Design procedure for photonic crystal fibers with ultra-flattened chromatic dispersion

A simple design procedure is used to generate photonic crystal fibers (PCFs) with ultra-flattened chromatic dispersion. Only four parameters are required, which not only considerably saves the computing time, but also distinctly reduces the air-hole quantity. The influence of the air-hole diameters of each ring of hexagonal PCFs (H-PCF, including 1-hole-missing and 7-hole-missing H-PCFs), circular PCFs (C-PCF), square PCFs (S-PCF), and octagonal PCFs (O-PCF) is investigated through simulations. Results show that regardless of the cross section structures of the PCFs, the 1st ring air-hole diameter has the greatest influence on the dispersion curve followed by that of the 2nd ring. The 3rd ring diameter only affects the dispersion curve within longer wavelengths, whereas the 4th and 5th rings have almost no influence on the dispersion curve. The hole-to-hole pitch between rings changes the dispersion curve as a whole. Based on the simulation results, a procedure is proposed to design PCFs with ultra-flattened dispersion. Through the adjustment of air-hole diameters of the inner three rings and hole-to-hole pitch, a flattened dispersion of 0±0.5 ps/(nm·km) within a wavelength range of 1.239 – 2.083 μm for 5-ring 1-hole-missing H-PCF, 1.248 – 1.992 μm for 5-ring C-PCF, 1.237 – 2.21 μm for 5-ring S-PCF, 1.149 – 1.926 μm for 5-ring O-PCF, and 1.294 – 1.663 μm for 7-hole-missing H-PCF is achieved.     

一种晶体光纤基模色散特性的矢量法分析

利用矢量有效折射率方法(矢量法)对光子晶体光纤基模的色散特性进行了数值模拟，并与双正交归一基矢量法以及标量有效折射率方法(标量法)的模拟结果进行了对比.发现所用矢量法的结果与双正交归一基矢量法的结果符合很好，而标量法在低空气填充率f或较高归一化波数A/λ时是一种较好的近似，在空气填充率f较高或归一化波数A/λ较低时，要得到精确的结果必须利用矢量法对光子晶体光纤的特性进行模拟.讨论了光子晶体光纤包层有效折射率与光纤结构的关系. 关键词： 光子晶体光纤 矢量法 有效折射率 色散     

混合纤芯光子晶体光纤超平坦色散的研究

利用平面波展开法,系统地研究了一种具有混合纤芯结构的光子晶体光纤的色散特性. 数值计算结果表明,通过优化结构参量,这种新型结构的光子晶体光纤在通信窗口1.55 μm 附近可以获得带宽超过800 nm的超平坦色散区域（色散曲线的变化范围不超过 ±0.6 ps·km－1·nm－1）.     

双零色散光子晶体光纤中超连续谱的产生及控制

 通过数值模拟飞秒脉冲在具有双零色散波长的光子晶体光纤中的传输过程,详细分析了超连续谱的产生和控制机制.结果表明：中心波长处于反常色散区的泵浦脉冲在高阶非线性和高阶色散等作用的调制下,将演化为基孤子和正常色散区的两个色散波|该色散波进而经与之相位匹配的基孤子相干加强而使频谱展宽形成超连续谱,同时两个色散波上出现了干涉引起的振荡现象.进一步对比三种结构的光子晶体光纤中超连续谱的特点,定量分析了两色散波对超连续谱的限制作用,阐述了结构参量对超连续谱的影响.基于上述结论,结合对色散波的中心波长与光子晶体光纤的色散曲线、结构参量之间关系的分析,提出了设计光子晶体光纤的结构来控制超连续谱的方法.作为例证,通过优化光子晶体光纤结构理论上实现了频谱分量覆盖可见光区的平坦超连续谱.     

光子晶体光纤色散补偿特性的数值研究

利用矢量有效折射率方法对光子晶体光纤（PCF）的色散补偿特性进行了数值模拟，研究发现通过调节光子晶体光纤包层的空气穴节距或空气穴大小可以灵活地设计光子晶体光纤的色散系数D、色散斜率Dslope以及κ值，可以设计在波长1.55μm附近具有较大绝对值的正常色散和负色散斜率的色散补偿光子晶体光纤，使光通信中的普通单模光纤（G.652）或非零色散位移光纤(G.655)在1.55μm低损耗窗口得到较好的色散补偿.数值模拟和分析表明色散补偿光子晶体光纤的研制具有很大的发展潜力. 关键词： 光子晶体光纤 色散 色散斜率 色散补偿     

