How to Measure losses in a tapered multimode fiber simulation



How can losses be measured in an optical tapered multimode to singlemode fiber simulation?

I have reviewed this article ( Optical losses in multimode simulation ) and the Wikipedia article that it references regarding S-matrices, and found that my system was lossless ( conj(S)^T * S = Identity ), according to the Wikipedia article.

It seemed that one could also take the total E field, summed over all modes, at each cell along the propagation direction ( from input source to output ) and after normalizing by the total input E field, calculate the loss as a function of propagation direction in this way. However, when I did this I found that the effective refractive indices increased as the taper narrowed, and similarly this method showed a marked decrease in power ( from normalized 100% at input to 20% at output ) for a taper starting at radius of 30 microns decreasing to a radius of 8 microns. What am I missing?



My system is lossless as demonstrated by the S-Matrix approach and also by the corrected E-field approach explained here.

I had errantly been calculating loss as derived by Cell E-fields as,
E_over_all_mode_at_one_cell = sum( (E1^2 + E2^2 + E3^2)^0.5 ) / sum(E1)
whereas it should be calculated as,
E_over_all_mode_at_one_cell = sum( E1^2 + E2^2 + E3^2 ).

The script file looks like:

ncells = 70;
calc_power = matrix(1,nc);

for (i=1:ncells) {
data = getresult("::model::EME::Cells::cell_" + num2str(i),"mode fields");

# Shown for three modes
E1 = reshape(data.E1,[201,201,3]);
E2 = reshape(data.E2,[201,201,3]);
E3 = reshape(data.E3,[201,201,3]);

# Correct: see paragraph relating to Fig-22 of
calc_power(1,i) = sum( E1^2 + E2^2 + E3^2 );

# Incorrect
# calc_power(1,i) = sum( (E1^2 + E2^2 + E3^2)^0.5 );



Hi @ebreitfeller
I am glad that your definition of normalising modes worked for you and thank you for sharing your code and the paper. I was a bit concerned why the refractive index has increased as taper narrows, but I assume you might have a different geometry than just a taper with surrounding air.
Basically for situations where a multi-mode fibre is connected to single-mode fibre, you can add ports to your input, each resembling a mode, and one port at your output or have one port for the input and select the modes of interest from user select in EME port Edit window. This page summaries all the parameters that you can set to get the results you are looking for. Also, it is a good idea to have a high number of modes for all cell groups (10 is enough in most cases) to count for coupling to higher order modes within each unit cell.


Hi Behzad,

The refractive index actually decreased as the taper narrowed - I was more
focused on reconciling the S-matrix loss approach (sHs = s^H * s = I) with
the sum of the E-field approach, and they both were in good agreement. The
columns/rows of sHs that were not unity were mapped onto the mode numbers
that had losses.

Thanks for your reply.