单模光纤的三维模场分布资料讲解

1、单模光纤的三维模场分布精品资料1单模光纤12单模光纤模场分布近似13 MATLAB语言63.1主程序63.2调用函数 93.3程序运行说明114总结16仅供学习与交流，如有侵权请联系网站删除谢谢精品资料1单模光纤在工作波长中，只能传输一个传播模式的光纤，通常简称为单模光纤（SMF SingleModeFiber）。由于光纤的纤芯很细（约10pm而且折射率呈阶跃状分布，当归一化频率V参数v 2.4时，理论上只能形成单模传输。2单模光纤模场分布光纤中的电磁波可以看成时谐场，满足亥姆霍兹方程，与电磁波理论中的做法一样,先求解z方向分量，然后再由麦克斯韦方程组求得其他分量采用柱坐标，z方向的分量满足亥

2、姆霍兹方程dr r dtp仅供学习与交流，如有侵权请联系网站删除谢谢20如果求得z方向的分量，其他各横向分量可以用 z分量表示出来阶跃光纤中的电磁场解及导波模的截止参数心=si n池心=庞V角叫皿小H諒=疋%心（歹）m朴肚o w厂w貯r > a0 W F W Br > a式中，A、B待疋常数，Jm : m阶第一类贝塞尔函数，Km m阶第二类变形贝塞尔函数。U=kcaWfeuau表示导波模场在纤芯内部的横向分布规律， w表示它在包层中的横向分布规律，两者结合起来，就可以完整地描述导波模的横向分布规律 ；B是轴向的相位传播常数，表明导波模的纵向传输特性。与电磁学公式比较11 11111

3、 J ''一1F1 1!111 A3li1几个低阶第二类变形贝塞尔函数曲线用纵向分量表示的其他分量利用边界条件得到特征方程:r几(u) 甩爲(甲)屛几2) 兄k爲(审) /ujjin WKtn( W)1 UJm(U) + WK Wy J对于实际使用的光钎可以引入弱导条件而得到的简化方程。 简化的特征方程，n 心(炉)I丄亠_iUJm ( in + WKm W) = 士叫 IJ2 + JF2/22 2 _1 _12 2u wJ'(u)uJv(u)上面这些公式与电磁场与电磁波中公式完全相同，求解很困难，一般用数值法，如果只求各 种模式的截止条件，只需令 W2二0，求解满足边

4、界条件的U,则相对简单一些K；(w) k2 J：(u) k2 K；(w)w©(w) . 1 uJv(u) 2 wKv(w)本征方程是反映导波模涉及到的参数 u、w和B之间相互关系的方程，对于弱导光纤 (n 1F2)则可得到本征方程Jv'(u) Kv'(w)uJ v(u) wK v(w)当W=o,对应包层中导波模和辐射模的转折点或临界点，可以在此条件下求解纤芯内的归一 化相位常数Uo导波模一共可以分成4种模式即，TE)n、TMn、EHmn、H®。在电磁波课程中我 们已经得到了这些模的截止波长，下面直接写出结果。2 -唱八T%模的截止液长4(TE0n，0n )

5、=-%EH耐模的截止波长%2 HE时模的截止菠长，m>2/ (肛詁=丄冬曲一喝卩HE甸模的截止液长5"&(HE= 3(卅-卅卡巩I亠上面这些式子中，uxy表示x阶贝塞尔函数的第y个零点，下面表5.1是几个低阶贝塞尔函 数的零点位置。HE11模对应0阶贝塞尔函数的第零个零点JntU的第n个根Umnn m012312.404833.831715.135626.3801625.520087.015598.417249.7610238.6537310.1734711.6198413.01520411.7915312.3236914.7959616.22347514.930492

6、16.6317.9598214.40942定义另一个重要的特征参量，V,称为光纤的归一化频率，是一个无量纲的参数V = nJ 局）2 二 | aV2 = U2 + 叨二 ka2（ n-局）当W2 = 0时，相应的u记为Uc, V记为Vc, Vc称之为归一化截止频率。显然，此时 Uc=Vc 且:Vca（n：2n2这样，光纤中任意一个模式的传播条件是:2 a 222V Vc（ni 匕）2c光纤中单模传播的条件是：0 V 2.4053 MATLA语言3.1主程序1、运行框位置大小抬头默认文本绘图相框位置背景颜色运行框位置大小框gcc=figure( 'Positi on'设置程序抬头

7、,10,50,1100,660);set(gcc,uic on trol(gcc,'String' ,0.8 0.9);设置交互区域框'Menubar', 'none' , 'Name','单模光钎的三维模场分布','NumberTitle''Style' , 'text' , 'Units' , 'normalized'单模光钎的三维模场分布，Fontsize',24,'Position''Horiz

