Limits to the encoding and bounds on the performance of coherentultrashort light pulse code-division multiple-access

The authors obtain lower and upper bounds on the peak intensity of a spectrally phase encoded ultrashort light pulse as a function of the length of spectral phase encoding. It is shown that using random phase codes for spectral encoding of ultrashort light pulses in a coherent ultrashort light pulse code-division multiple-access (CDMA) system is almost optimal. Furthermore, simple upper bounds and an asymptotic approximation on the bit error rate (BER) for a wide class of ultrashort light pulse CDMA systems are obtained. It is shown that, in spite of being simple, these upper bounds can be used to evaluate the performance of a coherent ultrashort light pulse CDMA system     

基于小波变换的超短脉冲相位回归

针对频率分辨光学门法(FROG)要用傅里叶变换迭代算法耗时较长不利于实时检测的缺点,及光谱相位相干直接电场重构法(SPIDER)中用传统傅里叶方法滤波过程会产生相位噪声的缺点,提出了用小波变换回归相位的方法。对FROG迹线进行时-频分析直接提取脉冲相位,从SPIDER方法的光谱干涉条纹的小波变换中直接读取相位,对两种方法的小波变换进行了数学模拟,并与傅里叶变换结果进行对比,得到:小波变换能准确地回归超短脉冲相位。最后采用SPIDER方法测量了KLM钛宝石激光器输出脉冲的光谱干涉条纹,并用小波变换和傅里叶变换重建了光谱相位,消除了窗口滤波引入的噪声,证明了方法的正确性和可靠性,更适用于超短脉冲的评价。     

利用频率分辨光学门回归超短脉冲振幅和相位

本文首先介绍频率分辨光学门（RFOG）技术的原理和算法。对于倍频情况（SHG-FROG），我们编程实现了利用计算机快速回归。文中给出了利用该程序所获得的回归结果及对传统算法的改进。事实证明，该算法在分析各种性质的超短脉冲时既准确又方便。     

Recent progress toward real-time measurement of ultrashort laserpulses

Frequency-resolved optical gating (FROG) is a technique that produces a spectrogram of an ultrashort laser pulse optically. While a great deal of information about the pulse can be gleaned from its FROG trace, often it is desirable to obtain of the pulse information immediately, in real time. Quantitative information about the guise is not readily obtainable from its spectrogram without the use of a two-dimensional phase retrieval algorithm. While current algorithms are quite robust, retrieval of all the pulse information can be slow. In this paper, I describe a recently developed FROG trace inversion algorithm called Principal Component Generalized Projects that is fast, robust, and can invert FROG traces in real time. A femtosecond oscilloscope based on second-harmonic generation FROG is also described that uses this new algorithm to rapidly (up to 2.3 Hz) and continuously display the intensity and phase of ultrashort laser pulses     

介质中超短光脉冲的自位相调制和光谱超增宽

本文描述了介质中超短激光脉冲自位相调制理论,并讨论了超短光脉冲产生的光谱超增宽、时间分布和脉宽压缩的实验结果。     

高相干度超连续谱的产生和脉冲压缩的研究

为了研究全波段正常色散光子晶体光纤中高相干度超连续谱的产生及其脉冲压缩,采用分步傅里叶法数值模拟了超短光脉冲在全波段正常色散光子晶体光纤中的非线性传输和超连续谱的产生;利用1阶相干因子分析了抽运波长和入射峰值功率对超连续谱相干特性的影响。结果表明,色散效应越弱,越有利于高相干度超连续谱的产生;在色散效应较小处抽运时,获得了带宽为587nm、平坦度小于7dB的高相干度的超连续谱;超连续谱的相干性越高,越有利于脉冲压缩,采用光栅对压缩器对高相干度超连续谱脉冲进行压缩,获得了8.4fs、压缩质量因子为88.88%的超短光脉冲。因此,抑止色散效应,利用自相位调制可获得高相干度的超连续谱及高质量的脉冲压缩。     

Numerical study on a frequency-tunable actively mode-locked fiber laser

We have numerically presented an actively mode-locked fiber laser with tunable repetition rate based on phase modulator. By finely optimizing intra-cavity parameters, the ultrashort pulses with tunable repetitive frequency at giga hertz level can be easily generated due to the balance between dispersion and nonlinearity in the fiber laser cavity. When the pulse frequency is changed from 1.0 GHz to 4.2 GHz, the spectral width increases from ~15.65 nm to ~27.25 nm. In addition, the corresponding pulse duration decreases from ~81.59 ps to ~31.57 ps. Moreover, these output pulses with giga hertz repetitive rates and the picosecond widths can be further compressed by using the reasonable dispersion medium. For the pulse regime with repetition frequency at giga hertz level, the obtained smallest pulse duration is about ~62 fs based on chirp pulse compression. We hope that these simulation results can promote further research and application in the ultrashort pulse lasers with high repetition rate.     

