Pulse width measurement of high-order harmonics by autocorrelation

Pulse widths of the 7th and 9th harmonics of a Ti:sapphire (TiS) laser have been measured by an autocorrelation technique using two-photon and three-photon ionization of He and Ar as nonlinear phenomena. The pulse widths of the 7th and 9th harmonics were 47 fs and 27 fs, respectively, where the pulse width of the fundamental pulse was 34 fs. The pulse width of the 9th harmonic depends strongly on the peak intensity of the fundamental pulse. These results can be explained by quantum theory by taking into account the temporal and spatial distribution of the fundamental beam. Received: 15 June 1999 / Revised version: 8 October 1999 / Published online: 2 February 2000     

Pulse dynamics in inhomogeneous optically coupled amplifying optical fibers with high-order dispersion effects taken into account

The evolution of the envelope of a two-mode wave packet in an inhomogeneous-over-length amplifying optical fiber is analyzed with the third-order dispersion effects taken into account, the presence of which leads to modulations of one or both edges of the wave packet. High degrees of compression of the pulse and the complete suppression of oscillations of its time envelope can be attained by an appropriate choice of the type of inhomogeneity of the dispersion parameters.     

Pulse compression of a high-order harmonic

The fifth harmonic pulses of an intense femtosecond Ti:sapphire laser were experimentally shown to be negatively chirped by using an LiF plate as a positive dispersive medium. The chirp of the harmonic pulse originates from the intensity-dependent atomic dipole phase, which is estimated to be proportional to 25 U_p, where U_p is the ponderomotive energy. Consequently, we have succeeded in compressing the chirped pulses to 13 fs by compensating the intrinsic negative chirp. Chirp effects of the fundamental laser on the pulse width of the fifth harmonic were consistent with the negative chirp of the fifth harmonic.     

Visualization of high-order dispersion for compression of few-cycle pulses

We present a visually intuitive method for higher-order dispersion compensation based on multi-photon interpulse interference pulse scans. The dispersion values obtained from these scans are fed back as a correction to an acousto-optical programmable dispersive filter to compensate residual higher-order dispersions up to fifth order. This method is applied to the dispersion management of a non-collinear optical parametric chirped-pulse amplifier. A grism-pair stretcher is designed based on a global dispersion balance which provides a large stretching factor and supports a spectral bandwidth of up to 320 nm. It is implemented in a two-stage three-pass non-collinear optical parametric chirped-pulse amplifier and stretches 6-fs seed pulses to about 80 ps from 700 to 1,000 nm. The amplified pulses are compressed by material dispersion. Pulses of less than 10-fs duration with a pulse energy of 125 μJ are obtained at 20-kHz repetition rate.     

Pulse dispersion in a lens-like medium

An analysis is given of dispersion in an optical fibre waveguide having a continuous radial variation of refractive index using the scalar wave approximation. Solutions are presented for the particular case of Selfoc fibre taking into account mode dispersion, material dispersion and group delay. It is shown that for a correctly matched input Gaussian beam the pulse dispersion is small although in practice it is likely to be 1 ns over a length of 1 km.On leave from the Nippon Sheet Glass Co., Japan.     

Pulse dispersion in partially-excited graded-index fibres

Simple analytical results are obtained for the mode distribution and impulse response of graded index fibres under a variety of excitation conditions relevant to practical systems. It is found that the choice of an optimum refractive index profile depends quite strongly on the source distribution of or, that one can significantly improve the impulse response of a particular profile by appropriate choice of launching conditions. Furthermore the r.m.s. pulse width is not necessarily reduced simply by partially filling the numerical aperture of the fibre.     

Single 10-fs deep-ultraviolet pulses generated by broadband four-wave mixing and high-order dispersion compensation

Broadband chirped-pulse four-wave mixing and a pulse compressor consisting of a prism pair and a grating pair are used to generate 10.3-fs deep-ultraviolet pulses. A large proportion of the dispersion up to 1000 fs² is compensated without inducing third-order dispersion, which together with the smooth spectral and temporal profiles of the pulses makes them suitable for ultrafast spectroscopy. Unexpected spectral narrowing is observed when short input pulses were used for four-wave mixing. This narrowing is explained in terms of other third-order nonlinear phenomena, namely self-phase and cross-phase modulations, which occur simultaneously with four-wave mixing.     

高阶色散对高双折射光纤增益谱的影响

根据参量放大和拉曼效应共同作用下的耦合波方程,在考虑高阶色散情况下,当输入泵浦波偏振方向同双折射轴成45时,通过引入拉曼增益的洛伦兹模型,研究了高双折射光纤中,参量放大和拉曼效应共同作用下的增益谱随相关参量的变化关系。结果表明：高双折射光纤中,在不同色散区,不同的输入参量（输入功率、群速度失配等）条件下,参量放大和拉曼效应共同作用下的增益谱受到高阶色散的影响,增益谱的结构、强度和谱宽产生了变化, 高阶色散对增益谱的影响不可忽略;可以利用增益谱在大群速度失配区域远离中心频率偏移的性质,提取T频率脉冲。     

Optical solitons in the parabolic law media with high-order dispersion

The transmission equation of ultrashort optical pulse in the high-order dispersion media with the parabolic law (cubic–quintic) nonlinearity has been studied with the help of the subsidiary ordinary differential equation expansion method. As a result, the optical solitons and triangular periodic solutions are obtained, and the conditions for exact solutions to exist are also given.     

