Dear Prof. Steven, OKey! I got it. I have used a non-orthogonal supercell for calvulating triangular lattice. That may be the problem. I chose the supercell like this: o o X o o I will change it into orthogonal supercell (rectangle) when calculating slab mode. Professor, Thank you very much for your kind help~
Best wishes Yours, Ryan On Nov 16, 2007 7:19 AM, Steven G. Johnson <[EMAIL PROTECTED]> wrote: > On Thu, 15 Nov 2007, Ryan Hao wrote: > > I know sent the supercell with no defect to calculate slab mode. > > But how to project it to the waveguide direction? > > Just plot it as a function of the waveguide-parallel k vector. > > The only thing you need to be careful of is to arrange your supercell so > that one lattice vector points along the waveguide direction and one > lattice vector is perpendicular. e.g. in a triangualr lattice you would > use a supercell something like > > o o o o o o o o o o x > o o o o x o o o o | > o o o o o o o o o o |____ y > > (where "o" is a hole and "x" is the defect, for example, and the x > direction is parallel to the line defect and y is perpendicular). > > > Just a large supercell is enough? why? Could you please talk into > > it a little bit more in details? > > There are two ways to proceed. > > One is just to use a large supercell with no defect, in which the slab > bands are folded many times...in the limit as the supercell becomes > infinitely large, the slab bands will form a continuous region when > plotted vs. k_x. > > More efficiently, use a small supercell (even just a single unit in the y > direction), and compute the bands for many k_y values from 0 to 0.5. When > plotted as a function of k_x, this will outline your continuum slab-band > regions. > > In principle, you could also take the bands in the primitive > non-orthogonal unit cell (for a triangular lattice) of the defect-free > system and project them. This requires some care, however, as described > in my paper "Linear waveguides in photonic-crystal slabs," in Phys. Rev. > B. 62, p. 8212 (2000). It is easier to use the supercell technique above > to get an orthogonal unit cell. > > Regards, > Steven G. Johnson > > > _______________________________________________ mpb-discuss mailing list mpb-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss