定义：非线性和色散介质中的光脉冲，其时间和光谱形状发生周期性振荡。

一种基本的孤子为传播在色散介质（例如，光纤）中，具有固定的时间强度曲线（即色散不会引起任何时间展宽）的光脉冲。
当脉冲具有固定形状并且能量由介质中的参数（尤其是色散和非线性）和脉冲长度决定。 

高阶孤子是能量为基本孤子整数的平方倍（即，4,9,16等）的孤子脉冲。该脉冲的时间兴中并不是常数，而是在传播过程中周期性变化（见图1和图2）。 

  
图1：三阶孤子的时间演化

图2：三阶孤子的光谱演化。 

图3：三阶孤子的时间演化。彩色温标代表光功率。孤子周期为50.4 m，即显示的范围约为两个孤子周期。 

 图4：三阶孤子的光谱演化。彩色温标代表功率谱密度。 

高阶孤子可以用于非线性脉冲压缩：具有合适能量的sech2形状的脉冲注入到具有反常色散的光纤中，演化过程为高阶孤子演化，传播一定距离后，脉冲长度显著较小。较高的孤子阶数可以实现很强的压缩，还对泵浦波长有严格的选择。 

基本孤子通常比较稳定，而高阶孤子会由于受到各种效应（例如高阶色散，拉曼散射，双光子吸收）的影响分裂成基本孤子。孤子分裂在有些过程中发挥主要的作用，例如，光子晶体光纤中的超连续谱产生。
 

Definition: optical pulses in a nonlinear and dispersive medium which exhibit periodic oscillations of their temporal and spectral shape

A fundamental soliton is an optical pulse which can propagate in a dispersive medium (e.g. an optical fiber) with a constant shape of the temporal intensity profile, i.e., without any temporal broadening as is usually caused by dispersion. This can happen when the pulse has a certain shape and an energy which is determined by the parameters of the medium (in particular, by the dispersion and nonlinearity) and the pulse duration.

A higher-order soliton is a soliton pulse the energy of which is higher than that of a fundamental soliton by a factor which is the square of an integer number (i.e. 4, 9, 16, etc.). The temporal shape of such a pulse is not constant, but rather varies periodically during propagation (see Figures 1 and 2). The period of their evolution is the so-called soliton period.

Figure 1: Temporal evolution of a third-order soliton.

Figure 2: Spectral evolution of a third-order soliton.

Figure 3: Temporal evolution of a third-order soliton. The color scale shows the optical power. The soliton period is 50.4 m, i.e. the displayed range corresponds to about two soliton periods.

Figure 4: Spectral evolution of a third-order soliton. The color scale shows the power spectral density.

Higher-order solitons can be used for nonlinear pulse compression: a sech²-shaped pulse with a suitable energy, injected into an optical fiber with anomalous dispersion, can evolve as a higher-order soliton, and after a certain propagation distance the pulse duration can be substantially decreased. High soliton orders allow for strong compression, but also lead to a critical choice of the pump wavelength.

Whereas fundamental solitons are usually fairly stable, higher-order solitons can break up into fundamental solitons under the influence of various effects, such as higher-order dispersion, Raman scattering, or two-photon absorption. Such soliton breakup sometimes plays an essential role in the process of supercontinuum generation in photonic crystal fibers.

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