脈沖在光纖中的傳輸PPT課件

1、你應(yīng)該掌握什么?1.光纖中的光場(chǎng)遵循什么規(guī)律?2.如何描述光場(chǎng)?3.如何描述光場(chǎng)與光纖介質(zhì)的相互作用?4.如何描述脈沖？5.如何描述光脈沖在光纖中的傳播?6.如何數(shù)值求解非線性Schrodinger方程?I recommend that you grasp them.I recommend that you grasp them.第1頁(yè)/共35頁(yè)Electric (E) and magnetic (B) fields are in phase. The electric field, the magnetic field, and the propagationdirection are al

2、l perpendicular. 第2頁(yè)/共35頁(yè)MHBPED00 ,. 0,BDDJHBEfttMaxwells equations govern the propagation of light !But 光與物質(zhì)如何聯(lián)系呢光與物質(zhì)如何聯(lián)系呢?物質(zhì)方程Especially, 對(duì)于光纖介質(zhì)對(duì)于光纖介質(zhì): =0, J= 0, M = 0第3頁(yè)/共35頁(yè)第4頁(yè)/共35頁(yè)Derivation of the Wave Equation from Maxwells Equations Take of: Change the order of differentiation on the RHS: BE

3、t BEt EBt 第5頁(yè)/共35頁(yè)Derivation of the Wave Equation from Maxwells Equations (contd)But: Substituting for , we have: where c2=1/ 0 0 BPEDHB0000tt2202221ttcPEE第6頁(yè)/共35頁(yè)For P = 0, homogeneous Wave Equation;But here P 0, Inhomogeneous Wave Equation. The polarization is the driving term for a new solution t

4、o this equation.22022022221tttcNLLPPEEEEEE220ED第7頁(yè)/共35頁(yè) P 與光場(chǎng)的關(guān)系如果瞬時(shí)性和局域性成立, 則 P 與 E 的關(guān)系為 )3(0)2(0)1(0EEEEEPEPPPPNLLNLL但是, 事項(xiàng)總是有因果性, 前因后果. 所以瞬時(shí)性一般不成立, 那么 P 與 E 的關(guān)系如何呢?第8頁(yè)/共35頁(yè) P 與光場(chǎng)的普適關(guān)系 如果局域性仍然成立, 并考慮到三階非線性, 則 光纖中P 與 E 的關(guān)系為 321321321)3(0)1(0, ,dtdtdttrtrtrttttttt dtrtttrNLLNLLEEEPEPPPP 問(wèn)題太復(fù)雜, 可簡(jiǎn)化嗎?

5、第9頁(yè)/共35頁(yè) P 與E的簡(jiǎn)單關(guān)系2)3()1()3(0)1(000,431 trEEPEPPPEEPxxxxNLxxLNLLxxxxxNLNLxxLNLLNLL 極化率是復(fù)數(shù)極化率是復(fù)數(shù), , 實(shí)部和虛部分別與介質(zhì)的折實(shí)部和虛部分別與介質(zhì)的折射率和吸收系數(shù)有關(guān)射率和吸收系數(shù)有關(guān). .第10頁(yè)/共35頁(yè) P 與E的簡(jiǎn)單關(guān)系222)3(002)3(20)1(020202,83 2,4312trEntrEnnnntrEnnnnnnnxxxxxxxxNLxxLNLL 奇怪奇怪! ! 介質(zhì)的折射率怎么與光場(chǎng)有關(guān)介質(zhì)的折射率怎么與光場(chǎng)有關(guān)? ?這就是非線性這就是非線性光學(xué)光學(xué), ,沒(méi)什么復(fù)雜的沒(méi)什么復(fù)

