曾　辉，杨乔云，卓　辉

(1.珠海汉胜科技股份有限公司，广东 珠海　519180；2.湖南大学，湖南 长沙　410012；3.湖南农业大学，湖南长沙　410128)



时域有限差分法在超高速通信系统中带隙型光子晶体光纤瞬态三维截面上特性研究

曾辉1,2，3，杨乔云1，卓辉2，3

(1.珠海汉胜科技股份有限公司，广东 珠海519180；2.湖南大学，湖南 长沙410012；3.湖南农业大学，湖南长沙410128)

摘 要：利用时域有限差分法针对满足带耦合腔PCFS条件的Maxwell方程组进行电磁场三维矢量变换，来建立关于入射光在光子晶体光纤传播物理数值模型。通过数值仿真表明：在波导色散作用下，当空气间隙增大，其TE波在直角坐标系中三维矢量数值大小与网格步长递增呈正比变化，且瞬态截面分裂速度减缓且数目递减、体积变大；反之，当空气孔间隙减小，其TM波三维矢量随着传输网格步长递增，瞬态截面分裂呈细丝状且数目递增、体积变小。同时，随着角频率w0增大，磁场x,y方向中心强度随时间网格呈对称式变化且峰值强度逐渐递增；同时在L+Nd=150(N=0,1,2;l>0)处存在拐点；在电场z方向，振幅抖动愈加频繁且峰值连续上涨，相位峰值逐渐递减且脉宽呈压缩变化。

关键词：时域有限差分法；波导色散；空隙带隙型光子晶体光纤；Maxwell方程组

空隙带隙型光子晶体光纤(photonic crystal fiber，PCF)[1-3]指由SiO2为主要材料的石英和空气间隙呈周期性六边形分布[4-5]；具有波长为微量级的新型光学材料。其包层含有的排列不对称的微结构气孔在宽带中表现出较为明显的的非线性效用[6]与单模传输[7-9]、以及在可见光波段表现出强烈的双折射效应[10-11]、反常色散[12-14]、瑞丽散射损耗[15]等特征。为此，它也成为目前光子晶体应用领域中研究最热的前沿课题。本文采用时域有限差分法能有效对入射激励源连续时间、空间离散化问题进行处理以及解决光源在PGB-PCFS中电场、磁场散射现象。其主要原理为：第一，对入射波源垂直方向的电磁场在时空域角度三维矢量分解；第二，设置时间轴与空间轴网格固定值为L；第三，运用FDTD算法逐级跳跃递增方法计算出第N-1个网格TE波、TM波数值大小进而推算出第n个网格电场值和磁场值；通过计算编码程序循环往复运算求得L,……,L+(N-1)d,L+Nd所有不同时空域变化所处的电磁场值。数值模拟结果表明：当存在带耦合腔作用时，空气间隙∧大小与瞬态截面分裂数目呈反比；同时在电场z方向，随着频率增大，振幅抖动愈加频繁且峰值连续上涨，相位峰值逐渐增大且脉宽呈压缩变化。

1时域有限差分算法及物理数值模型

在直角坐标系中，从满足光子晶体光纤TE波和TM波Maxwell方程组电磁场出发：

(1)

(2)

(3)

(4)

2数值仿真结果与分析

图1　网格步长为804；空气间隙系数为4.6、2.3、1.15、0.575

图2　网格步长为1 000；空气间隙系数为4.6、2.3、1.15、0.575

(a)

(b)

(c)图3　角频率分别为∧=2.3；∧×10-6/4，∧×10-6/2，∧×10-6

3结论

本文从满足超高速通信系统中空隙带隙型光子晶体光纤电磁场Maxwell方程组出发，利用时域有限差分法对其方程组在直角坐标系中三维矢量变换和差分离散求解，以此建立适合合适入射激励源光波传输模型。通过数学建模与程序模拟发现：当角频率w0数值增大，TM波x,y方向中心强度与网格增大呈正比变化，在三维矢量z方向TE波其振幅随着网格步长递增抖动愈加频繁，且峰值大小与步长呈正比变化、脉冲波形逐渐压缩变化；同时，随着超高速通信系统中空隙带隙型光子晶体光纤空气间隙增大，其TE波在直角坐标系中三维矢量数值大小与网格步长递增呈正比变化，且瞬态截面分裂速度减小、体积变大；反之，当空气孔间隙减小，其TM波三维矢量随着传输网格步长递增，瞬态截面分裂呈细丝状、体积变小。因此，上述研究为进一步研究超高速通信系统中空隙带隙型光子晶体光纤中电磁场关系提供一定理论基础。

参考文献：

[1]Haque M M,Rahman M S,Habib M S,et al.Design and characterization of single mode circular photonic crystal fiber for broadband dispersion compensation[J].Optik-International Journal for Light and Electron Optics,2014,125(11):2608-2611.

[2]Ahmad,Redwan,et al."Design of a photonic crystal fiber for dispersion compensation over telecommunication bands." Electrical Information and Communication Technology (EICT),2013 International Conference on.IEEE,2014.

