Hi,

I want to find effective index of one unit cell.

I used index monitor and mode source but these objects solve effective index in 2D surface.

But I want to find it in volume.Is it possible in lumerical(fdtd)?

simulation file is:

unit.fsp (1.4 MB)

# How to find Effective index of unit cell?

**m.dezyani**#1

**fgomez**#3

Hi Dezyani,

Sorry for the long wait. I am not sure I understood what kind of effective index you want to find. For effective index calculations you would typically have some waveguide or cavity mode but that not seems to be the case here. The index monitor in FDTD will return the material index for the structures, so no effective index is calculated there. Can you provide some more information about the system and what you want to characterize with the effective index?

**m.dezyani**#4

Hi,

in simulation file,you can see unit cell of structure.

before,I could find effective index in 2-D surface by mode source.

because my structure is not symmetric in layers(for holes),I could not find valid result by mode source.

For above reason I want to find eff index in a unit cell(3-D).

Is it possible?

Thank you so much Federico.

Dezyani

**aalam**#5

I am not sure if this applies to your case but one thing you can do is to calculate the average effective index in your unit cell. You can divide the unit cell into multiple segments where there is no (or little) variation in the propagation direction. Then use MODE to calculate the effective index of each segments. Finally, you can calculate the average index for the entire unit cell.

**m.dezyani**#6

Hi,

Thanks for reply.

I wrote script from your advise.

1.lsf (290 Bytes)

Is it a valid result?

Best regards,

Dezyani

**aalam**#7

Thanks for sharing the script. It is consistent with what I had in mind. However, I am not so sure about the validity of this approach now. When you calculate the optical mode on different slices, there will be lots of available modes. When the optical signal passes through the structure, power will flow from one slice to the next one by coupling multiple modes from one slide to multiple modes of the other slice. As a result, I do not think we can just pick a single mode at each slice and get their average. Can you tell me what is the final quantity that you want to calculate? Are you trying to replicate some measured result? In that case what is this quantity that you are trying to compare with?

**m.dezyani**#8

Hi,

I know that Rsoft photonics CAD can calculate eff index in a volume.

I do not know that what is exactly!!

Best regards,

Dezyani