How to plot the polarisation distributions in bessel poincare beam showing all singularities present in them

I want to have a plot of normal poincare beam and bessel poincare beam as shown in the figure, does anyone know how to plot like this, Please help me

Answer 1

[Milan Bansal]

Hi Aswathi K

You can use the quiver plot in MATLAB to plot the arrows with specified directional components at the specified Cartesian coordinates. It cannot plot the directional ellipses. However, for a workaround, you can refer to the following steps and the code snippet given below to plot the ellipses for polarization.

1. Define the grid: Create a grid of points where you want to plot the polarization ellipses.
2. Calculate the ellipse parameters: For each point on the grid, calculate the parameters of the polarization ellipse (orientation, major and minor axes).
3. Plot the ellipses: Use the plot function to draw ellipses at each grid point.

% Parameters
N = 30; % Number of points in each direction
radius = 5; % Radius of the outer circle
[X, Y] = meshgrid(linspace(-radius, radius, N), linspace(-radius, radius, N));
Z = X + 1i*Y;

% Plot 
figure;
hold on;
axis equal;
axis off;
theta_circle = linspace(0, 2*pi, 100);
plot(radius*cos(theta_circle), radius*sin(theta_circle), 'k'); % Draw the circle boundary

for i = 1:N
    for j = 1:N
        if X(i,j)^2 + Y(i,j)^2 <= radius^2 % Only plot points within the circle
            % Polarization states
            r = sqrt(X(i,j)^2 + Y(i,j)^2);
            theta = atan2(Y(i,j), X(i,j));
            phi = r; 
            
            % Compute the semi-major and semi-minor 
            % For demonstration, let's vary the axes lengths as a function of r and theta
            semi_major = 0.1 + 0.05 * sin(r);
            semi_minor = 0.05 + 0.03 * cos(r);
            semi_axes = [semi_major, semi_minor]; 
            
            angle = 2*theta + phi; % Orientation of ellipse
            color = 'r'; 
            plot_ellipse([X(i,j), Y(i,j)], semi_axes, angle, color);
        end
    end
end
hold off;

% Function to plot ellipses
function plot_ellipse(center, semi_axes, angle, color)
    theta = linspace(0, 2*pi, 100);
    ellipse_x = semi_axes(1) * cos(theta);
    ellipse_y = semi_axes(2) * sin(theta);
    R = [cos(angle), -sin(angle); sin(angle), cos(angle)];
    ellipse_coords = R * [ellipse_x; ellipse_y];
    plot(center(1) + ellipse_coords(1, :), center(2) + ellipse_coords(2, :), color, 'LineWidth', 1);
end

The above code is only for demonstration, please modify it as per your requirement.

Please refer to the following documentation link to learn more about quiver function.

• https://www.mathworks.com/help/matlab/ref/quiver.html

Hope this helps!

[Aswathi K]

Thank you so much, This is one thing I am struggling with but i couldnt understand how we are plotting that along with intensity profile, If You are able to answer that also. then it will be really helpful. Thanks for helping at the needful time