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
>
>
>
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