Finding the weight of the modes contained in the E field.

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;

where, , and l is the mode no.(also known as azimuth mode no.)

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;

, where is the weight of a mode no. l

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.

Thanks,

Biplob Biswas

PhD Research Scholar

Answer 1

[Chaitanya]

Hi @Biplob,

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!

[Biplob]

Hi Chaitanya,

Thank you for the answer.

I have 2 queries.

1st: What is the reason for taking the ratio of sum of complex E-field over sum of magnitude of E-field, in the calculation of weights?

2nd: When I provide the E-field matrix, I already know the mode no.(l) in the E-field. For example: When I specify (l = +2), I expect the weight value to be higher for(l = +2). But in this code, I am getting a high weight value for (l=+1) everytime. What could be the reason behind this?

Thank you,

Biplob