Quick question about k_point and periodic boundary conditions

[pwflanigan]

Let's say I wanted to make a system (cell_size = (sx,sy,sz)) periodic in the x and y directions. When I specify the k_point in the simulation object, if I set k_point=(sx,sy,0) then the system would repeat itself at exactly the boundary, correct? So if I did something like k_point=(sx+1,sy,0), then there would be a gap of 1 length unit in between each instance of the system as I go along the x direction?

I was looking at the example https://github.com/NanoComp/meep/blob/master/python/examples/holey-wvg-bands.ipynb and I wasn't sure why the specified k_point was set at (0.4,0,0) even though sx was 1.0.

EDIT: to clarify, I do know that you can achieve two-directional periodicity by putting PML's on just the z direction, but want to understand what exactly k_point is doing, since I was kind of confused by the manual's explanation. If my understanding is correct, what does it mean physically to set k_point=(0,0,0)?

Thanks for the help.

[stevengj]

You are making a category error — k_point is not the kind of thing you think it is.

For periodic or Bloch-periodic/quasi-periodic boundary conditions, the period in each direction is always corresponding the cell size. This has nothing to do with k_point. There is never a "gap".

k_point specifies a phase relation between one period and the next. k_point=(0,0,0) corresponds to ordinary periodic boundaries. The elements of k_point have units of 1/distance, so k_point=(sx,sy,0) is nonsensical (wrong units). From the manual: