【光波电子学】MATLAB绘制光纤中线性偏振模式LP之单模光纤的电场分布(光斑)

向右看齐 2022-11-16 08:28 297阅读 0赞

### 目录 ###

*  1 理论
 *  2 单模光纤的二维分布
 *  3 单模光纤的三维分布

多模光纤的分析参考本人另一篇博客  
[【光波电子学】MATLAB绘制光纤中线性偏振模式LP之多模光纤的电场分布(光斑)][MATLAB_LP]

# 1 理论 #

光纤中，在弱导近似下，由 H E l + 1 , m HE\_\{l+1,m\} HEl\+1,m模和 E H l − 1 , m EH\_\{l-1,m\} EHl−1,m模组合的模式是一个线性偏振模式英文是(linear polorized mode)简称为 L P l m LP\_\{lm\} LPlm。根据资料以下是 L P l m LP\_\{lm\} LPlm模和导出或构成它的模式、简并度及模式特征方程。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center]

单模光纤中 L P 01 LP\_\{01\} LP01模在纤芯和包层的归一化电场分布公式表示为  
 E ( R a ) = \{ J 0 ( R R a ) R a ≤ 1 J 0 ( U ) K 0 ( W R a ) K 0 ( W ) R a > 1 E(R\_a) = \\begin \{cases\} J\_0(RR\_a) &R\_a \\leq 1 \\\\ J\_0(U) \\frac\{K\_0(WR\_a)\}\{K\_0(W)\} & R\_a >1 \\end \{cases\} E(Ra)=\{ J0(RRa)J0(U)K0(W)K0(WRa)Ra≤1Ra>1  
利用此关系，既可得到归一化的 L P 01 LP\_\{01\} LP01模在纤芯和包层区的电场分布曲线  
根据求解的 L P 01 LP\_\{01\} LP01的U、V、W 关系的得到以下表格，当V = 2.4000时，U= 1.6453， W= 1.7473  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 1]

# 2 单模光纤的二维分布 #

V =2.4000;
    U =1.6453;
    W = 1.7473;
    
    Npoint = 501;
    R1 = linspace(-5,5,Npoint);
    R2 = linspace(-5,5,Npoint);
    
    X= meshgrid(R1,R2);
    Y= meshgrid(R2,R1);
    Y = Y';
    R = sqrt(X.^2+Y.^2);
    
    % Theta = atan(Y./(X+eps));
    
    % 光纤中光芯光场分布
    E1 = besselj(0,U*R);
    I1 = E1.^2;
    
    % 光纤中包层的光场分布
    E2 = besselj(0,U).*besselk(0,W.*R)./besselk(0,W);
    I2 = E2.^2;
    I = I1 ;
    pos = find(R>=1);
    I(pos) = I2(pos);
    
    % 作图
    imagesc(R1,R2,I,[0 1]);
    colormap(gray);
    colorbar
    xlabel('x')
    ylabel('y')
    zlabel('z')
    zlabel('z')

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 2]

# 3 单模光纤的三维分布 #

clear
    close all
    V =2.4000;
    U =1.6453;
    W = 1.7473;
    
    Npoint = 201;
    R1 = linspace(0,1,Npoint);
    R2 = linspace(1,5,Npoint);
    Theta1 = linspace(0,2*pi,Npoint);
    Theta2 = linspace(0,2*pi,Npoint);
    
    E1 = zeros(Npoint,Npoint);
    E2 = zeros(Npoint,Npoint);
    I1 = E1;
    I2 = E2;
    
    for i = 1:Npoint
        E1(:,i) = besselj(0,U*R1);
        I1(:,i) = E1(:,i).^2;
    end
    
    for i = 1:Npoint
        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)
    colorbar
    xlabel('x')
    ylabel('y')
    zlabel('z')

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 3]

[MATLAB_LP]: https://betterbench.blog.csdn.net/article/details/115492365
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center]: /images/20221022/55bd5f2bb341495ea6f22c1e6323ee64.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 1]: /images/20221022/10928c856482479992afcb721fb4daa3.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 2]: /images/20221022/239d92913b9144f1a2a065c7d22cb527.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkzNTY5Ng_size_16_color_FFFFFF_t_70_pic_center 3]: /images/20221022/783696b35bab432186fc25ee5bfebc05.png