Pulse dispersion in a clad lens-like medium

The effects of a homogeneous cladding on the dispersion of a square-law dielectric guide are investigated using a perturbation technique. Assuming a Gaussian, band-limited input it is shown that for single mode operation the waveguide dispersion is of the order of the material dispersion. For multimode operation the effect of the cladding on the uniformly polarized modes is examined and it is shown that a significant interaction occurs only for the two modes closest to cut-off. Comparison is made between theoretical and experimental results. The perturbation technique is used to analyse the optimum index profile proposed by Okamoto and Okoshi. It is shown that this variation reduces the dispersion to below that of the infinite medium approximation.     

Grid stabilization of high-order one-sided differencing II: Second-order wave equations

We demonstrate the stable boundary closure of difference methods of order up through 16 for the solution of wave equations in second order form. Our method combines the introduction of 1–2 judiciously placed subcell grid points near the boundary with minimal-stencil, one-sided difference operators of the same order as the interior scheme. The method is tested on a variety of problems including the scalar wave equation discretized on mapped grids and overlapping composite grids, as well as an integrable nonlinear system.     

Generation of single dispersion precompensated 1-fs pulses by shaped-pulse optimized high-order stimulated Raman scattering

We propose and theoretically analyze a new approach for generating and shaping 1-fs pulses. It combines the ideas of strong-field molecular optics and optimal control to manipulate light generation in a pump-probe Raman regime. Flexible phase control over the generated spectrum of about 3 eV width is achieved by controlling the input pulses and maximizing the coherence of medium excitation by adiabatically aligning molecules in the medium with a specially shaped pump pulse. The generated pulse is optimized for an output window, precompensating for its dispersion to all orders.     

Influence of high-order dispersion on self-focusing. II. Numerical investigation

The self-focusing described by the nonlinear Schrödinger equation with a higher-order derivative term is investigated numerically. We demonstrate that, depending on the sign before this term, it may lead in the final stage either to defocusing or to a steady homogeneous wave beam. In both cases the transition to the final state is shown to be oscillatory.     

Influence of high-order dispersion on self-focusing. I. Qualitative investigation

The self-focusing, described by the nonlinear Schrödinger equation with a higher-order derivative term, appearing from dispersive corrections, is considered. A qualitative investigation shows that this term, even if it is small, may play an important role in the final state of the self-focusing. Depending on the sign of a coefficient before this term, it may lead either to a tunneling of the self-trapped radiation, which finally results in defocusing, or to a steady homogeneous wave beam.     

Statistical determination of the length dependence of high-order polarization mode dispersion

We describe a method of characterizing high-order polarization mode dispersion (PMD). Using a new expansion to approximate the Jones matrix of a polarization-dispersive medium, we study the length dependence of high-order PMD to the fourth order. A simple rule for the asymptotic behavior of PMD for short and long fibers is found. It is also shown that, in long fibers (~1000 km), at 40 Gbits/s the third- and fourth-order PMD may become comparable to the second-order PMD.     

高阶色散和指数饱和非线性光纤的调制不稳定性

采用线性稳定性分析法,解析和计算了指数饱和非线性和高阶色散光纤中的调制不稳定条件和增益谱。结果表明:当二阶和四阶色散同为负时,随着参数的不同,增益谱可能只有一个谱区,也可能出现两个分离的谱区;当二阶和四阶色散分别为正和负时,无调制不稳定性;在其它色散区,则只有一个谱区。指数饱和非线性可能使各谱区的谱宽、峰值增益随入纤功率的增大呈现出先增大后减小的特点,即出现两个不同的输入功率对应同一个不稳定增益峰值和谱宽的情形。在其它参数相同时,指数饱和非线性下增益谱的谱宽和峰值增益随入纤功率的变化速度将比传统饱和非线性更快。     

Pulse compression without chirp control and frequency detuning by high-order coherent Raman scattering in impulsively excited media

It is shown that phase-locked pulses as short as 3 fs can be generated by coherent scattering in impulsively excited Raman media without the necessity of external phase control. The underlying mechanism, temporal characteristics, spectra, phase relations, physical limitations owing to competition processes, and precompensation of dispersion by the hollow waveguide window are studied analytically and numerically without the use of the slowly varying envelope approximation and with a global approach to dispersion. Additionally, the large frequency shifts in both the Stokes and anti-Stokes directions of as much as half the carrier frequency raise the possibility of generating widely tunable ultrashort pulses.     

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.     

Optical pulse compression using the combination of phase modulation and high-order dispersion compensation

Optical pulse compression using high-order dispersion compensation is proposed and theoretically analyzed. Firstly, the required dispersion profile for the high-order dispersion compensation is derived, according to the linear chirp and the nonlinear chirp of a phase-modulated continuous-wave (CW) laser source. With the use of the high-order dispersion compensation, such as the combination compensation of the second order dispersion (SOD) and the fourth order dispersion (FOD), an efficient pulse compression having a less time-bandwidth product and a greater peak power is realized. A sampled fiber Bragg grating (FBG) with both the SOD and the FOD is then designed using the equivalent chirp and the reconstruction algorithm. Finally, in the numerical simulation an optical pulse with a time-bandwidth product of 0.79 is generated via high-order dispersion compensation that is performed by using the sampled FBG.     

Pulse timing stabilization of a mode-locked Cr:LiSAF laser

The pulse repetition frequency of a mode-locked Cr:LiSAF laser has been stabilized to an electrical reference oscillator by use of an electrical feedback technique. The phase and frequency differences between the laser and the reference are detected by use of a digital phase detector, which overcomes the difficulties of a conventional double-balanced mixer. We obtained rms timing jitters of 20 fs (25 mHz-10 kHz) and 7 fs (25 mHz-1 kHz) relative to the reference.