Re: How to calculate the surface bands of photonic crystal slab

Dear Steven,thanks for your advices, and I have make an input file
accordingly to make the supercell, as follows


; supercell scheme
; *  *  *  o  o  o  o  *  *  *         --------layer one
;* *  *  o  o  o  o  o  *  *  *        --------layer two

(define-param supercell-x 9) ; the (odd) number of lateral supercell
periods,layer two

(set! geometry-lattice (make lattice
             (basis1 (/ (sqrt 2) 2) (/ (sqrt 2) 2))
             (basis2 (/ (sqrt 2) -2) (/ (sqrt 2) 2))
             (size supercell-x 2 no-size)))

(define-param eps 12) ; the dielectric constant of background
(define-param barhigh (* (sqrt 2) 0.2)) ; the heighty of the air bars in the
bulk crystal
(define-param barwidth (* (sqrt 2) 0.5)) ; the Width of the air bars in the
bulk crystal
(define-param slabhigh (+ (* (sqrt 2) 4) 1)) ; the heighty of the air area
in the Left side
(define-param slabwidth (+ (* (sqrt 2) 2) 1)) ; the Width of the air area in
the Left side
(define-param airwidth (* (sqrt 2) 3)) ; the Width of the air area in the
right side
(define-param airhigh (+ (* (sqrt 2) 2) 1)) ; the heighty of the air area in
the right side

(set! default-material (make dielectric (epsilon eps)))

;make periodic crossing holes
(set! geometry
        (list (make block (center 0 0 0) (material air) (size barwidth
barhigh infinity)))
        (append
             (list (make block (center 0 0 0) (material air) (size barhigh
barwidth infinity)))))

(set! geometry
      (append
       ; duplicate the crossings over the supercell:
       (geometric-objects-lattice-duplicates geometry)))

;make Left air area
(set! geometry
        (append  (list (make block (center (- (* (sqrt 2) -3.5) 0.25) (+
(sqrt 2) 0.25) 0)
        (material air) (size airwidth airhigh infinity)))))

;make Right air area
(set! geometry
        (append  (list (make block (center (+ (* (sqrt 2) 3.5) 0.25) (+
(sqrt 2) 0.25) 0)
        (material air)  (size airwidth airhigh infinity)))))


The problem is that the crossing is not duplicated. It seems that the
"Apend" command doesnot work, why? Thanks a lot.

First of all, that paper was looking at two-dimensional photonic crystals,
> *not* photonic-crystal slabs (although of course one could do an analogous
> calculation for a slab).
>
> Although I don't have the input file that was used for that figure in the
> paper, I don't think you can infer the supercell from figure 3(a), for two
> reasons.
>
> First of all, for a surface-state calculation, you want to use only a
> single unit cell in the periodic direction(s) parallel to the surface.  In
> figure 3(a), several unit cells are shown for illustration purposes.
>
> Second, in the direction perpendicular to the surface, you want a
> supercell, with enough air (on one side of the surface) and photonic
> crystal (on the other side of the surface) that the exponentially
> localized surface mode(s) don't "see" the boundary of the supercell.  How
> big your supercell has to be therefore depends on the structure and on
> what wavevector you are looking at, which determines how localized your
> states are.
>
> I'm not sure exactly what you mean by "one-dimensional photonic crystal".
> It is true that a surface in a 2d photonic crystal is periodic only along
> one dimension, as I mentioned above.  But the dielectric function is not
> univariate, so the system is not "one-dimensional" per se.
>
> Cordially,
> Steven G. Johnson
>
> PS. Because of the periodic boundary conditions of the supercell, your
> surface-state calculation will have two surfaces of the photonic crystal
> (there is no way to make the crystal semi-infinite).  There are two
> approaches to dealing with this.  One approach is to make the surfaces
> symmetric, as in figure 3 of the PRB, and look at say the even modes (or
> the odd modes, it doesn't matter), which will have identical surface
> states on both surfaces, with the same dispersion relation if the
> supercell is large enough.  Another approach is to terminate *one* of the
> surfaces with a termination that doesn't support surface states; this
> requires some experimentation if you don't know what termination you need,
> however.

_______________________________________________
mpb-discuss mailing list
[email protected]
http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/mpb-discuss