Learning Forum

[teddie smith]

I have a question about periodic boundary conditions.
When set to PBC, the boundary condition consists of two lines, and the width seems to be equal to one mesh. 
Also, it was judged that the inner line is the simulation area I set, and the refractive index monitor shows the outer line as well. 
At this time, I want to know that line and if the area shown in (b) is repeated or if it is repeated like (c).

[Guilin Sun]

 

This is a good question and you are correct with a keen eye. However to understand it clearly we need come to the FDTD algorithm its self.

In the continuous world the inner line is the math boundary.

In FDTD, which is a discrete mesh world, there is NO such clear line boundary! This is because in the Yee cell, Ex,Ey,Ez and Hx,Hy, Hz are not located in the same point. Please refers to this image:

I can assure you that FDTD will keep the discrete mesh periodic for all the 6 field components. 

 

[teddie smith]

 

Thank you for your reply.

Can I understand like this? To obtain the E field and H field from the boundary conditions of the simulation area, calculation on the outer line, which include the mesh is also required. So, the location used for the calculation is indicated by the outer line.

In addition, when the actual periodic is implemented, the inner lines will overlap. If the structure is set incorrectly and the E and H values ​​at the left and right boundaries are different, does the simulation derive the average value? (And I found my figure to be a bit erroneous.) Furthermore, when checking the 6 fields separately, is it correct to understand that the calculated grid is different?

[Guilin Sun]

You are right that the extra mesh is required.

since it is discrete, we cannot use the continuous view to explain it. Internally the 6 field components are not collocated. however by default the exported data from the monitor is interpolated to one location so you will not notice the difference. Lumerical gives customers the option to export the raw data. However, without proper treatment of the raw data, the power calculation will be incorrect, even though the difference can be very small. Please refer the analysis group ("power absorption advanced").

Due to this reason, the periodic BC should lay on uniform objects if possible.