Re: How to define and calculate the surface mode in 2D-PC of trianular lattice?

One difficulty with your computational cell is that you actually have  
two surfaces -- one on the left and one on the right.  Remember that  
there are periodic boundary conditions.

The solution is to intentionally have two equal surfaces that are  
mirror symmetric along the y direction, and then use run-yeven to  
avoid getting the same mode twice.

That is, have a computational cell like:

     --> y direction

|                                  o      o      o      o      o       
o      o      o      o                                  |
|                              o      o      o      o      o       
o      o      o      o      o                              |
|                                  o      o      o      o      o       
o      o      o      o                                  |
                          left  
surface                                                  right surface

When you simulate this structure, if there is a surface state at the  
left surface there will also be the same surface state at the right  
surface, by symmetry.    The exponential tails of these surface states  
will cause them to couple into even (+    +) and odd (+     -)  
combinations with slightly different frequencies.  If the supercell  
size is big enough, however, this coupling is negligible (decreasing  
exponentially with the size of the crystal), so essentially you have  
two copies of the same mode.  To get just one, you use run-yeven (or  
run-yodd, it doesn't matter), which will pick out one of the linear  
combinations.

Steven


On Sep 2, 2009, at 10:39 PM, Chad Huskow wrote:
> Dear Steven and MPB users,
>         I have solved the problem about the surface mode in 2D-PC  
> triangular structure of air holes in dielectric background. You can  
> see my PC structure in the attach. My problem is the surface mode  
> along Gamma-M direction (by changing the surface termination along  
> Gamma-M). In that case, the surface termination factor C=0.5. I want  
> to investigate the surface band structures for various the surface  
> termination factors.
>  I don't know how to define that structure MPB.

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