單模光纖的三維模場分布

1、 目 錄1單模光纖1 2單模光纖模場分布近似13 MATLAB語言6 3.1主程序63.2調(diào)用函數(shù)93.3 程序運(yùn)行說明114 總結(jié)16 231單模光纖 在工作波長中，只能傳輸一個(gè)傳播模式的光纖，通常簡稱為單模光纖（SMF：Single ModeFiber）。由于光纖的纖芯很細(xì)（約10pm）而且折射率呈階躍狀分布，當(dāng)歸一化頻率V參數(shù)2.4時(shí)，理論上只能形成單模傳輸。2單模光纖模場分布光纖中的電磁波可以看成時(shí)諧場，滿足亥姆霍茲方程， 與電磁波理論中的做法一樣，先求解z方向分量，然后再由麥克斯韋方程組求得其他分量。采用柱坐標(biāo)，z方向的分量滿足亥姆霍茲方程: 如果求得z方向的分量，其他各橫向分量可以

2、用z分量表示出來。階躍光纖中的電磁場解及導(dǎo)波模的截止參數(shù) 式中，A 、B 待定常數(shù)， Jm ：m 階第一類貝塞爾函數(shù)，Km：m 階第二類變形貝塞爾函數(shù)。U=kca W=aca u表示導(dǎo)波模場在纖芯內(nèi)部的橫向分布規(guī)律，w表示它在包層中的橫向分布規(guī)律，兩者結(jié)合起來，就可以完整地描述導(dǎo)波模的橫向分布規(guī)律; 是軸向的相位傳播常數(shù)，表明導(dǎo)波模的縱向傳輸特性。與電磁學(xué)公式比較 幾個(gè)低階第一類貝塞爾函數(shù)曲線 幾個(gè)低階第二類變形貝塞爾函數(shù)曲線用縱向分量表示的其他分量利用邊界條件得到特征方程：對(duì)于實(shí)際使用的光釬可以引入弱導(dǎo)條件而得到的簡化方程。簡化的特征方程,上面這些公式與電磁場與電磁波中公式完全相同，求解很困

3、難，一般用數(shù)值法，如果只求各種模式的截止條件，只需令W20，求解滿足邊界條件的U，則相對(duì)簡單一些.本征方程是反映導(dǎo)波模涉及到的參數(shù)u、w和之間相互關(guān)系的方程，對(duì)于弱導(dǎo)光纖（n1n2）則可得到本征方程當(dāng)W2=0,對(duì)應(yīng)包層中導(dǎo)波模和輻射模的轉(zhuǎn)折點(diǎn)或臨界點(diǎn)，可以在此條件下求解纖芯內(nèi)的歸一化相位常數(shù)U。導(dǎo)波模一共可以分成4種模式即，TE0n、TM0n、EHmn、Hemn。在電磁波課程中我們已經(jīng)得到了這些模的截止波長，下面直接寫出結(jié)果。上面這些式子中，uxy表示x階貝塞爾函數(shù)的第y個(gè)零點(diǎn)，下面表5.1 是幾個(gè)低階貝塞爾函數(shù)的零點(diǎn)位置。 HE11模對(duì)應(yīng) 0 階貝塞爾函數(shù)的第零個(gè)零點(diǎn)Jm(U)的第n個(gè)根um

4、nnm012312.404833.831715.135626.3801625.520087.015598.417249.7610238.6537310.1734711.6198413.01520411.7915312.3236914.7959616.22347514.93049216.6317.9598214.40942 定義另一個(gè)重要的特征參量，V,稱為光纖的歸一化頻率，是一個(gè)無量綱的參數(shù)。 當(dāng)W20時(shí)，相應(yīng)的 U 記為 Uc，V 記為Vc， Vc稱之為歸一化截止頻率。顯然，此時(shí)Uc Vc 且： 這樣，光纖中任意一個(gè)模式的傳播條件是： 光纖中單模傳播的條件是：3 MATLAB語言3.1 主程

5、序1、運(yùn)行框位置 大小 抬頭 默認(rèn)文本框 繪圖相框位置 背景顏色運(yùn)行框位置 大小gcc=figure('Position',10,50,1100,660);設(shè)置程序抬頭set(gcc,'Menubar','none','Name','單模光釬的三維模場分布','NumberTitle','off');uicontrol(gcc,'Style','text','Units','normalized','Positi

6、on',0.01,0.35,0.05,0.6,'String','單模光釬的三維模場分布','Fontsize',24,'Horizontal','center','Back',0.5 0.8 0.9); 設(shè)置交互區(qū)域框uicontrol(gcc,'Style','Frame','Units','normalized','Position',0.15,0.015,0.8,0.24,'Back',1

