# How to calculate the effective index of bioperiodic SWG structures

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How to calculate the effective index of biperiodic SWG structures having the same period of SWG1 and SWG2 but different in fill factor as shown in the figure above (our structure) ?

The fill factor of SWG1=0.5, Period =200 nm

The fill factor of SWG2=0.54, period is 200nm

We use the example provided by Lumerical to calculate the effective refractive index of the SWG waveguide. The effective index for each SWG is calculated based on the Lumerical example which can be found in https://www.lumerical.com/learn/video/swg-bandstructures/

When we use this method to calculate the neff of the two SWG respectively and then using neff_total=neff1*0.5+neff2*0.5 to get the neff of the whole neff (here our SWG1 and SWG2 which are of same period and calculate the transmission response (theoretically)which doesn’t match with 2.5 FDTD.

Why is so mismatch happening?

SO my concern is

1.Can we use this method to get the neff of the whole SW1+SWG2 ?

2.If the individual neff calculation is correct then how to calculate the total effective index ?

Calculating neff using lumerical examples:

neff using lumerical examples:

Thank you in advance!

## Answers

61Ansys EmployeeHello Lizzie,

I think that it is more accurate to simulate the gratings with FDTD. The central assumption for varFDTD is that there will not be light scattered into or out of the device plane. This is not the case with subwavelength gratings. The most accurate way of doing this would be similar to this example https://support.lumerical.com/hc/en-us/articles/360042304394-Bragg-grating-initial-design-with-FDTD.

Your mode analysis is likely pretty accurate, but you are simply taking the average effective index. This will be close to the composite effective index, but the simple average will not tell the entire story. Large variations from this would suggest to me that the varFDTD simulation is not set-up correctly. I would suggest using FDTD or EME to more accurately model this structure.

Best,