Learning Forum

[Samantha]

Hello,

I am trying to reproduce Fig. 5(a) (Boundary lines for the single mode condition cutoff dimensions as a function of photonic wire dimensions) of the following paper: 

https://opg.optica.org/oe/fulltext.cfm?uri=oe-15-18-11061&id=140927

Paper shows that at wavelength=1330nm, Si waveguide with width=350nm, height=220nm, has 1TE mode and 1TM mode.

After simulating the waveguide using Palik's material model, I get 3 modes, that satisfy neff>nclad_SiO2:

neff of the first 3 modes: 2.46 (TE=98%), 2 (TE=2%), 1.473 (TE=62%). For the third mode, Ex has much smaller amplitude inside the core compared to Si-SiO2 interface and clad:

My first query is, whether the 3rd mode is guided/unguided. How can I understand seeing the mode profile whether a mode is guided/not. If the above mode is guided, then the result does not match with the paper's result.

Similarly, for w=250nm,h=220nm, at wavelength=1330nm, the paper shows that waveguide has only one TE mode (no TM). I get  3 modes: the 3rd mode has neff

Similarly for w=450nm, h=220nm, the paper shows that waveguide has a single TE mode (no TM) at 1550nm (Fiig. 5b). However, from my simulation, I again get 3 guided modes:

Could you please explain the discrepancy of my simulation results and the paper's results? 

 

[Amrita Pati]

Hi Samantha,

I apologize for the late response. May I ask if you're solving the modes with PML or metal boundaries? I ran the simulation based on the parameters of the first configuration and I obtain 1 TE and 1 TM mode. Sometimes you might get additional modes as a result of the artifacts of the boundary conditions. These modes are not physical solutions. If you're using Metal boundaries, I would suggest you to change to PML and check if you still observe the additional mode.

Regards,
Amrita

[Samantha]

Hello Amrita,

I solve it using PML boundary condition and 5nm*5nm mesh. Could you please let me know what is the effective index of the 3rd mode you are getting? Is it less than nSiO2 (1.44)? Here is the file I simulated:

https://drive.google.com/drive/folders/1269qX-0XT5w4Rx-sISoPjcOdba0u_CXx?usp=sharing

Could you please check it or share your file? 

Also, seeing the snapshots of the 3rd mode for all the 3 configurations I gave in the previous response, how may I understand that they are artifacts?  

[Amrita Pati]

 

Hi Samantha,

I ran the first configuration for 1550 nm earlier, which is why I was getting different number of modes. I reran the simulations and my results are very close to yours. I don’t think the third mode is due to numerical errors. I believe it is a higher order TE mode.

Also, one thing that confused me in the paper is that at some places they have mentioned 1310 nm while at others 1330 nm. I did find a more recent textbook, that had results for these configurations and they are very close to yours. But the caveat is that they have also used Lumerical for simulating these structures.

And sorry I wasn't able to look at your files as we are not allowed to exchange files here.


Regards,
Amrita

 

[Samantha]

Hi Amrita,

Thanks for the reply.

Yes, It seems that the paper made some mistakes while writing the wavelength value. 

My question, in the end, is, 'How can I understand seeing the mode profile (|E| or E components) whether a mode is guided/not'? Is it only from seeing the neff value? 

Regards,

Samantha

[Amrita Pati]

Hi Samantha,

Yor are correct, n_eff is useful for determining if a mode is guided or leaky. Mode profile is also important. In this case, for the third mode if you visualize all the field components E_x, E_y, E_z, and compare it to existing literature you can see that it resembles a higher-order TE mode. The overall power resides around the Si-SiO2 interface, or the edges of the waveguide because the effective index of this mode is very close to the cladding index.

You can also change the boundary conditions (BCs) between Metal and PML to check if there are any changes to rule out BCs as the cause of an unphysical mode. 

Regards,
Amrita

[Samantha]

Thank you for the clarification.