Finding the weight of the modes contained in the E field.
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Hi,
I have the values of E-field on a transverse plane(Both magnitude and phase values are known). Let us say it is a matrix of N x N.
The E-field expression is given by;
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1429498/image.png)
where,
, and l is the mode no.(also known as azimuth mode no.)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1429503/image.png)
Here, I want to compute the weight of the mode no. l from the values of the E-field which is known to me on a transverse plane.
Alternatively, one could also say the magnitude of the field values for a given mode l.
The expression that I want to compute is given by the following expression;
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1429508/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1429513/image.png)
The desired plot is a 2D plot with mode no. l on the x-axis,(say -8,-7,-6,....-1,0,1....6,7,8) and
on the y-axis.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1429518/image.png)
Thanks,
Biplob Biswas
PhD Research Scholar
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Risposte (1)
Chaitanya
il 11 Lug 2023
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!
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