八边形光子晶体光纤色散补偿特性分析

利用多极法对八边形光子晶体光纤的色散补偿特性进行数值模拟,分析了结构参数变化对色散补偿特性的影响;计算了具有相同参数的六边形结构光子晶体光纤的色散系数和非线性系数;研究表明八边形光子晶体光纤比六边形结构的光子晶体光纤的大负色散特性明显提高,非色散系数低,更有利于进行色散补偿.因此,本文设计了一种新型的八边形色散补偿光纤,在λ=1.55μm时色散值为-1434.9ps·nm^-1·km^-1,色散斜率为-4.6338ps·nm^-2· 关键词： 光子晶体光纤 多极法 色散斜率 色散补偿     

光子晶体光纤的导波模式与色散特性

利用有效折射率方法基于标量近似理论对光子晶体光纤的传播模式和色散特性进行了数值模 拟，发现通过调节光纤包层的空气填充率或包层空气穴节距及其有效芯径可以在很宽的波长 范围实现单模传播，可以设计零色散波长小于1.27μm的光子晶体光纤和在较宽的波段接近 于零色散的色散平坦光纤，以及具有较大的正常色散值的色散补偿光纤. 关键词： 光子晶体光纤 有效折射率 标量近似 导波模式     

用阶跃有效折射率模型研究光子晶体光纤色散特性

在采用阶跃有效折射率模型研究光子晶体光纤的可行性方面，提出了将普通单模光纤、色散位移光纤、色散平坦光纤作为一定极限条件下的折射率引导型光子晶体光纤特例的观点.通过编程计算，并与文献报道的实验数据对比，表明应用本模型可以揭示光子晶体光纤所具有的奇异的色散机理.特别是应用本模型具有更快的计算速度.还用本模型分析了空气孔直径、周期及芯径对色散特性的影响. 关键词： 折射率引导型光子晶体光纤 阶跃有效折射率模型 色散     

Zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres

This paper investigates the zero dispersion wavelength and dispersion slope control of hollow-core photonic bandgap fibres (PBGFs) by using a full-vector finite element method. By simulation we found that theoretically the zero dispersion wavelength can be tailored by respectively changing the rounded diameter of air holes, pitch, refractive index, normalized thickness of core rings, and hole diameter to pitch ratio. At the same time the tailoring of dispersion slope can also be realized by changing the rounded diameter of air holes or pitch or normalized thickness of core rings. To illustrate the reasonability of fibre designs, this paper also gives the variance of normalized interface field intensity which measures the scattering loss relatively versus wavelength for different designs. From the viewpoint of loss, varying the rounded diameter and the thickness of core ring could shift zero wavelength but it is difficult to get the required parameters within so tiny range in practical drawing of PBGFs, on the other hand, it is possible in practice to respectively alter the pitch and refractive index to shift zero wavelength. But varying hole diameter to pitch ratio is not worthwhile because they each induce large increase of loss and narrowness of transmission bandwidth. The zero dispersion wavelength can be engineered by respectively varying the rounded diameter of air holes, pitch, refractive index, and normalized thickness of core rings without incurring large loss penalties.     

Anomalous dispersion in a solid, silica-based fiber

We demonstrate an all-solid (nonholey), silica-based fiber with anomalous dispersion at wavelengths where silica material dispersion is negative. This is achieved by exploiting the enhanced dispersion engineering capabilities of higher-order modes in a fiber, yielding + 60 ps/nm km dispersion at 1080 nm. By coupling to the desired higher-order mode with low-loss in-fiber gratings, we realize a 5 m long fiber module with a 300 fs/nm dispersion that yields a 1 dB bandwidth of 51 nm with an insertion loss of approximately 0.1 dB at the center wavelength of 1080 nm. We demonstrate its functionality as a critical enabler for an all-fiber, Yb-based, mode-locked femtosecond ring laser.     

Differential toolbox to shape dispersion behavior in photonic crystal fibers

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabrication tolerances.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

一种阶梯结构的色散平坦光子晶体光纤的研究

以多极法理论为基础,提出了一种阶梯结构的光子晶体光纤.通过改变其内四层的三个结构参量(内两层孔孔径,外两层孔孔径和孔间距),实现色散绝对值在1.1～1.8μm的波段内变化仅为0.05～2 ps/(km·nm)的平坦甚至超平坦的特性.在此情况下对其有效模场面积进行数值模拟,充分展示了达到色散平坦和超平坦时,相对于传统光子晶体光纤,此种结构的光纤对芯区内光场的局域能力有很大程度的增强,其有效模场面积可仅为传统光子晶体光纤的1/30.最后,经过大量的数值计算和理论分析,归纳出若要此种阶梯结构的光纤在1.1～1.8μm的波段内达到色散平坦甚至超平坦特性的设计依据.     

