# Hexagonal 3D photonic crystal

#1

Hello
I am a new user to lumerical. I am trying to simulate photonic crystal bandstructure for 3D geometry. I have gone through the examples of palanr 3D and planar 3D hex. I see, in both cases symmetric boundary condition is applied along z direction to simulate TE modes only. Can you please explain how is this working? How can I excite only TE modes using electric dipoles and taking symmetric boundary condition?

#2

Hi @kanak
I suppose that you mean the following examples. For â€śplanar 3Dâ€ť https://kb.lumerical.com/en/index.html?diffractive_optics_pc_bandstructure_3d_planar.html and for "planar 3D hex"
https://kb.lumerical.com/en/index.html?diffractive_optics_pc_bandstructure_3d_planar_hex.html

You can excite TE or TM modes selectively by changing the orientation of the dipoles.

#3

Hiâ€¦@konslekk
Yesâ€¦but the example description says thatâ€¦ its for TE modes and electric dipoles have been used.
By orientation do you mean using magnetic instead of electric?

Thanks.

#4

Hi, @kanak

In the case, the dipoles are created by the script. You can click right button on dipole_cloud. Edit object -> Setup -> Script. You can find that the theta, phase and phi of a dipole are set by random numbers generated by â€śrandreset()â€ť.

#5

Hi @kanak

For TE case, we use vertically polarized magnetic dipoles and symmetric BCs along the z-direction. This means that electric filed will be on the material plane.

If you want to excite TM modes, you will need to change the dipole to Electric dipoles while they are still vertically polarized (theta (degrees) = 0). Alternatively, you can use magnetic dipoles and set theta (degrees) = 90. If you want that results are not identical, please let me know.

While this excites the TM modes of the cavity, its not enough yet as excited modes might get suppressed as the result of choosing inappropriate BCs. Since TM modes are perpendicular to cavity surface, you need to use antisymmetric boundary in the z-direction. For more information regarding selecting the BCs please see this direct.

I hope this clarifies the problem, and best of luck using Lumerical.

Thanks

Photonic band structure and how to separate TE and TM modes
#6

Yes, I guess I understand it now, how the dipoles are working. But I still have a question. If I am exciting TM modes with magnetic dipoles having theta= 90 degrees, why should I still apply antisymmetric boundary condition along Z to cancel electric field? It should not be required, right?

#7

Dear @kanak

Applying an antisymmetric BC along z-direction will suppress the TE modes:

For TM modes, electric fields will have only z-component and this can be done by setting z BCs to antisymmetric. Please note that choosing symmetric/antisymmetric BCs will lower the simulation time by half (in this case). You can get the full spectra by setting BCs to PML.

Thanks

#8

I think I am little confused here again. If you please look at the 3D hexagonal example:

https://kb.lumerical.com/en/index.html?diffractive_optics_pc_bandstructure_3d_planar_hex.html

You said that: â€śFor TE case, we use vertically polarized magnetic dipoles and symmetric BCs along the z-direction. This means that electric filed will be on the material plane.â€ť

Does the material plane refer to XY plane here?

Another thing, this example does not use magnetic dipole, it uses electric dipole.
Using symmetric boundary condition and both magnetic and electric dipole I got the same bandstructure. I donâ€™t understand why this is happening. Can you please help? I am attaching the bandstructure figures.

#9

Dear @kanak

Yes. Material is in the xy plane. Thus TE field means that dominant electric field is in the x or y direction and z component of the electric field is almost zero (or very small value).

I guess there are two things to consider in these simulations: how to excite modes and the effect of BCs. To excite the modes you need to properly choose dipolesâ€™ location and polarization. For example if your dipoles are positioned in the node of a mode, you can not excite that specific mode. Basically you want to properly locate dipoles and their polarization to excite all the modes supported by the structure. However, using symmetric or asymmetric BCs you can suppress TM or TE modes so that you study only a specific type of modes (TE or TM modes).

While I was expecting that you need electric dipoles on the xy plane to properly excite the TE modes, based on your findings and this KX post, it looks like simulation is more sensitive on the location of dipoles (and not much on their polarization), thus your plots look identical. Please note that the band structure plots in your post contains only TE modes and TM modes are suppressed as the result of choosing symmetric BC along z.

Please choose asymmetric BC on the z-direction and update me with your plots. I expect that you get a different bandstructure diagram.

Also this recorded webinar might be very informative.

#10

Yes â€¦I got different from before but same bandstructureâ€¦I guess its the TM mode.

I am confused only at the point, how choosing symmetric BC is giving me TE modes in the structure irrespective of magnetic and electric dipole sources. Same issue with the TM mode. Only changing boundary condition to asymmetric is exciting TM modes. The first one is using electric dipole and the second one is magnetic dipole. Both uses asymmetric boundary condition.

It will be highly helpful if I could get some help regarding this confusion.
Thanks
Kanak

#11

Dear @kanak

Maybe scattering from TE to TM modes (and vise versa) happens? I guess generally this is not a bad thing. We want to be able to excite all the modes with the minimum number of sources (location and polarization wise).