7、,1,1); 設(shè)置繪圖框b=axes('Position',0.15,0.3,0.8,0.68); 設(shè)置程序背景顏色set(gcc,'color',0.5 0.8 0.9); 2、視圖縮放功能 通過改變坐標(biāo)軸的值改變視圖大小uicontrol(gcc,'Style','text','Units','normalized','Fontsize',15,'Position',0.04,0.21,0.075,0.04,. 'String','同比例縮

8、放','Fontsize',12,'Horizontal','left','Back',1 1 0.4); COM='j=get(hdxyz,''Value'');','f=5*j;','g=1*j;','set(b,''xlim'',-f,f,''ylim'',-f,f,''zlim'',0,g);'hdxyz=uicontrol(

9、gcc,'Style','slider','Units','normalized','Position',0.015,0.18,0.12,0.04,. 'Min',0,'Max',2,'Value',1,'Call',COM);uicontrol(gcc,'Style','text','Units','normalized','Fontsize',15,'Posit

10、ion',0.043,0.13,0.07,0.04,. 'String','z方向縮放','Fontsize',12,'Horizontal','left','Back',1 1 0.4); COM0='l=get(hdz,''Value'');','set(b,''zlim'',0,l);'hdz=uicontrol(gcc,'Style','slider',&#

11、39;Units','normalized','Position',0.015,0.1,0.12,0.04,. 'Min',0,'Max',2,'Value',1,'Call',COM0);uicontrol(gcc,'Style','text','Units','normalized','Fontsize',15,'Position',0.04,0.05,0.075,0.04,. 'St

12、ring','xy方向縮放','Fontsize',12,'Horizontal','left','Back',1 1 0.4); COM1='k=get(hdxy,''Value'');','set(b,''xlim'',-k,k,''ylim'',-k,k);'hdxy=uicontrol(gcc,'Style','slider','Un

13、its','normalized','Position',0.015,0.02,0.12,0.04,. 'Min',2,'Max',10,'Value',5,'Call',COM1); 3、加設(shè)菜單 更改圖像背景顏色 截圖運(yùn)行程序 建立程序使用說明hsz=uimenu(gcc,'Label','設(shè)置');hview=uimenu(hsz,'Label','轉(zhuǎn)換視角','Separator','on'

14、;); uimenu(hview,'Label','側(cè)視圖','Accelerator','z','Call','view(90,0)'); uimenu(hview,'Label','俯視圖','Accelerator','x','Call','view(0,90)'); uimenu(hview,'Label','原視圖','Accelerator',&

15、#39;c','Call','view(-37.5,30)');建立旋轉(zhuǎn)動(dòng)畫COM='for el=-10:1:150','view(-37.5,el);','grid off;','drawnow;','grid on;','end'hxz=uimenu(hview,'Label','旋轉(zhuǎn)動(dòng)畫','Accelerator','v','Call',COM);建立更改繪圖圖像的背景顏

16、色菜單htbjs=uimenu(hsz,'Label','圖像背景顏色','Separator','on'); uimenu(htbjs,'Label','草綠色','Call','set(gca,''Color'',0.7 0.9 0.4)'); uimenu(hzbc,'Label','天青色','Call','set(gca,''Color''

17、,0.5 0.8 0.9)'); uimenu(hzbc,'Label','橙紅色','Call','set(gca,''Color'',0.9 0.4 0.3)'); uimenu(hzbc,'Label','取消顏色','Call','set(gca,''Color'',1 1 1)');建立截圖菜單COM1='saveas(gcc,''Mypictures'&

18、#39;,''jpg'');'hSPC=uimenu(gcc,'Label','文件'); uimenu(hSPC,'Label','運(yùn)行程序截圖','Call',COM1); uimenu(hSPC,'Label','打開程序路徑','Call','winopen(pwd);');uimenu(hSPC,'Label','打開程序截圖','Call','b

19、=strcat(pwd,''Mypic.jpg'');','winopen(b)');建立程序使用說明菜單COM2='a=strcat(pwd,''單模光纖的三維模場分布.doc'');','winopen(a);'hhelp=uimenu(gcc,'Label','幫助');uimenu(hhelp,'Label','程序使用說明','Call',COM2); 4、滑動(dòng)條滑動(dòng)條主程序hsli1=

20、uicontrol(gcc,'Style','slider','Units','normalized','Position',0.2,0.14,0.4,0.04,'Min',0.1,'Max',2.1845,'Value',1.6453,'CallBack','set(azmcur,''String'','num2str(get(hsli1,''Value'');'