色散介质中超短脉冲厄米-高斯光束在相位奇点附近的光谱异常特性

基于索末菲(Sommerfeld)衍射积分公式,对色散介质中超短脉冲厄米-高斯光束在相位奇点附近的光谱异常行为进行了研究,并与真空中的光谱异常行为进行了比较.结果表明,超短脉冲厄米-高斯光束的轴上光谱蓝移,蓝移大小与群速度及脉冲宽度有关,而与群速度色散无关.色散介质中的相对光谱移动略小于真空中的相对光谱移动,脉冲宽度越大,相对光谱移动越小.光谱开关的位置与横向距离、传输介质和厄米函数阶数m,n有关,而与脉冲宽度无关.光谱开关的横向距离小于真空中的相应阶的光谱开关的横向距离,并且随光谱开关的阶数增加,真空和色散介质的相对光谱移动均缓慢减小.     

玻璃介质中感应超连续的研究

在用一束弱的530nm超短激光脉冲入射到一块K_9玻璃中,在产生频谱上的超连续输出的基础上,同时把强的1060nm基频也入射到样品中,产生感应超连续,在不同的频率范围内观察到感应超连续功率谱增强4～15倍并且频谱也显著加宽。     

Compressible frequency chirping due to slow and fast self-phasemodulation of ultrashort pulses and high-gain dye laser amplifiers

A theoretical investigation was conducted of the amplitude and phase changes in high-gain ultrashort pulse dye laser amplifiers for cases when the beam area is rather small and the pulse spectral center is not located at the amplifier gain peak. Due to high energy densities as well as high intensities, both slow (saturation-induced) and fast (Kerr-type) self-phase modulation can take place. Under certain conditions, these effects can together produce a considerable amount of mostly linear carrier chirp, resulting in compressible bandwidth enhancement. Compression of the amplified pulses is also calculated using quadratic and quadratic-plus-cubic phase compensation     

基于小波分析的光谱相干电场法的误差分析

为了更精确地评价超短脉冲的特性,利用小波变换的时间频率联合分析和多尺度分析特性,将小波变换应用于光谱位相相干电场重构法（SPIDER）,对给定脉冲进行了数值模拟,讨论了小波函数的形状因子对还原误差的影响,确定了形状因子的选取原则,采用与傅里叶变换互校的方法来找到合适的形状因子来减小形状因子对还原结果的影响。最后对KLM钛宝石激光器输出的脉冲采用SPIDER法进行了测量,并与傅里叶变换结果进行了比较,证明了方法的准确性和可行性。     

Generation of pedestal-free 22-fs ultrashort pulse using highly nonlinear fiber and reverse-dispersion fiber

We present an all-fiber system for generating pedestal-free 22-fs ultrashort pulses with a single-peak spectrum. High-power Raman soliton pulses and a normally dispersive highly nonlinear fiber are used to generate a smooth, broadened single-peak spectrum. Then, the higher order dispersion is compensated for using a hybrid fiber composed of a reverse-dispersion fiber and a standard single-mode fiber, which allows pedestal-free ultrashort pulses to be successfully generated. To our knowledge, this is the first demonstration of pedestal-free 20-fs-class ultrashort pulse generation without spectral distortion using an all-fiber configuration.     

Spectral extent and pulse shape of the supercontinuum for ultrashort laser pulse

The pulse shape and the generated supercontinuum spectral distribution associated with the propagation of an ultrashort intense pulse in a cubic (X^(3)) nonlinear medium are obtained by solving the electromagnetic field wave equation using the method of multiple scales. New forms for the set of quasi-linear partial differential equations describing the system, pulse distortion, and the spectral extent of the supercontinuum are the focus of this paper.     