8、ontal','off');,0.01,0.35,0.05,0.6,'center' , 'Back' ,0.5uic on trol(gcc,24, 'Back' 设置绘图框'Style' , 'Frame' , 'Units' , 'normalized' ,1,1,1);，Positi on',0.15,0.015,0.8,0.b=axes('Positi on'设置程序背景颜色,0.15,0.3,0.8,0.68);set(gc

9、c, 'color',0.5 0.8 0.9);2、视图缩放功能通过改变坐标轴的值改变视图大小uic on trol(gcc,'Style' , 'text'，Un its'，no rmalized',0.21,0.075,0.04,.'String' ,'同比例缩放，COM= 'j=get(hdxy z, ''Value'');'f,f,''ylim'',-f,f,''zlim'',0,g);&

10、#39;，Fon tsize',15, 'Positio n',0.04'Fon tsize','f=5*j;',12, 'Horizo ntal','g=1*j;','left','set(b,''xlim'',-,'Back' ,1 1 0.4);hdxyz=uic on trol(gcc, ,0.12,0.04,.'Style'，slider','Units' , 'normaliz

11、ed','Position',0.015,0.18'Mi n',0, 'Max' ,2, 'Value',1, 'Call',COM);uicontrol(gcc,'Style', 'text','Units','normalized','Fontsize',15,卩 ositio n',0.043,0.13,0.07,0.04,.'String', 'z 方向缩放','Fonts

12、ize',12, 'Horiz on tal','left', 'Back',1 1 0.4);COM0= 'l=get(hdz,''Value'');','set(b,''zlim'',0,l);'hdz=uic on trol(gcc,'Style','slider','Units', 'normalized', 'Position',0.015,0.1,0.1

13、2,0.04,.'Mi n',0, 'Max' ,2, 'Value',1, 'Call',COM0);uicontrol(gcc,'Style', 'text','Units','normalized','Fontsize',15,卩 ositio n',0.04,0.05,0.075,0.04,.'String', 'xy 方向缩放','Fontsize',12, 'Horiz on

14、tal','left', 'Back',1 1 0.4);COM仁'k=get(hdxy,"Value");'，set(b,"xlim",-k,k,"ylim",-k,k);'hdxy=uicontrol(gcc,'Style' , 'slider' , 'Units' ，normalized' , 'Position',0.015,0.02,0.12,0.04,.'Min' ,2,

15、'Max' ,10, 'Value' ,5, 'Ca ll',COM1);3、加设菜单更改图像背景颜色截图运行程序建立程序使用说明hview=uime nu(hsz,'Label','转换视角，'Separator','on');uime nu(hview,'Label','侧视图:,'Accelerator','z','Call','view(90,0)'uime nu(hview,'Label

16、','俯视图:,'Accelerator','x','Call','view(0,90)'uime nu(hview,'Label','原视图:,'Accelerator','c','Call','view(-37.5,30)'建立旋转动画COM= 'for el=-10:1:150','view(-37.5,el);','grid off;','drawnow;'

17、, 'gridon;' , 'end'hxz=uime nu(hview,'Label','旋转动画，'Accelerator','v','Call',COM);hsz=uime nu(gcc,'Label','设置);建立更改绘图图像的背景颜色菜单htbjs=uime nu(hsz,'Labe l','图像背景颜色，uime nu(htbjs,'Label','草绿色','Call'uime n

18、u(hzbc,'Labe l','天青色','Call'uime nu(hzbc,'Labe l','橙红色，Call'uime nu(hzbc,'Labe l','取消颜色','Call'建立截图菜单COM1= 'saveas(gcc,''Mypictures'',''jpg'');'Separator' , 'on');,'set(gca,'&#

19、39;Color'',0.7 0.9 0.4)');,'set(gca,''Color'',0.5 0.8 0.9)');,'set(gca,''Color'',0.9 0.4 0.3)');,'set(gca,''Color'',1 1 1)');hSPC=uime nu(gcc,'Label','文件');uime nu(hSPC,'Label','运行程序截图,

20、9;Call',COM1);uime nu(hSPC,'Label','打开程序路径,'Call','winopen(pwd);')uime nu(hSPC,'Label','打开程序截图','Call', 'b=strcat(pwd,''Mypic.jpg'');','winopen(b)');建立程序使用说明菜单COM2=单模光纤的三维模场分布.doc'');', 'winopen(a

21、);'hhelp=uime nu(gcc.'Label','帮助');uime nu(hhelp.'Label' ,'程序使用说明','Call' ,C0M2);4、滑动条滑动条主程序hsli1=uic on trol(gcc,'Style' , 'slider'，Un its'，no rmalized','Position',0.2,0.14,040.04,'Min' ,0.1, 'Max' ,2.1845,

22、'Value' ,1.6453, 'CallBack','set(azmcur,''String');','num2str(get(hsli1,''Value'');'set(gcc,''Positio n'',10,50,1100,660);'标记滑动条最小值azm min=uic on trol(gcc,'Style','text','Units', 'normalized&#

