Re: How to define various widths of waveguides in triangular lattice PC slab?

With the (basis1) and (basis2) commands, you have indicated that  
coordinates will use this non-rectangular basis. You then want to  
shift the holes in the y direction, which is not parallel to either of  
your basis vectors. You have two options, convert the shift for the  
holes into your specified basis, or work in a rectangular basis. My  
personal feeling is that the rectangular basis is a bit easier to use.  
See the revised code below which uses a rectangular basis.
-Mark Patterson
Dept. of Physics
Queen's University at Kingston

(define-param h 0.6) ; the thickness of the slab
(define-param eps 12) ;
(define-param subeps 2.1025) ;
(define-param r 0.3335 ) ; the radius of the holes
(define-param supercell-h 4) ; height of the supercell

(define-param dy (/ 0.65 2))
(define-param supercell-y (+ 10 (* 2 dy))) ; the (odd) number of  
lateral supercell periods

(set! geometry-lattice (make lattice (size 1 supercell-y supercell-h)
    (basis1 1 0)
    (basis2 0 (/ (sqrt 3) 2))))

(set! geometry
      (list (make block (material (make dielectric (epsilon subeps)))
                  (center 0 0 (* 0.25 supercell-h)) (size infinity  
infinity (* 0.5 supercell-h)))
            (make block (material (make dielectric (epsilon eps)))
                  (center 0) (size infinity infinity h))))

(set! geometry
        (append geometry
             (list (make cylinder (material air)
                     (center 0.5 (+ 1 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0 (+ 2 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0.5 (+ 3 dy) 0) (radius r) (height h))
                     (make cylinder (material air)
                     (center 0 (+ 4 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0.5 (+ 5 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0.5 (- -1 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0 (- -2 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0.5 (- -3 dy) 0) (radius r) (height h))
                     (make cylinder (material air)
                     (center 0 (- -4 dy) 0) (radius r) (height h))
                   (make cylinder (material air)
                     (center 0.5 (- -5 dy) 0) (radius r) (height h))
                     )))
;define the defect of the clad layer(fill in)

; 1st Brillouin zone of a triangular lattice:
(define Gamma (vector3 0 0 0))
;(define K' (lattice->reciprocal (vector3 0.5 0 0))) ; edge of  
Brillouin zone.
;(define-param k-interp 8)   ; the number of k points to interpolate
; (set! k-points (interpolate k-interp (list Gamma K')))
(set! k-points (list Gamma))
(set-param! resolution (vector3 24 24 24))
; (set-param! mesh-size 7)
; (set-param! num-bands 15)
(set-param! num-bands 1)
; Run even and odd bands, outputting fields only at the K point:
(run-zeven)

On 2008-09-17, at 10:36 , Jin Hou wrote:

> Dear Steven and MPB's users,
>
>      I would like to calculate the waveguide dispersion of  
> triangular PCs slab.
> The waveguide width is not equal to conventional width of W1  
> waveguide, and is formed by moving (up and down) the nearest  
> neighbor air holes around the linear defect (For example,   
> W=0.65*sqrt3 =0.65*W1).  The same question was already asked by Nils  
> Jensen on 21 Apr 2008 in the mpb-discussion, his mail titled  
> "Waveguide in 2D-PCs of triangular symmetry". But I did not find the  
> solution.
>     I would like to define the structure like the usual W1  
> waveguide, but with different waveguide width.  But when I used the  
> similar codes like Nils Jensen used, the same problem appeared. The  
> two nearest neighbor holes are not symmetry by y axis, as the  
> attached picture showed.
>     I tried several other ways to define the structure, but the  
> problem remains. Below is one of the codes, and the attached picture  
> is the unexpected structure of the result. Other ways have the same  
> result of structure output in the *.out file.
>     Is there someone know how to define the structure correctly?
>     Thanks!
>
>
> (define-param h 0.6) ; the thickness of the slab
> (define-param eps 12) ;
> (define-param subeps 2.1025) ;
> (define-param r 0.3335 ) ; the radius of the holes
> (define-param supercell-h 4) ; height of the supercell
> (define-param supercell-y 10.3) ; the (odd) number of lateral  
> supercell periods
>
> (set! geometry-lattice (make lattice (size 1 supercell-y supercell-h)
>    (basis1 (/ (sqrt 3) 2) 0.5)
>    (basis2 (/ (sqrt 3) 2) -0.5)))
>
> (set! geometry
>      (list (make block (material (make dielectric (epsilon subeps)))
>                  (center 0 0 (* 0.25 supercell-h)) (size infinity  
> infinity (* 0.5 supercell-h)))
>            (make block (material (make dielectric (epsilon eps)))
>                  (center 0) (size infinity infinity h))))
>
>
> (set! geometry
>        (append geometry
>             (list (make cylinder (material air)
>                     (center 0 0.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 1.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 2.65 0) (radius r) (height h))
>                     (make cylinder (material air)
>                     (center 0 3.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 4.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 -0.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 -1.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 -2.65 0) (radius r) (height h))
>                     (make cylinder (material air)
>                     (center 0 -3.65 0) (radius r) (height h))
>                   (make cylinder (material air)
>                     (center 0 -4.65 0) (radius r) (height h))
>                     )))
> ;define the defect of the clad layer(fill in)
>
> ; 1st Brillouin zone of a triangular lattice:
> (define Gamma (vector3 0 0 0))
> (define K' (lattice->reciprocal (vector3 0.5 0 0))) ; edge of  
> Brillouin zone.
> (define-param k-interp 8)   ; the number of k points to interpolate
>  (set! k-points (interpolate k-interp (list Gamma K')))
> (set-param! resolution (vector3 24 24 24))
> (set-param! mesh-size 7)
> (set-param! num-bands 15)
> ; Run even and odd bands, outputting fields only at the K point:
> (run-zeven)
>
>
>
> Best wishes,
>                            Yours,
>                           Jin Hou　　 
> 　　　　　　　　　　　　　　　　　　　
> Wuhan National Laboratory for Optoelectronics,
> College of Optoelectronic Science and Engineering,
> Huazhong University of Science & Technology,
> Wuhan, 430074, P.R.CHINA
> Phone: 86-027-87792195
> Web:  http://oe.hust.edu.cn/sub_web/zzp/lab_web/Index.html
>
> 开心过好每一天！
>
> 雅虎邮箱，您的终生邮箱！ 
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