# Algorithm of EME.

Hi,

I want to know whether I am understanding it right or not.
Is FDE solver follows fully vectorial 2D Eigenmode solver ?
Is EME based on Finite Element Method?
I want fully-vectorial 3D Eigenmode solver, What solver can I use?

Sincerely,
Anitharaj

Yes, its fully vectorial 2D solver in frequency domain that uses Yee cells to calculate electromagnetic fields. You can read more about this here

Not exactly. In EME, eigenmodes are calculated in the cross section of each cells (similar to as FDE) and then propagated within each cell. Then scattering matrices are calculated on each boundary. This technique is fully vectorial and considers both forward and backward propagating modes. You can read more about this here.

As you realized, since EME relies on 2D FDE solver it is not a 3D eigenmode solver. This solver is quite strong if you want to propagate modes inside a long waveguide for example.

If you can provide me with the specific application of your interest, we can discuss it further and decide on what software to use.

FDTD might be a good approach for some of the 3D Eigenmode solver applications.

Thanks

It helped me.
Hi Dear,

I am wroking on polarization mode converter based on Silicon on Insulator.
My waveguide is asymmetric cross-section.
To obtain rotation parameter, I need Finite Element Method.
For this which solver should I use?

Secondly, In example https://kb.lumerical.com/en/index.html?pic_passive_tapers_polarization_converter.html
polarization_rotator.lsf contain the script for calculating TE and TM polarization power.
Is this the power that could be used to calculated conversion efficiency ( = Pte / (Pte + Ptm)).

For an asymmetric cross section you need to use EME solver. Simply replace the middle waveguide B with your design in this KB example and use enough cells for it from EME setup so that it captures the cross section asymmetry.

I am not quite sure what you are referring to here. The script finds overlap between guided modes of waveguides at waveguide boundaries. Conversion efficiency normalizes output field to input field so I would say it is P_TEout/P_TEin and P_TMout/P_TEin assuming that TE is your input field.

Also, transmission command and Mode Expansion are used in S-paramter to calculate transmission if you are referring to this technique in EME. This is basically how EME works and the idea behind the polarization-rotator.lsf script.