21、set(gcc,''Position'',10,50,1100,660);');標(biāo)記滑動(dòng)條最小值azmmin=uicontrol(gcc,'Style','text','Units','normalized','Fontsize',12,'Position',0.155,0.14,0.045,0.04,'String',num2str(get(hsli1,'Min'),'Back',1,1,1); 標(biāo)記滑動(dòng)條最大

22、值azmmax=uicontrol(gcc,'Style','text','Units','normalized','Fontsize',12,'Position',0.61,0.14,0.045,0.04,'String',num2str(get(hsli1,'Max'),'Back',1,1,1); 設(shè)置輸出值位置uicontrol(gcc,'Style','text','Units','no

23、rmalized','Position',0.25,0.2,0.04,0.04,'String','U =','Fontsize',15,'Horizontal','left','Back',1,1,1); 滑動(dòng)條返回值azmcur=uicontrol(gcc,'Style','text','Units','normalized','Fontsize',15,'Position',

24、0.29,0.2,0.06,0.04,'String',num2str(get(hsli1,'Value'),'Back',0.9,0.8,0.9); 觸發(fā)函數(shù)COM3='n=str2num(get(azmcur,''String'');','set(UW,''String'',num2str(dataUW(n);'設(shè)置文本區(qū)域UW=uicontrol(gcc,'Style','Text','Units'

25、,'normalized','String',1.7473,'Fontsize',15,'Position',0.48,0.2,0.07,0.04,'Back',0.9 0.8 0.9); 函數(shù)觸發(fā)按鈕uicontrol(gcc,'Style','Push','Units','normalized','Position',0.38,0.2,0.07,0.04,'String','對(duì)應(yīng)W值','fo

26、ntSize',10,'Call',COM3); 第二個(gè)滑動(dòng)條程序雷同 此處不作贅述 5、計(jì)算歸一化函數(shù)值 觸發(fā)函數(shù)COM5='aa=str2num(get(azmcur,''String'');','bb=str2num(get(elvcur,''String'');','set(scz,''String'',num2str(cc(aa,bb);' 設(shè)置輸出文本區(qū)域scz=uicontrol(gcc,'Style

27、9;,'Text','Units','normalized','String',2.405,'Position',0.81,0.17,0.12,0.05,'Horizontal','center','Fontsize',15,'Back',0.9 0.8 0.9); 函數(shù)觸發(fā)按鈕uicontrol(gcc,'Style','Push','Units','normalized','P

28、osi',0.67,0.17,0.12,0.05,'String','計(jì)算歸一化頻率 V','fontSize',10,'Call',COM5); 6、繪圖按鈕 關(guān)閉按鈕uicontrol(gcc,'Style','push','Units','normalized','Fontsize',18,'Position',0.67,0.04,0.12,0.1,'String','繪 圖','C

29、all','COMM(hsli1,hsli2)'); uicontrol(gcc,'Style','push','Units','normalized','Fontsize',18,'Position',. 0.765,0.045,0.08,0.08,'String','動(dòng) 畫','Call',COM); uicontrol(gcc,'Style','push','Units',&

30、#39;normalized','Fontsize',18,'Position',0.81,0.04,0.12,0.1,'String','關(guān) 閉','Call','close all'); 3.2調(diào)用函數(shù)（1） COMM 繪圖函數(shù)function COMM(hsli1,hsli2)如果歸一化頻率大于2.4048 程序?qū)?huì)報(bào)錯(cuò) 并不會(huì)執(zhí)行繪圖指令U=get(hsli1,'Value');W=get(hsli2,'Value');M=sqrt(U.2+W.2);

31、if M>2.4048msgbox('歸一化頻率大于2.4048，請更換計(jì)算公式！','提示!')如果歸一化頻率小于等于2.408 程序?qū)?huì)運(yùn)行繪圖指令else N=201; R1=linspace(0,1,N); R2=linspace(1,5,N); Theta1=linspace(0,2*pi,N); Theta2=linspace(0,2*pi,N); E1=zeros(N,N); E2=zeros(N,N); I1=E1;I2=E2; for i = 1:N E1(:,i)=besselj(0,U*R1); I1(:,i)=E1(:,i).2; end for i = 1:N E2(:,i)=besselj(0,U).*besselk(0,W.*R2)./besselk(0,W); I2(:,i)=E2(:,i).2; end Theta1, R1=meshgrid(Theta1,R1); Theta2, R2=meshgrid(Theta2,R2); X1, Y1=pol2cart(Theta1,R1); X2, Y2=pol2cart(Theta2,R2); mesh(X1,Y1,I1); hold on mesh(X2,Y2,I2