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