# Optical losses in multimode simulation

#1

In my simulations I would like to calculate return loss (RL) and insertion losss (IL) of a multimode fiber system. I am using EME Solver to obtain s-matrix and then to calculate the desired parameters according to this article.

The issue here is that it works just fine for singlemode simulations and not for multimode ones.
I tried to use 20 modes and get 40x40 user s-matrix. From what I understand, each element corresponds to a specific combination of mode from port 1 and/or mode from port 2 - so if I am not wrong it is similar to having 20 input and 20 output ports.
Knowing this how can I calculate the overall RL and IL? I can calculate those losses for each separate mode, but I do not know how to combine it into one value for the whole multimode system.

How to Measure losses in a tapered multimode fiber simulation
can the optical loss from fiber to waveguide be calculated by lumerical?
#2

@mdudek: To answer your question, I think it is useful to consider a simpler example where you have two modes for both ports as shown in the diagram below:

This situation is equivalent to having 4 ports, each one with an input and output; for example a2 and b2 would be the input and output for port 2 in the 4-port picture. Presumably, the overall losses that you want to calculate are related to the net incoming and outgoing powers on each side of the box. For instance, one could imagine measuring the net incoming power coming from the left, |a1|^2 +|a2|^2 and comparing it with the outgoing power on the right, |b3|^2 + |b4|^2. The s-matrix alone cannot give you this information since you need to know the composition of the input; that is, you need to know how much of each mode is being injected.

Another way to see this is that you cannot reduce the 4 port configuration to a 2 port configuration in general because the mode composition of the input or output is important.

I think that the losses you want to calculate would be the result of a post-processing step that requires additional information, such as the mode composition of the input. Since the s-matrix calculation is independent of this composition, the s-matrix alone does not provide you enough information.

#3

Thank you for this clarification. That explains a lot.
At first what I thought should be natural, was to use a sum of the all output parameters for all input parameters (|S13|^2 + |S14|^2 + |S23|^2 + |S24|^2) or all output parameters for each one input parameter, so: |S13|^2 + |S14|^2 and |S23|^2 + |S24|^2. Unfortunately it did not give any proper results, although what seems to be a power conservation is still correct: |S11|^2 + |S12|^2 + |S13|^2 + |S14|^2 = 1.

Do you think of any other way (either in FDTD or MODE Solutions) to obtain overall IL and RL for multimode system?

#4

Hi Michal,

For a lossless system the S-matrix is unitary, so that is probably why you are getting |S11|^2 + |S12|^2 + |S13|^2 + |S14|^2 = 1.

If you know the field profile of the input (for example from an experiment) you can import it to FDTD to find the transmission and reflection. I think this would give you the desired IL and RL for the multimode system and the specific input under consideration.

Hope this helps.

#5

So what I need should be a single source with multimode profile (several modes represented as just one source). And I guess, I should also use the same profile for transmission and reflection mode profiles monitors. Am I right?
I have already tried importing to FDTD a single source from several modes obtained with MODE but somehow it did not work and I abandoned this idea.

#6

An idea that should probably work (although I havenâ€™t tested it myself) is the following:

(1.) If you know the theoretical composition of the input, you can use a bunch of mode sources in FDTD (one for each component mode) and right in front of the sources use a field profile monitor to record the combined field from the sources. You can use the amplitude of each source to control how much each mode contributes; for example, if you had a combination of three modes that contribute 50%, 20% and 30%, you could set the amplitudes to 0.5, 0.2 and 0.3.

(2.) In EME you could import the field profile from FDTD at each port with the â€śuser importâ€ť option (see the image below). If you have the field profile already, say from an experiment, you can use it directly here, skipping step 1.

(3.) The S matrix from the EME calculation should give you the desired optical losses.

#7

Thank you, @fgomez. I will try it.