  # How to define periodic boundaries with symmetry or/and anti-symmetry?

In this tutorial graphene structure is periodic in x-axis.
but you set y-min &y.max periodic and x-boundary asymmetric.
please tell me how do you set it?
I have read [boundary conditions] (https://kb.lumerical.com/en/index.html?ref_sim_obj_boundary_conditions_tab.html) completly.
I never find solution for define boundary conditions.
thanks for any help.

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Excellent question. To correctly answer, let’s first have a look at the simulated structure: This structure is periodic in x and y direction. The x direction has a varying character where one graphene ribbon and one strip of uncovered SiO2 create one unit cell with period of 300nm. The structure can be also considered infinite in the y direction, which can be neatly simulated by using periodic boundaries. The size of one period in this direction is fairly irrelevant as there is no variation. Hence, it makes sense to choose some smaller length to save on simulation time.

For the reasons described above, this structure can be simulated with periodic boundaries in both x and y direction. On the other hand we must simulate full 300nm in the x direction as the simulation must include at least one unit cell. The anti-symmetric boundaries is a trick to cut the simulation time in half by simulating only half of the structure/fields by using its natural symmetry as described here.

The important part is that by setting the antisymmetry on both sides(x_min and x_max) we specify that the boundaries are periodic while simulating only half of the simulation region volume. If you set x_min anti-symmetric and x_max as PML, the simulated structure would NOT be periodic, but you would be still simulating only half of the volume.

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I have a question regarding this, how can I know that some structure is symmetric or anti-symmetric? It confuses me.

Well, the physical structure itself must be geometrically symmetrical. The decision whether to use symmetric or anti-symmetric boundaries is dependent on the orientation of E and H field components. I think that this is best explained under this link:
https://kb.lumerical.com/en/index.html?ref_sim_obj_symmetric_anti-symmetric.html

The pictures and the 5min long video nicely explain which boundary should be used based on the field components orientation.

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