Breakdown of the slowly varying envelope approximation in the self-focusing of ultrashort pulses

We show theoretically and experimentally that with ultrashort pulses much longer than a single optical cycle, the effects of self-steepening and space-time focusing are important for describing the nonlinear dynamics of self-focusing. Asymmetric temporal splitting of the pulse envelope is observed in which the relative magnitudes of the peaks are reversed as the input power is increased.     

Temporal shaping of femtosecond solitary pulses in photoionized media

Femtosecond light pulses interacting with solids are studied. With a power close to the self-focusing threshold, an optical pulse evolves like a solitary wave with a temporal duration shrunk to a few femtoseconds through the defocusing action of multiphoton ionization. Self-steepening and space-time focusing are shown to form shock profiles, which do not prevent the pulse from keeping a shorter duration over one Rayleigh length. Theoretical estimates justify the key mechanisms leading to pulse compression, whose influence on the power spectra is finally discussed.     

Gas-induced solitons

The self-guiding of femtosecond laser pulses in air is investigated. For powers close to the threshold for self-focusing, we show that the balance between the nonlinear focusing of the beam and its defocusing by multiphoton sources produces a new kind of solitonlike structure. Over considerably long distances, the radial profile of the pulse relaxes to a steady-state shape, whereas its temporal profile shrinks along propagation. The influence of the normal group-velocity dispersion is finally discussed.     

Nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide

We present a theoretical investigation of the self-focusing dynamics of femtosecond pulses in a hollow waveguide. We show that transverse effects play an important role in these dynamics, even for pulses that are significantly below the critical power for self-focusing in free space, and that excitation of higher-order modes of the waveguide results in the spreading of the pulse in time. Inclusion of self-steepening and space-time focusing in our model is necessary for properly capturing the pulse dynamics.     

Femtosecond pulse switching in a fiber coupler with third order dispersion and self-steepening effects

A numerical study of femtosecond pulse propagation and switching in a dual-core nonlinear directional coupler with the consideration of third order dispersion and self-steepening effects is reported. The Split Step Fourier Method (SSFM) is used to investigate the switching characteristics of nonlinear directional couplers. It is observed that the energy transfer from core to core is not affected by changing the input pulse shapes except super-Gaussian. While the normalized coupling co-efficient and the input peak power dominate the coupling characteristics, the effects of third order dispersion (TOD) and self-steepening (SS) are also reported.     

Pulse compression and supercontinuum at different powers of femtosecond pulses in water

Propagation of femtosecond light pulses in water is investigated. By changing input power from slightly above to highly above threshold for self-focusing, it is shown that either group velocity dispersion (GVD)or multi-photon ionization (MPI) and multi-photon absorption (MPA) may arrest the collapse. When MPI and MPA dominate the propagation, the pulse can be self-compressed to a few optical cycles. In spectral domain, MPI alone induces a strong blue shift. MPA can restrain this strong blue shift.     

Catastrophic collapse of ultrashort pulses

We investigate theoretically the self-focusing dynamics of an ultrashort laser pulse both near and above the threshold at which the pulse effectively undergoes catastrophic collapse. We find that, as a result of space-time focusing and self-steepening, an "optical shock" wave forms inside the medium that gives rise to a broad blueshifted pedestal in the transmitted pulse spectrum. Our results are in good agreement with the primary features observed in experiments and thus provide a theoretical understanding for the underlying process that gives rise to "white-light" generation.     

Spatiotemporal transformation of a focused femtosecond pulse in the absence of self-focusing

The spatiotemporal transformation of a focused femtosecond pulse in fused silica at power much less than the critical power for self-focusing was numerically studied. We found that the pulse experiences unusual spatiotemporal reshaping, such as refocusing of the near-axis portion of the defocused pulse tail, even when the self-focusing effect was not taken into the calculation. Further studies revealed that a tubelike spatiotemporal distribution of the plasma is formed during pulse propagation and that it plays a decisive role in the transformations of the pulse. In addition, the tubelike plasma was found to exist universally under different external focusing conditions if the input pulse had sufficient power.     

Femtosecond soliton generation induced by intrapulse stimulated Raman scattering in optical fibers

ＦｅｍｔｏｓｅｃｏｎｄｓｏｌｉｔｏｎｇｅｎｅｒａｔｉｏｎｉｎｄｕｃｅｄｂｙｉｎｔｒａｐｕｌｓｅｓｔｉｍｕｌａｔｅｄＲａｍａｎｓｃａｔｔｅｒｉｎｇｉｎｏｐｔｉｃａｌｆｉｂｅｒｓＣＡＯＷｅｎｈｕａ；ＬＩＡＯＣｈａｎｇｊｕｎ；ＧＵＯＱｉ；ＺＨＡＮＧＹｏｕ；...     

All-optical limiting using nonlinear directional couplers composed of a self-focusing and a self-defocusing waveguide

We numerically demonstrate the all-optical limiting features in a mismatched nonlinear directional coupler (NLDC) composed of a self-focusing and a self-defocusing waveguide for both continuous wave and pulse cases. The working conditions required are analyzed. To obtain the limiting feature, the propagation constant of the self-focusing waveguide should not be larger than that of the self-defocusing waveguide. Cascaded asymmetric NLDCs are investigated to improve the limiting characteristics. The limiting threshold and the limiting output power can be adjusted by varying the coupler length or the ratio of the nonlinearity coefficients of the self-defocusing and self-focusing waveguides. Analytical solutions are presented in the case of a continuous wave. For the pulse case, numerical solutions show that the top part of the output pulse, if it exceeds the limiting threshold, will be tailored, while the rising and falling edges of the output pulse are almost the same as the input pulse. There is almost no pulse breakup. The influence of the second order dispersion and the intermodal dispersion on the limiting characteristics are analyzed. PACS 42.79.Gn; 42.79.Ta     

光子晶体光纤中调制不稳定现象与超连续光谱的产生

研究了光子晶体光纤中调制不稳定性效应.从非线性薛定谔方程出发，计算和分析了光子晶体光纤中反常色散区以及正常色散区内的调制不稳定性现象，详细讨论了超短脉冲的脉宽、峰值功率、高阶色散和高阶非线性效应（如脉冲内喇曼散射、自陡峭效应）对调制不稳定性产生的影响.结果表明：二阶色散对调制不稳定性的影响要远大于三阶色散，同时也发现随着初始脉冲宽度的减小，调制不稳定性旁瓣增大但是强度有所降低.另外还发现高阶非线效应如自陡峭和喇曼效应会在不同程度上抑制调制不稳定性.     