23、39;,'Fon tsize',12,卩 osition',0.155,0.14,0.045,0.04,'Str in g',n um2str(get(hsli1,'Mi n'),'Back',1,1,1);标记滑动条最大值azmmax=uic on trol(gcc,'Style','text','Units', 'normalized','Fon tsize',12,卩 osition',0.61,0.14,0.045,0.04,&

24、#39;Stri ng',n um2str(get(hsli1,'Max'),'Back',1,1,1);设置输出值位置uic on trol(gcc,'Style','text','Units','normalized','Position',0.25,0.2,0.04,0.04,'String', 'U =', 'Fontsize',15, 'Horizontal', 'left','

25、Back',1,1,1);滑动条返回值azmcur=uic on trol(gcc,'Style','text','Units', 'normalized','Fon tsize',15,卩 osition',0.29,0.2,0.06,0.04,'Stri ng',n um2str(get(hsli1,'Value'),'Back',0.9,0.8,0.9);触发函数COM3= 'n=str2num(get(azmcur,''

26、String'');' );'设置文本区域,'set(UW,''String'',num2str(dataUW(n)UW=uic on trol(gcc,'Style' , 'Text' , 'Units','normalized','String',1.7473,'Fontsize'15, Position',0.48,0.2,0.07,0.04,'Back' ,0.9 0.8 0.9);函数触发按钮u

27、ic on trol(gcc,'Style' , 'Push' , 'Units','normalized','Position',0.38,0.2,0.07,0.04,10, 'Ca ll' ,COM3);,'String' ，'对应 Wt' , 'fontSize'第二个滑动条程序雷同此处不作赘述5 、计算归一化函数值触发函数C0M5= 'aa=str2num(get(azmcur,"String");''

28、;,'set(scz,''String'',num2str(cc(aa,bb);','bb=str2num(get(elvcur,"String'');；scz=uic on trol(gcc,'Style' , 'Text' , 'Units'，no rmalized','String' ,2.405,'Position'0.81,0.17,0.12,0.05,'Horiz ontal','cente

29、r' , 'Fontsize',15, 'Back' ,0.9 0.8 0.9);设置输出文本区域函数触发按钮uic on trol(gcc,'Style' , 'Push' , 'Units', 'normalized'，卩 osi',0.67,0.17,0.12,0.05,10, 'Ca ll' ,COM5);String' ,'计算归一化频率 V' , 'fontSize'6 、绘图按钮关闭按钮uic on trol(gc

30、c,'Style','push','Units','normalized','Fontsize',18,卩 ositio n',0.67,0.04,0.12,0.1,'Str in g','绘图','Call', 'COMM(hsli1,hsli2)')；uic on trol(gcc,'Style','push','Units','n ormalized','Fontsi

31、ze',18,卩 ositio n'J 0.765,0.045,0.08,0.08,'Str in g','动画','Call',COM);uic on trol(gcc,'Style','push','Units','n ormalized','Fontsize',18,卩 ositio n',0.81,0.04,0.12,0.1,'Stri ng'I5关闭','Call','close all

32、')；3.2调用函数(1) COMM绘图函数fun ctionCOMM(hsli1,hsli2)如果归一化频率大于2.4048程序将会报错并不会执行绘图指令U=get(hsli1,'Value');W=get(hsli2,'Value');M=sqrt(U.A2+W.A2);if M>2.4048msgbox('归一化频率大于2.4048 ，请更换计算公式！如果归一化频率小于等于2.408程序将会运行绘图指令elseN=201;R1=li nspace(0,1,N);R2=li nspace(1,5,N);Theta1=li nspace(

33、0,2*pi,N);Theta2=li nspace(0,2*pi,N);E1= zeros(N,N);E2=zeros(N,N);I1=E1;I2=E2;for i = 1:NE1(:,i)=besselj(0,U*R1);I1(:,i)=E1(:,i).A2;endfor i = 1:NE2(:,i)=besselj(0,U).*besselk(0,W.*R2)./besselk(0,W);I2(:,i)=E2(:,i).A2;endThetal, R1=meshgrid (T heta1,R1); Theta2, R2=meshgrid (T heta2,R2); X1, Y1=pol2

34、cart(Theta1,R1);X2, Y2=pol2cart(Theta2,R2);mesh(X1,Y1,l1);hold onmesh(X2,Y2,I2);colorbarxlabel('x')ylabel('y')zlabel('z')pause(1)hold offend(2) cc计算归一化频率，若大于2.4048程序将会报错 程序计算完后将会返回V值fun cti on V=cc(aa,bb)V1=sqrt(aa.A2+bb.A2);if V1>2.4048msgbox('请确认归一化频率0<V<2.408',' 提示!');endV=sqrt(aa.A2+bb.A2);(3) function W=data_UW(n)用于对输入的U查询对应的W值 并将其返回到原函数fun ctio n W=data_UW( n)U2=因数据过于庞大故略; W2=因数据过于