频率分辨光学开关法测量飞秒脉冲的研究

在详细分析频率分辨光学开关法(FROG)的基础上,对几种类型的FROG迹线进行了模拟,并运用Matlab软件编制程序还原出脉冲信息。用二次谐波型频率分辨光学开关法(SHG-FROG)测量了KLM钛宝石激光器的输出脉冲,并运用算法进行了处理,得到脉冲的振幅和相位信息,与干涉自相关法的测量结果一致。     

线性啁啾脉冲频谱干涉特性的模拟研究

为了研究宽带脉冲因受外界瞬态扰动而引起的相移随频谱变化的规律,利用啁啾脉冲与扰动在频域上的卷积特性,采取将频谱干涉技术和线性啁啾脉冲相结合,当两束线性啁啾脉冲在频率域相遇时,相同的频谱成分产生干涉,从其干涉图中得到随脉冲频谱变化的相对相移。根据傅里叶变换的频谱干涉技术,对从两束线性啁啾脉冲的频谱干涉图中提取相移进行了数值模拟。结果表明,对假设具有不同类型的相移进行重构,还原出随频谱变化的相位扰动。这一结果对超快光学中的瞬态测量是有帮助的。     

Description of laser pulses using Fourier analysis

The output of lasers in various modes of operation is described in a unified way, using Fourier analysis. A novel model for treating an active Fabry-Perot cavity, including the case of high gain, is developed resulting in a more exact expression for the spectral width of the cavity modes. Simple mathematical tools are given to relate the observed pulse length with the average gain and with the initial population inversion in the laser medium. It is shown that lasers with homogeneously broadened spectral lines have cavity modes of equal width and that if the modes are locked together the resulting ultrashort pulses are of equal duration. For lasers with inhomogeneously broadened spectral lines the cavity modes vary in width along the gain curve and, when mode-locked, the ultrashort pulses increase monotonically in duration along the emitted pulse train.     

Self-referencing spectral interferometry for measuring ultrashortoptical pulses

This paper describes a novel self-referencing interferometric method for measuring the time-dependent intensity and phase of ultrashort optical pulses. The technique, spectral phase interferometry for direct electric-field reconstruction (SPIDER), measures the interference between a pair of spectrally sheared replicas of the input pulse. Direct (noniterative) inversion of the interferogram yields the electric field of the input pulse without ambiguity. The interferogram, which is solely a function of frequency, is resolved with a spectrometer and recorded with a slow detector. Moreover, the geometry is entirely collinear and requires no moving components. This paper describes in detail the principle of operation, apparatus, and calibration of SPIDER and gives experimental examples of reconstructed pulses     

Chirped Microwave Pulse Generation Based on Optical Spectral Shaping and Wavelength-to-Time Mapping Using a Sagnac Loop Mirror Incorporating a Chirped Fiber Bragg Grating

In this paper, we propose and demonstrate an approach to optically generating chirped microwave pulses with tunable chirp profile based on optical spectral shaping using a Sagnac loop filter incorporating a chirped fiber Bragg grating (CFBG) and linear wavelength-to-time mapping in a dispersive element. In the proposed approach, the optical power spectrum of an ultrashort optical pulse is shaped by a CFBG-incorporated Sagnac loop mirror that has a reflection spectral response with a linearly increasing or decreasing free spectral range. The spectrum-shaped optical pulse is then sent to a dispersive element to perform the linear wavelength-to-time mapping. A chirped microwave pulse with the pulse shape identical to that of the shaped spectrum is obtained at the output of a high-speed photodector. The central frequency and the chirp profile of the generated chirped microwave pulse can be controlled by simply tuning the time delay in the Sagnac loop mirror. A simple mathematical model to describe the chirped microwave pulse generation is developed. Numerical simulations and a proof-of-principle experiment are implemented to verify the proposed approach.      

Performance Analysis of Internally Coded Time-Hopping Coherent Ultrashort Light Pulse CDMA Scheme in Fiber-Optic Communication Systems

We consider an internally coded time-hopping coherent ultrashort light pulse code division multiple access scheme (TH-CULP CDMA) and analyze its performance in the fiber-optic communication systems. This system combines the TH and CULP CDMA techniques and exploits the advantages of both. In our method, each bit time interval is divided into $N_{s}$ frames, and the spectral phase-coded pulse is transmitted in one of these frames. Two exclusive PN sequences are assigned to each user. One is added to a superorthogonal convolutional encoder output to select the transmission frame, and the other is used to encode the phase of the ultrashort pulse in the spectral domain. We evaluate the bit error rate (BER) of the system considering the effects of the multiple access interference (MAI) and thermal noise for both soft and hard decoders. The BER is evaluated using both the Chernoff bound and saddle point approximation. We compare the performance of our proposed system with that of the conventional CULP CDMA system. The numerical results indicate that for the same bit rate and processing gain, the performance of our proposed system (TH-CULP CDMA) is substantially better than that of the conventional CULP CDMA system. In addition, we observe that the hard decoder has a better performance at large number of users compared to the soft decoder.