Learning Forum

[Seyed Safaee]

I want to find the effective index of a sub-wavelength structure for different modes. I have already checked the SWG bandstructure example in FDTD which calculates the effective index by phase velocity extraction; this is limited to the fundamental mode.

Since I need to extract this for the second order mode (TE1), I moved to the Lumerical Mode tool using the EME solver so I reviewed the existing Bragg reflector simulation example. The problem is that EME extracts the effective index for each cell and not for the whole structure. What is the best way to extract the effective index of the whole SWG structure for the second fundamental mode (TE1)?

An analytical methodology could be a weighted averaging of the neff for two cells: neff_total=neff_cell1*(fill_factor_cell1)+neff_cell2*(fill_factor_cell2); however, I am not fully sure if this is correct.

[Guilin Sun]

First, this method neff_total=neff_cell1*(fill_factor_cell1)+neff_cell2*(fill_factor_cell2) is an estimation and sometimes people do use it. 

I do not find any guideline in our official webaite, and nor find any publications on how to simulate the band structure of higher order modes.  However, there might be different ways doing this. For example, you can either use TE1 excitation and get the phase of the mode though Fourier transform. Please refer to this example  https://optics.ansys.com/hc/en-us/articles/360042800113-Group-delay-analysis  Once you have the phase function as frequency, you can get neff and ng based on defintion.  You can have a DFT monitor and check if the final field profile is the same as the 2nd order mode.