6、雜的, ,只不過(guò)光強(qiáng)改變了折射率罷了只不過(guò)光強(qiáng)改變了折射率罷了. . 假設(shè)介質(zhì)沒(méi)有吸收假設(shè)介質(zhì)沒(méi)有吸收, ,則極化率為實(shí)數(shù)則極化率為實(shí)數(shù)第11頁(yè)/共35頁(yè)下一步做什么? cctzitzAyxFxtrE.exp,21,00快變振蕩部分第12頁(yè)/共35頁(yè)你若有興趣, 請(qǐng)參考試一試, 考考你的數(shù)學(xué)能力. 你若嫌麻煩, 那么只要你承認(rèn)這個(gè)方程并理解各項(xiàng)的物理意義就行了. 以后的工作全指望了!第13頁(yè)/共35頁(yè)第14頁(yè)/共35頁(yè)第15頁(yè)/共35頁(yè)到底用哪個(gè)方程？需考慮哪些項(xiàng)？ 脈沖寬度：T0 5 ps, 不考慮高階項(xiàng)；50fsT00) or decreases (0) linearly with tim

7、e.0( )exp( )E titt2( ) tt 0( )/insttddt0( )2insttt第23頁(yè)/共35頁(yè)-6-4-202460.00.10.20.30.40.50.60.70.80.91.01/e0.52T0TFWHM IntensityT Gaussian S-Gaussian Sech第24頁(yè)/共35頁(yè)The Time-Bandwidth Product of a Chirped Gaussian Pulse 無(wú)啁啾情況下（C=0）, Fourier-Transform Limited. 有啁啾情況下（C0）, 若T0不變，則譜加寬；若譜寬不變，則脈寬加寬。201CT第25頁(yè)

8、/共35頁(yè)Anjan Biswas， J. Opt, A, 2002, 4: 84-97J. Santhanam, Opt. Commun., 222: 413-420第26頁(yè)/共35頁(yè)The NLSE can be generally written asThe dispersion operator, , and the nonlinear operator, . For dispersion step, , this equation can be easily solved by using Fourier transformation, For nonlinear step, , t

9、he equation has the former solution, Thus, the solution to the NLSE isANDzA2222tiD2AiNADzA tzAzzAzDzAzizAzzAzzAizzzAtempFFT,exp,exp,12222AAiANzA2 zzzdztzAitzAtzzA2,exp, zzztemptempdztzAitzAtzzA2,exp,第27頁(yè)/共35頁(yè)第28頁(yè)/共35頁(yè)第29頁(yè)/共35頁(yè) )4()3()2()1(11,2expexp2exp,tzAFDzFdzNFDzFtzzAzzz 2222222example,For iDtit

10、DDtDitsmall. very for zzNdzNzzz第30頁(yè)/共35頁(yè) Step 1. Define the initial data (e.g. Gauss or sech); Step 2. linear propagation half a step z/2 (i.e., Fourier transform the data, multiply by the quadratic phase factor , and invert the transform); Step 3. multiply by the nonlinear exponential term; Step 4.

11、 linear propagation a full step z (i.e., Fourier transform the data, multiply by the quadratic phase factor , and invert the transform); Step 5. repeat step 3 until the point (L- z/2) is reached, and then branch to step 6; Step 6. linear propagation half a step z/2 (i.e., Fourier transform the data,

12、 multiply by the quadratic phase factor , and invert the transform). Dz2exp Dz2exp Dz2exp第31頁(yè)/共35頁(yè)P(yáng)roblems about Numerical Simulations on NLSE How to sampling an initial pulse; 如果時(shí)間域取樣間隔為0.5fs, 取樣點(diǎn)數(shù)為2048， 那么頻率域分辨率是多少？ 如何實(shí)現(xiàn)線性傳輸； 使用Fourier正變換和逆變換的目的是什么？ 如何實(shí)現(xiàn)非線性傳輸？第32頁(yè)/共35頁(yè)Summary 光是一種電磁波, 它遵循Maxwell方程組; 光與物質(zhì)的相互作用體現(xiàn)在感應(yīng)極化上. 在光纖中, 它具體表現(xiàn)為光強(qiáng)導(dǎo)致介質(zhì)的折射率發(fā)生改變; 光場(chǎng)是隨時(shí)間變化的三維矢量場(chǎng). 對(duì)于光纖中的光場(chǎng), 可表