  # How to calculate power imbalance of MMI in mode solution?

HI, I want to know how to calculate power imbalance in MMI.

MMI is characterized by insertion loss and power imbanlance. Also, MMI has power distribution ratio.
Sugggesting, there is a 1X2 MMI, the insertion loss can be calculated by S Matrix component S21 and S31：

trans=abs(S21)^2+abs(S31)^2
loss=-10log10(trans)

Then, how to calculate the power imbalance and power distribution ration on the premise that S parameters are already available in MODE solution?

This question may be somewhat silly and inappropriate, but I really want to know.

Hi @1683324,

If the S parameters are known, the power transmitted to the two output ports will be proportional to |S_{21}|^2 and |S_{31}|^2. The power imbalance IB in a 1x2 MMI would then be

IB = -10\textrm{log}_{10}\left(\frac{|S_{21}|^2}{|S_{31}|^2}\right)

and the power ratio would be |S_{21}|^2/|S_{31}|^2.

I hope that helps. Let me know if you have any questions.

Thank you for your respond. It is very kind of you!

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