[3]Saitoh K,Koshiba M.Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window[J].Optics Express,2004,12(10):2027-2032.

[4]Cao L,Wei B.Scattering of targets over layered half space using a semi-analytic method in conjunction with FDTD algorithm[J].Optics express,2014,22(17):20691-20704.

[5]Sa Z,Poo Y,Wu R,et al.An implementation of directional antenna by self-biased magnetic photonic crystal[J].Applied Physics A,2014,117(2):427-431.

[6]曾辉,卓辉.超高速光纤通信系统中孤子间稳定传输滤波器补偿效应研究[J].激光杂志,2015,01:87-89.

[7]Gebert F,Frosz M H,Weiss T,et al.Damage-free single-mode transmission of deep-UV light in hollow-core PCF[J].arXiv preprint arXiv:1404.6159,2014.

[8]Nakajima K,Zhou J,Tajima K,et al.Ultrawide-band single-mode transmission performance in a low-loss photonic crystal fiber[J].Lightwave Technology,Journal of,2005,23(1):7-12.

[9]Nicholson J W,Mangan B,Meng L,et al.Low-loss,low return-loss coupling between SMF and single-mode,hollow-core fibers using connectors[C]//CLEO:Applications and Technology.Optical Society of America,2014:JTu4A.71.

[10] Okaba S,Takano T,Benabid F,et al.Lamb-Dicke spectroscopy of atoms in a hollow-core photonic crystal fibre[J].Nature communications,2014,5.

[11] Muduli N,Palai G,Tripathy S K.Analysis of nonlinear PCF for birefringence application using FDTD method[J].Optik-International Journal for Light and Electron Optics,2014.

[12] Debord B,GéF,Alharbi M,et al.High energy pulse compression regimes in hypocycloid-core kagome hollow-core photonic crystal fibers[C]//CLEO:Science and Innovations.Optical Society of America,2014:SF2N.4.

[13] Hooper L E,Mosley P J,Muir A C,et al.Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion[J].Optics express,2011,19(6):4902-4907.

[14] Azhar M,Wong G K L,Chang W,et al.Raman-free nonlinear optical effects in high pressure gas-filled hollow core PCF[J].Optics express,2013,21(4):4405-4410.

[15] Jie Z X,Lu X N.HF scattering induced by field-aligned irregularities in the equatorial-region during total solar eclipses[J].Journal of atmospheric and terrestrial physics,1985,47(8):945-949.

[16] 郭俊杰.基于STM32单片机的视频摇控小车[J].大学物理实验，2015，4(15)：47-50.

Research Gap Transient Three-Dimensional Photonic Crystal Fiber Section Properties FDTD Method in the Ultra-High-Speed Communication System

ZENG Hui1,2,3,YANG Qiao-yun1,ZHUO Hui2,3

(1.Technology Co.,Ltd.Zhuhai Hamilton Sundstrand，Guangdong Zhuhai 519180；2.Hunan University,Hunan Changsha 410012；3.Hunan Agricultural University，Hunan Changsha 410128)

Abstract：The finite difference time-domain electromagnetic method for three-dimensional vector transformation to meet with a coupled-cavity PCFS conditions Maxwell equations to build on the incident light propagation in photonic crystal fibers physics numerical models.Numerical simulations show that:in the waveguide dispersion effect,when the air gap increases,the TE wave in the Cartesian coordinate system and the grid size three-dimensional vector value is proportional to the change in increments,and the transient section split speed decreases,the volume change large；on the contrary,when the air hole gap decreases,its three-dimensional vector with TM wave transmission grid in increments,transient section was split filaments,smaller size.Meanwhile,with the angular frequency w0 increases,the magnetic field direction of the center of intensity with time change and the grid was symmetrical peak intensity gradually increasing；while in L + Nd = 150 (N = 0,1,2；L> 0) exist at inflection point；the direction of the electric field amplitude peak jitter increasingly frequent and continuous rise,gradually decreasing the peak phase and pulse compression was changed.

Key words：FDTD method；waveguide dispersion；gap bandgap photonic crystal fiber；Maxwell equations

中图分类号：TN 913.7

文献标志码：A

DOI：10.14139/j.cnki.cn22-1228.2016.001.001

文章编号：1007-2934(2016)01-0001-07

基金项目：国家863 计划(2004AA84ts12)、 国家自然科学基金(10576012)、国家自然科学基金重点项目(60538010)；国家自然科学基金项目(10674045)；国家科技部“国家星火计划”项目(2011GA770001);国家科技部“十二五”重点课题(2011BAD21B03)；国家科技部“十二五”重点课题(2012BAD35B05)；国家科技部“十二五”科技支撑计划课题(2012BAD35B00)；教育部新世纪优秀人才支持计划项目；高等学校博士点基金资助项目( YB2010B024)；湖南省教育厅科学研究重点项目(12A062)；湖南省科技厅计划重点项目(2013GK3106)；湖南农业大学人才引进基金项目(08YJ02)；湖南省研究生科研创新课题(2014YJS540401001)；新型农业信息传感技术创新团队项目(92020200004)

收稿日期：2015-09-09