Prediction of photonic crystal fiber characteristics by Neuro–Fuzzy system

The most common methods applied in the analysis of photonic crystal fibers (PCFs) are finite difference time/frequency domain (FDTD/FDFD) method and finite element method (FEM). These methods are very general and reliable (well tested). They describe arbitrary structure but are numerically intensive and require detailed treatment of boundaries and complex definition of calculation mesh. So these conventional models that simulate the photonic response of PCFs are computationally expensive and time consuming. Therefore, a practical design process with trial and error cannot be done in a reasonable amount of time. In this article, an artificial intelligence method such as Neuro–Fuzzy system is used to establish a model that can predict the properties of PCFs. Simulation results show that this model is remarkably effective in predicting the properties of PCF such as dispersion, dispersion slope and loss over the C communication band.     

Dispersion and polarization properties of elliptical air-hole-containing photonic crystal fibers

In this paper, we investigate the dispersion and polarization properties of photonic crystal fiber with one ring or more rings of elliptical air-holes using plane-wave expansion (PWE) method. By introducing three rings of elliptical air-holes, PCF with ultra-low and ultra-flattened dispersion is designed and a total dispersion curve between ±0.5 ps/nm/km from 1315 to 1855 nm wavelength range is demonstrated. Furthermore, the polarization property of these elliptical air-hole-containing PCFs is analyzed and the variation of the birefringence with the area and ellipticity of the elliptical air-holes are discussed.     

Designing of a polarization beam splitter for the wavelength of 1310 nm on dual-core photonic crystal fiber with high birefringence and double-zero dispersion

We have proposed a novel kind of photonic crystal fiber which contains two asymmetric cores. The bireti＇ingence and the dispersion are numerically analyzed based on finite element method when the size of the air holes and the pitch of two adjacent air holes are changed. It is shown that the proposed photonic crystal fiber has high birefringence up to the order of 10-2 and double-zero dispersion points are at the wavelengths of 1310 nm and 800 rim, simultaneously. At the same time, the normalized power and the extinction ratios of the proposed photonic crystal fiber have been simulated. It is demonstrated that, at the wavelength of 1310 rim, the x-polarized mode and the y-polarized mode are separated when the propagation distance is 2.481 ram.     

长脉冲抽运光子晶体光纤四波混频和超连续谱的理论研究

本文数值研究了长脉冲抽运光子晶体光纤四波混频和超连续谱的产生.依据准连续波近似下的相位匹配条件和能量守恒定律,能够理论上确定在光子晶体光纤正常色散区抽运时,四波混频效应产生的信号光和空闲光波长;以及在光纤反常色散区抽运时,调制不稳现象产生的两个对称旁瓣波长.利用自适应分步傅里叶法,定量地模拟了利用波长为1064 nm的亚纳秒激光器抽运两种不同色散特性的光子晶体光纤四波混频效应和超连续谱的产生,模拟结果与实验结果符合非常好. 关键词： 光子晶体光纤 超连续谱 四波混频 自适应分步傅里叶法     

Simplified universal dispersion curves for channel waveguides

Simplified universal dispersion curves for graded-index diffused channel waveguides have been obtained with the new normalized WKB equation using the effective index method. It is shown that, similarly to planar guides, the propagation constant of all the guided modes of a particular channel can be obtained by two parameters, called the normalized mode orders. The dispersion relations between the propagation constant and the normalized mode order of the channel have been obtained for a number of profile shapes and waveguide dimensions.     

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.     

A unique approach in ultra-flattened dispersion photonic crystal fibers containing elliptical air-holes

In this paper, we report that it is possible to control chromatic dispersion of index guiding PCFs in wide wavelength range by arranging the major axis of the first inner ring perpendicular to that of the second inner ring. Using this unique arrangement, a newly PCF with ultra-low and ultra-flattened dispersion is designed through a finite difference method with anisotropic perfectly matched layers absorbing boundary condition. As an example, we have design a unique PCF with flattened dispersion of ±0.23 ps/(nm·km) from 1.5 to 1.8 μm wavelength and confinement losses of less than 10⁻¹³ dB/m in the wavelength range shorter than 1.8 μm.