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 ox
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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