曾　輝，楊喬云，卓　輝

(1.珠海漢勝科技股份有限公司，廣東 珠?！?19180；2.湖南大學(xué)，湖南 長沙　410012；3.湖南農(nóng)業(yè)大學(xué)，湖南長沙　410128)

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時域有限差分法在超高速通信系統(tǒng)中帶隙型光子晶體光纖瞬態(tài)三維截面上特性研究

曾輝1,2，3，楊喬云1，卓輝2，3

(1.珠海漢勝科技股份有限公司，廣東 珠海519180；2.湖南大學(xué)，湖南 長沙410012；3.湖南農(nóng)業(yè)大學(xué)，湖南長沙410128)

摘 要：利用時域有限差分法針對滿足帶耦合腔PCFS條件的Maxwell方程組進行電磁場三維矢量變換，來建立關(guān)于入射光在光子晶體光纖傳播物理數(shù)值模型。通過數(shù)值仿真表明：在波導(dǎo)色散作用下，當(dāng)空氣間隙增大，其TE波在直角坐標(biāo)系中三維矢量數(shù)值大小與網(wǎng)格步長遞增呈正比變化，且瞬態(tài)截面分裂速度減緩且數(shù)目遞減、體積變大；反之，當(dāng)空氣孔間隙減小，其TM波三維矢量隨著傳輸網(wǎng)格步長遞增，瞬態(tài)截面分裂呈細(xì)絲狀且數(shù)目遞增、體積變小。同時，隨著角頻率w0增大，磁場x,y方向中心強度隨時間網(wǎng)格呈對稱式變化且峰值強度逐漸遞增；同時在L+Nd=150(N=0,1,2;l>0)處存在拐點；在電場z方向，振幅抖動愈加頻繁且峰值連續(xù)上漲，相位峰值逐漸遞減且脈寬呈壓縮變化。

關(guān)鍵詞：時域有限差分法；波導(dǎo)色散；空隙帶隙型光子晶體光纖；Maxwell方程組

空隙帶隙型光子晶體光纖(photonic crystal fiber，PCF)[1-3]指由SiO2為主要材料的石英和空氣間隙呈周期性六邊形分布[4-5]；具有波長為微量級的新型光學(xué)材料。其包層含有的排列不對稱的微結(jié)構(gòu)氣孔在寬帶中表現(xiàn)出較為明顯的的非線性效用[6]與單模傳輸[7-9]、以及在可見光波段表現(xiàn)出強烈的雙折射效應(yīng)[10-11]、反常色散[12-14]、瑞麗散射損耗[15]等特征。為此，它也成為目前光子晶體應(yīng)用領(lǐng)域中研究最熱的前沿課題。本文采用時域有限差分法能有效對入射激勵源連續(xù)時間、空間離散化問題進行處理以及解決光源在PGB-PCFS中電場、磁場散射現(xiàn)象。其主要原理為：第一，對入射波源垂直方向的電磁場在時空域角度三維矢量分解；第二，設(shè)置時間軸與空間軸網(wǎng)格固定值為L；第三，運用FDTD算法逐級跳躍遞增方法計算出第N-1個網(wǎng)格TE波、TM波數(shù)值大小進而推算出第n個網(wǎng)格電場值和磁場值；通過計算編碼程序循環(huán)往復(fù)運算求得L,……,L+(N-1)d,L+Nd所有不同時空域變化所處的電磁場值。數(shù)值模擬結(jié)果表明：當(dāng)存在帶耦合腔作用時，空氣間隙∧大小與瞬態(tài)截面分裂數(shù)目呈反比；同時在電場z方向，隨著頻率增大，振幅抖動愈加頻繁且峰值連續(xù)上漲，相位峰值逐漸增大且脈寬呈壓縮變化。

1時域有限差分算法及物理數(shù)值模型

在直角坐標(biāo)系中，從滿足光子晶體光纖TE波和TM波Maxwell方程組電磁場出發(fā)：

(1)

(2)

(3)

(4)

2數(shù)值仿真結(jié)果與分析

圖1　網(wǎng)格步長為804；空氣間隙系數(shù)為4.6、2.3、1.15、0.575

圖2　網(wǎng)格步長為1 000；空氣間隙系數(shù)為4.6、2.3、1.15、0.575

(a)

(b)

(c)圖3　角頻率分別為∧=2.3；∧×10-6/4，∧×10-6/2，∧×10-6

3結(jié)論

本文從滿足超高速通信系統(tǒng)中空隙帶隙型光子晶體光纖電磁場Maxwell方程組出發(fā)，利用時域有限差分法對其方程組在直角坐標(biāo)系中三維矢量變換和差分離散求解，以此建立適合合適入射激勵源光波傳輸模型。通過數(shù)學(xué)建模與程序模擬發(fā)現(xiàn)：當(dāng)角頻率w0數(shù)值增大，TM波x,y方向中心強度與網(wǎng)格增大呈正比變化，在三維矢量z方向TE波其振幅隨著網(wǎng)格步長遞增抖動愈加頻繁，且峰值大小與步長呈正比變化、脈沖波形逐漸壓縮變化；同時，隨著超高速通信系統(tǒng)中空隙帶隙型光子晶體光纖空氣間隙增大，其TE波在直角坐標(biāo)系中三維矢量數(shù)值大小與網(wǎng)格步長遞增呈正比變化，且瞬態(tài)截面分裂速度減小、體積變大；反之，當(dāng)空氣孔間隙減小，其TM波三維矢量隨著傳輸網(wǎng)格步長遞增，瞬態(tài)截面分裂呈細(xì)絲狀、體積變小。因此，上述研究為進一步研究超高速通信系統(tǒng)中空隙帶隙型光子晶體光纖中電磁場關(guān)系提供一定理論基礎(chǔ)。

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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

中圖分類號：TN 913.7

文獻標(biāo)志碼：A

DOI：10.14139/j.cnki.cn22-1228.2016.001.001

文章編號：1007-2934(2016)01-0001-07

基金項目：國家863 計劃(2004AA84ts12)、 國家自然科學(xué)基金(10576012)、國家自然科學(xué)基金重點項目(60538010)；國家自然科學(xué)基金項目(10674045)；國家科技部“國家星火計劃”項目(2011GA770001);國家科技部“十二五”重點課題(2011BAD21B03)；國家科技部“十二五”重點課題(2012BAD35B05)；國家科技部“十二五”科技支撐計劃課題(2012BAD35B00)；教育部新世紀(jì)優(yōu)秀人才支持計劃項目；高等學(xué)校博士點基金資助項目( YB2010B024)；湖南省教育廳科學(xué)研究重點項目(12A062)；湖南省科技廳計劃重點項目(2013GK3106)；湖南農(nóng)業(yè)大學(xué)人才引進基金項目(08YJ02)；湖南省研究生科研創(chuàng)新課題(2014YJS540401001)；新型農(nóng)業(yè)信息傳感技術(shù)創(chuàng)新團隊項目(92020200004)

收稿日期：2015-09-09