersive delay line. When the fibre lengthZ>Z _opt the optical wave breaking effect distorts the linearity of the frequency chirp and thus deteriorates the quality of the compressed pulse. The region of NSE approximation accuracy is determined. It is demonstrated that at increase of the initial pulse power (initial pulse width makes no difference) the NSE approximation becomes inaccurate. So the pulse dynamics in the fibre were described by the modified NSE derived in the higher-order approximation of the method of slowly varying amplitudes from Maxwell's equations. In this case the shock wave appears at the trailing edge of the pulse, which accelerates the wave breaking process. This results in a decrease of the optimum fibre length and deterioration of compressed pulse parameters, compared with the NSE case. Spectral windowing of the extreme Stokes components of the pulse spectrum permits significant improvement in the quality of the compressed pulse. The main features of the compression of pulses with asymmetrical initial shape are also considered.     

Distortion of parabolic pulse due to higher-order effects in a dispersion-decreasing fiber

Considering Third-order Dispersion (TOD) and Stimulated Raman Scattering effect (SRS) simultaneously, the properties of the self-similar parabolic pulse evolution in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. Our results show that parabolic pulses are distorted and the characteristic of exactly self-similarity will be lost due to the High-order effects. When only the TOD is taken into account, the chirp still reveals highly linear but glows into asymmetric which causes the waveform appearing optical wave breaking. When only considering SRS, the pulse still reveals highly linear chirp only linearity range narrow down, resulting in delaying the self-similar evolution. When considering SRS and TOD simultaneously, parabolic pulses are distorted less and the characteristic of exactly self-similarity will be better due to SRS effect than only considering TOD effect. The highly linear chirp in optical pulse still allows for efficient and high-quality pulse compression by use of dispersion compensation technique.     

Evolution of hyperbolic-secant optical pulses towards wave breaking in quintic nonlinear fibers

Evolutions of the frequency chirps, shapes, and spectra of initial hyperbolic-secant pulses towards wave breaking are numerically investigated in the normal dispersion regimes of optical fibers with quintic nonlinearity and the developing chirps and the characteristic distances of wave breaking are analytically processed approximately. The results show that quite different mathematical expressions from those of initial Gaussian pulses are obtained. Moreover, the wave breaking here will be more intense for more oscillation peaks will appear in the pulse wings and the breaking process will last longer distance before rectangle-shaped pulses form at last. However, the quintic nonlinearity plays a similar role to the case of initial Gaussian pulses in developing chirps and bringing forward or retarding the wave breaking. The wave breaking distance will also decrease with increase of the quintic nonlinearity and the soliton order.     

双折射光纤中拉曼效应对参量放大增益谱的影响

根据激光脉冲在光纤中传输时, 所满足的波动方程, 导出了拉曼效应和参量放大共同作用下, 在双折射光纤中所遵循的耦合模方程, 并引入平行拉曼增益的洛伦兹模型, 给出了输入抽运波偏振方向同双折射轴成45^o 时, 拉曼效应和参量放大共同作用所导致的增益. 讨论并分析了拉曼效应在不同色散区对参量放大增益谱的影响. 结果表明, 在考虑拉曼效应后, 使得参量放大斯托克斯波与反斯托克斯波增益谱彼此不对称; 在反常色散区, 产生的增益以反斯托克斯波为主, 正常色散区则以斯托克斯波为主.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking(OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity(QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Ultrashort pulse breaking in optical fiber with third-order dispersion and quintic nonlinearity

The optical wave breaking （OWB） characteristics in terms of the pulse shape, spectrum, and frequency chirp, in the normal dispersion regime of an optical fiber with both the third-order dispersion （TOD） and quintic nonlinearity （QN） are numerically calculated. The results show that the TOD causes the asymmetry of the temporal- and spectral-domain, and the chirp characteristics. The OWB generally appears near the pulse center and at the trailing edge of the pulse, instead of at the two edges of the pulse symmetrically in the case of no TOD. With the increase of distance, the relation of OWB to the TOD near the pulse center increases quickly, leading to the generation of ultra-short pulse trains, while the OWB resulting from the case of no TOD at the trailing edge of the pulse disappears gradually. In addition, the positive （negative） QN enhances （weakens） the chirp amount and the fine structures, thereby inducing the OWB phenomena to appear earlier （later）. Thus, the TOD and the positive （negative） QN are beneficial （detrimental） to the OWB and the generation of ultra-short pulse trains.     

Pulse dynamics in an optical fiber with linear intermode coupling and Kerr nonlinearity dispersion

The effect of Kerr nonlinearity dispersion on the envelope duration and the velocity of the envelope maximum for a wave packet propagating in an optical fiber and formed by two coupled copropagating waves is studied. The critical (threshold) energy of wave packet collapse can substantially be diminished and the supraluminal mode of propagation of the pulse envelope maximum in a nonamplifying medium can be realized owing to a significantly higher nonlinearity dispersion in such systems in comparison with “single-wave” ones.     

Wave breaking in tapered holey fibers

We numerically study the propagation of 1-ps laser pulse in three tapered holey fibers (THFs).The curvature indices of the concave,linear,and convex tapers are 2.0,1.0,and 0.5,respectively.The central wavelength,located in the normal dispersion regime,is 800 nm.The nonlinear coefficient of the THFs increases from the initial 0.095 m-1· W-1 to the final 0.349 m-1·W-1.Wave breaking accompanied by oscillatory structures occurs near pulse edges,and sidelobes appear in the pulse spectrum.With the increase in propagation distance z,the pulse shape becomes broader and the pulse spectrum flattens.A concave THF is advantageous to the generation of wave breaking and enables easier achievement of super flat spectra at short lengths.     

The manipulation of light pulse from subluminal to superluminal propagation in a degenerate two-level Cs atomic system

We experimentally demonstrate the propagation of light pulse from subluminal to superluminal light based on quantum coherence in a degenerate two-level atomic system in a Cs vapor cell.It is shown that the group velocity of light pulse can be switched from subluminal to superluminal propagation via changing the coupling field from a traveling wave to a standing wave,while can also be continuously manipulated by varying the intensity of two waves superposed to form a standing wave.The observed maximum delay and advance times are about 0.45 and 0.54μs,corresponding to the group velocity of g=168km/s and g=138 km/s,respectively.This investigation may have the practical applications of devices for optical tunable delay lines,optical switching and optical buffering.     

Collisions and turbulence in optical rogue wave formation

We discuss optical rogue wave generation in terms of collisions and turbulence processes. Simulations of picosecond pulse propagation in optical fibres show rogue soliton generation from either third-order dispersion or Raman scattering independently. Simulations of rogue soliton emergence with dispersive perturbation in the long-distance limit are also presented.     

影响光孤子传输的因素分析和可能的解决方案

从光孤子传输所满足的非线性薛定谔方程出发,通过对方程中参数的分析和选择,对影响孤子传输的各种因素采用单独分析和综合分析对比方法得到了两个新的结论:(1)二阶色散参数在不太大的范围内变化只会影响脉冲的幅值,对脉冲形状影响不大,而输入脉冲的啁啾则是使脉冲发生畸变的主要原因;(2)在啁啾、三阶色散和五阶非线性同时存在的情况下,它们对脉冲都会产生很大的影响,且存在相互影响和制约关系,三者在某一参数值附近,对脉冲却存在着增益效应和"整容"作用。针对分析结果从理论上提出了改进光孤子传输特性的解决方案,这对光孤子通信的实践过程是有一定实际意义的。