Learning Forum

[NFrench]

Hello! I am trying to use FDE to find the power coupled into all the modes within a fiber optic from a gaussian beam. However, I am getting confused by the results of the power coupling calculations. Looking at the definition for power coupling, I was under the impression that I could simply sum up the power coupled in the individual modes from the beam to get the total power coupled in the fiber. Clearly 0.1788 + 0.858 is greater than 1, and I am confused why this would be so. Perhaps I am misunderstanding the definition for the power coupling calculation in FDE? Any advice is greatly appreciated!

[Guilin Sun]

This could be due to numerical error, in particular when more number of modes are used.
Are you using "overlap" or "expand2"?

[NFrench]

I am using "overlap"

[Guilin Sun]

If so, I have not seen any theory that guarantees the sum of overlaps to be unity, like transmission and reflection. "overlap" is to compute the similarity of the modes. The overlap assume no reflections, but in physics there is some reflection. Some details can be found here:
https://support.lumerical.com/hc/en-us/articles/360034396834-Understanding-the-mode-overlap-calculation
ideally, we would know the reflection, which is not necessarily part of the incident fields.
So, I would suggest that you can simply ignore the difference to unity.

[NFrench]

Okay, thanks for clarifying! I am trying to use the power coupling part of "overlap" to figure out at the beam angle at which power coupled in the fiber drops below a certain threshold (EX: 5%) though. Would this numerical error caused by the "power coupling" calculation be an issue or would it still be safe to ignore the difference to unity?

[Guilin Sun]

As the link suggested, if you want to have accurate coupling information, you will need to consider all the modes for the reflection and transmission. This can be done using EME. But you still meet some issues as how many modes to guarantee the error is small enough. "overlap" estimates the coupling, and its accuracy compared to actual power coupling will depend on the modes and the refractive index difference etc. I would suggest to simply ignore it, or use EME to accurately quantify the coupling with mode convergence, which might be a little challenge in some cases.