On Sun, 16 Apr 2006, Qi Wu wrote:
I used meep to calculate the band diagram of a FCC lattice. As a starting test, I want to find the modes for a FCC silicon sphere at Gamma point and compare the result with MPB. The unit cell in meep is a cubic which contain 4 primitive cells of FCC so I used four related point sources in the cubic. Since I only want to do it for Gamma k-point, the phase for all the four point sources are the same and their positions are related by FCC lattice vector.
Notice that some of your modes detected by harminv have very low amplitude, which probably means that you are exciting some of the "folded" bands due to the supercell.
In principle, the excitation of the folded bands would be exactly zero if you place your sources correctly in the supercell. However, this doesn't happen in FDTD because the finite grid spoils the symmetry slightly...it also means that the detection of folded bands will vary with resolution.
In the past, when I've wanted to compute band diagrams in FDTD for a non-orthogonal unit cell, I had to do two things to reliably filter out the folded bands. (e.g. suppose we have a triangular lattice, and are using a 1 x sqrt(3) rectangular supercell in FDTD).
1) First, for every point source you put in, also include its periodic copies with the periodicity of the underlying lattice, with phases related by exp(ikx) for the current Bloch wavevector. 2) Second, for every harminv point you put in, also analyze fields from the periodic copies of that point (with the periodicity of the underlying lattice). Then, reject any frequency that is not detected at *all* points, with a amplitude that is related by something close to the correct exp(ikx) phase. It sounds like you are doing (1) but not (2). Steven _______________________________________________ meep-discuss mailing list [email protected] http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
