Using quiver plot，how to show the states of polarization (SoP) in vector beams

As shown in the figure, I want to plot the polarization state of this radial or angular vector beam。

Answer 1

[Malay Agarwal]

Hi @明泽,

For a radially polarized beam, the electric field vectors point away from the center of the beam. The polarization vector at any point (x, y) in the plane can be represented as:

Similarly, for an angularly polarized beam, the electric field vectors are tangential to circles centered on the beam axis. The polarization vector at any point (x, y) can be represented as:

Given this information, the SOPs can be plotted as follows:

% Parameters
% TODO: Replace with your data for the vector beam
gridSize = 20; % Size of the grid
[X, Y] = meshgrid(linspace(-1, 1, gridSize), linspace(-1, 1, gridSize));

% Radial polarization vectors
Ex_r = X ./ sqrt(X.^2 + Y.^2);
Ey_r = Y ./ sqrt(X.^2 + Y.^2);

% Azimuthal polarization vectors
Ex_a = -Y ./ sqrt(X.^2 + Y.^2);
Ey_a = X ./ sqrt(X.^2 + Y.^2);

% Handling the singularity at (0,0)
Ex_r(isnan(Ex_r)) = 0;
Ey_r(isnan(Ey_r)) = 0;
Ex_a(isnan(Ex_a)) = 0;
Ey_a(isnan(Ey_a)) = 0;

intensityImage = getIntensityImage(X, Y, gridSize, 0.5);

subplot(1,2,1);
imagesc(unique(X), unique(Y), intensityImage, 'interp', 'bilinear');
hold on;
quiver(X, Y, Ex_r, Ey_r, 0.5, "filled", "Color", "black");
axis equal;
hold off;
title('Radial Polarization');

subplot(1,2,2);
imagesc(unique(X), unique(Y), intensityImage, 'interp', 'bilinear');
hold on;
quiver(X, Y, Ex_a, Ey_a, 0.5, "filled", "Color", "black");
axis equal;
hold off;
title('Angular Polarization');

function image = getIntensityImage(X, Y, gridSize, sigma)
    % Get intensity at each (x, y) point
    I = exp(-((X.^2 + Y.^2) / (2 * sigma^2)));
    
    % Normalize the intensity to be between 0 and 1
    I_normalized = (I - min(I(:))) / (max(I(:)) - min(I(:)));
    
    % Choose a colormap
    cmap = colormap(parula(256)); % Using 'parula' colormap with 256 colors
    
    % Map the normalized intensity values to indices in the colormap
    I_mapped = round(I_normalized * 255) + 1; % Scale and shift indices to 1-256
    
    % Initialize an RGB image
    image = zeros(gridSize, gridSize, 3);
    
    % Assign RGB values for each point
    for i = 1:gridSize
        for j = 1:gridSize
            image(i, j, :) = cmap(I_mapped(i, j), :);
        end
    end
end

The code:

• Generates the (x, y) coordinates for the vector beam. Please replace this with data for your vector beam.
• Creates the radial and angular polarization vectors.
• Creates an intensity map for the vector beam using the function “getIntensityImage”.
• Uses “subplot” with the “hold” command to plot the intensity map and overlay the radial and angular polarization states on the map.

Please refer to the following resources for more information:

• “meshgrid” function - https://www.mathworks.com/help/matlab/ref/meshgrid.html.
• “subplot” function - https://www.mathworks.com/help/matlab/ref/subplot.html.
• “hold” command - https://www.mathworks.com/help/matlab/ref/hold.html.

Hope this helps!

[明泽]

Thank you very much for your help