On Aug 2, 2008, at 11:11 PM, Juntao Xi wrote: > Is that true that the K-point is necessary when ONLY periodic > structure?
I'm not sure I understand this sentence. However, when you set the k-point, it immediately implies Bloch- periodic boundary conditions -- that is, it implies that the structure repeats periodically and the fields repeat periodically multiplied a phase exp(i*k*x). > Say I have a slab parallel to the x-y plane and the norally incident > planewave is incident along with -Z direction. > The thickness of slab is D in Z direction and size of X,Y is set > infinity. refractive index is 2. > Component of source is set as Ex. > > It is obviously that no periodicity in Z direction and the PML is > set in Z direction. Is that correct? No. PML and periodicity have nothing to do with each other. Periodicity is a boundary condition. PML is a material adjacent to the boundaries. You can have PML adjacent to a periodic boundary, or adjacent to a metallic (PMC) boundary, or PML adjacent to any other boundary condition that the code supports. In the libctl interface, as soon as you set the k-point to anything other than "false", *all* of the boundaries become periodic. (There is a way, using lower-level commands, to set some of the boundaries to be periodic and others to be metallic etc., but this usually isn't needed). However, in any direction where you have a PML, the boundary conditions are mostly irrelevant. e.g. if you have PML in front of a periodic boundary, the periodicity doesn't matter because the field will have decayed almost to zero by the time it "wraps around" to the other side of the cell. (The same goes for metallic boundaries, which reflect the light that hits them, but this doesn't matter if you have a PML in front of the boundary to absorb this "round-trip" reflection. > The problem is that should I take X, Y as periodic to set k-point? > As I think, every cell in X and Y direction is identical, > respectively and the k-point should be set. > If yes, how I set k-point? > k-point--->(0 0 0) > k-point--->(1 1 0) > k-point----.(k k 0) It depends on what you want the field to do. When you set the k-point to *anything*, the structure becomes implicitly periodic. But you still have to decide what relationship you want the *field* to have between adjacent periods. (Or, technically, you are deciding what relationship you want the sources to have between adjacent periods.) For a planewave incident in the +z direction, you should have kx = ky = 0, since a planewave in the +z direction has the same phase for all x and y. Regards, Steven G. Johnson PS. This goes back to what seems to be the biggest confusion about symmetry in physics. The symmetry of the structure is not necessarily the same as the symmetry of the solutions (e.g. the fields) in that structure, although the two are of course related (by group representation theory). e.g. in the present case, a periodic structure does not imply periodic fields....but it does imply that the field solutions can be chosen as Bloch-periodic. _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
