To compute the weight of a mode number `l` from the known values of the E-field on a transverse plane, you can use the given expression:
weight = sum(sum(E_field .* exp(-1i * l * angle(E_field)))) / sum(sum(abs(E_field).^2));
Here's how you can create a 2D plot with mode number `l` on the x-axis and the weight on the y-axis:
% Given E-field matrix (N x N)
E_field = ...; % Replace with your actual E-field matrix
% Parameters
N = size(E_field, 1);
l_values = -8:8; % Mode number values for the x-axis
% Compute weights
weights = zeros(size(l_values));
for i = 1:length(l_values)
l = l_values(i);
weights(i) = sum(sum(E_field .* exp(-1i * l * angle(E_field)))) / sum(sum(abs(E_field).^2));
end
% Plot
plot(l_values, weights, 'o-')
xlabel('Mode Number (l)')
ylabel('Weight')
title('Weight of Mode Number l')
Make sure to replace `E_field` with your actual E-field matrix, and adjust the range of `l_values` according to your desired mode number range.
This code will compute the weight for each mode number `l` using the given expression and create a 2D plot of mode number `l` on the x-axis and the weight on the y-axis.
Hope this helps!
