# Boundary selection for periodic structure but randomly polarized sources

#1

I am simulating one unit cell of the entire array. In this cell, I have structures and randomly polarized dipoles. However, the periodic BC requires both periodic structures and EM fields. So, which BC should I use? Or I should just create the entire array directly and use PML?

#2

Hi,

As you rightly mentioned, different configuration of sources make the whole system non-periodic.
Thus, in general, you have to model the whole array simultaneously.

However, the simulation can be simplified if you assume that the sources does not influence on each other,
i.e. the sources do not change the states of their neighbors. In this case, you can simulate the array by generating a series of cells with random dipoles. Then, from the superposition principle, you combine the fields from proper arranged cells to form a single random ensemble.

#3

Dear @w65yang

As you and @msaygin said, simulation with periodic boundary conditions assumes that you have an identical geometry and sources on each unit cell.

My idea would be to use the “super cell” idea. If we know that the field of each dipole decays to a negligible level after a few (say 3) unitcells on each direction, we can construct a supercell (with 4 cells on each direction), with random dipoles on each unitcell and PML boundary conditions. Then we can average the effect of these fields on the central unitcell to estimate the random field distribution at every location in the device. @msaygin: Please let me know if this makes sense (maybe we are saying the same thing in different words?).

@w65yang: I guess the answer to your question will depend on the case that you are working on. So, explaining your geometry and sharing the simulation file with us would be a great help.

Thanks

#4

Hi, @bkhanaliloo

In general I meant the same. The main idea to get around the full-scale modeling of the array is to construct reliable model that involves interaction between the sources. At first sight for me it is not clear how to take the interaction into account without sacrificing calculation precision, but your suggestion with super-cells seems legitimate.

@w65yang, should the dipoles interact with one another? i.e. does a dipole field alter the neighbor dipole ?

#5

Thank you for your reply, and no, the dipoles do not interact with one another.

#6

Thank you for your reply. The super cell idea sounds very interesting. I have not completed the simulation file yet because I did not know what to do with the BCs, so I will explain in words. We want to simulate a bowtie nano cavity. There is a substrate under the bowtie, and the dipoles are on the top surface of the substrate with random polarizations.

#7

Hi @w65yang

It sounds interesting. Can you please go ahead and start preparing the simulation file?
We have some examples in knowledge base that might be useful to read. The hexagonal OLED example might be a good one to review so that we can use some symmetries for positioning the dipoles.