Modeling interaction of ultrashort pulses with ENZ materials

In this work, the split-step Fourier method for beam propagation is used to investigate the interaction of ultra-short pulses with epsilon-near-zero materials. The propagation of pulses is governed by the nonlinear Schrödinger equation (NLSE) containing dispersion, gain-bandwidth, self-phase modulation, self-steepening, and absorption parameters. It is found that the intensity profile of the pulse is broadened and the phase of the pulse is shifted by dispersion phenomena. The gain/loss related to the imaginary part of the refractive index causes an increase or decrease in intensity and pulse edge effects. These effects do not favor the steady propagation of the pulse. The self-phase modulation is not noted to appreciably affect the intensity pulse profile. The self-steepening modifies the phase and energy of the pulse during propagation, as well as absorption, which influences the losses by both the linear and nonlinear effects.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

各向同性光纤中拉曼增益对光脉冲自陡峭的影响

运用数学解析法导出了关于拉曼增益与自陡峭综合效应的光脉冲传输方程,在此基础上引入洛伦兹模型将拉曼增益整合到非线性系数中来研究光脉冲中拉曼增益对自陡峭效应的作用,重点分析了高斯脉冲在各向同性光纤中传播时,拉曼增益对其自陡峭效应具体影响方式,结果表明拉曼增益会减弱自陡峭中后沿偏移程度,减小脉冲展宽,但不会影响其峰值大小.     

Induced focusing and conversion of a Gaussian beam into an elliptic Gaussian beam

We have presented an investigation of the induced focusing in Kerr media of two laser beams, the pump beam and the probe beam, which could be either Gaussian or elliptic Gaussian or a combination of the two. We have used variational formalism to derive relevant beam-width equations. Among several important findings, the finding that a very week probe beam can be guided and focused when power of both beams are well below their individual threshold for self-focusing, is a noteworthy one. It has been found that induced focusing is not possible for laser beams of any wavelength and beam radius. In case both beams are elliptic Gaussian, we have shown that when power of both beams is above a certain threshold value then the effective radius of both beams collapses and collapse distance depends on power. Moreover, it has been found that induced focusing can be employed to convert a circular Gaussian beam into an elliptic Gaussian beam.     

光纤放大器中的自相似抛物脉冲

本文研究在含有增益色散、增益饱和、三阶色散、自频移、自陡峭等效应的光纤放大器中自相似抛物脉冲的产生和传输。结果表明,在渐近约束条件下,自相似脉冲的中心区域可用倒置的抛物脉冲来描绘,并且它的有效脉宽和功率都是线性增长的,而峰值振幅和频谱宽度保持常量。数值模拟结果与理论预期符合的非常好,这表明:在光纤放大器中,在适当的条件下初始输入脉冲可自相似地演化为抛物脉冲。     

飞秒激光脉冲在正色散固体材料中的自压缩

实验研究了正色散固体介质中的激光脉冲自压缩现象,证明了无需任何外加色散补偿情况下，固体透明介质中的自聚焦传输过程可使高功率飞秒激光脉冲实现时域脉冲压缩，并详细研究了输出脉冲的时域和频域特性随入射脉冲强度的演化规律.实验结果表明脉冲自压缩量随入射脉冲强度的增加呈递增趋势，然而当入射光强增大到足以引起超连续谱及锥形辐射产生时，脉冲时域形状会发生分裂.此外还发现发散光束入射情况下同样可以观察到脉冲自压缩现象. 关键词： 超短激光脉冲 脉冲压缩 非线性传输     

Single-focusing regime of propagation of femtosecond light packets when self-focused in a condensed medium

Numerical simulations are used to investigate the propagation of tightly focused megawatt femtosecond light packets in a nonlinear condensed medium in the single-focusing regime. A plasma is shown to be generated in a small region whose length and diameter increase with power in the single-focusing regime of propagation of a femtosecond light packet in a transparent dielectric. The limiting electron density in the microplasma formation region is virtually independent of the laser pulse power but increases with numerical aperture of the focusing optics. At a fixed femtosecond pulse power exceeding the critical self-focusing power, the transmission of light by a dielectric layer decreases with increasing numerical aperture of the focusing optics.     

熔石英介质中强紫外激光自聚焦效应研究

 针对脉冲宽度约1 ns、波长为351 nm的三倍频紫外激光,定量分析了熔石英介质中的自聚焦长度、峰值光强与强紫外激光光束质量及环境条件等因素的关系,研究了产生紫外光非线性自聚焦效应的阈值条件。研究结果表明：在强紫外激光光束质量一定的前提下,可将B积分值定义为自聚焦的阈值条件;入射强紫外激光光束质量越差,在熔石英介质中产生自聚焦的阈值条件越低;即使对于空间分布均匀的理想光束,当空气中存在灰尘时,经过一段距离的传输后,在熔石英介质中将导致强紫外激光自聚焦效应的产生,且灰尘尺寸较大时的自聚焦效应较明显,自聚焦的阈值条件也相对较低。