3D doubts

Vincent Paeder <[email protected]> Thu, 09 Nov 2006 16:09:26 +0100

Newsgroups	gmane.comp.science.photonic-bands
Message-ID	<1163084966.28927.28.camel@localhost>

hi all,
I want to simulate a 3D slab of rods (see attached file rods-3d.ctl). I
started with the 2D case and supposed that, if the slab fills the cell
entirely in the z direction, I'd find the same band diagram as in 2D.

However, I don't, and I don't either understand why. With increasing z,
one can see flat bands appearing here and there.

I don't see for what kind of physical reason that may happen. Therefore,
I thought of groping around the following things: 
	1) influence of the resolution for fixed z
	2) influence of the mesh size for fixed z
	3) influence of the cell size (in z)
	4) influence of the number of bands

Nothing seems to help. Changing z is the only thing that really makes a
difference and it's the only thing that shouldn't.

Now I'm running out of ideas. Does anybody have a clue?

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

rod-3d.ctl (text/plain, 1.3 KB)

(define-param r 0.3)      ; radius of cylinders
(define-param nout 1.457) ; index of outer medium
(define-param n 1.5)      ; index of slab
(define-param rodn 3.52)  ; index of cylinders
(define-param z 2.0)      ; cell height
(define-param sthk 0.4)   ; slab thickness
(define-param resol 48)   ; resolution
(define-param mesh 10)    ; mesh size
(define-param nb 8)       ; number of bands

(set! geometry-lattice (make lattice (size 1 1 z)
                         (basis1 (/ (sqrt 3) 2) 0.5 0)
                         (basis2 (/ (sqrt 3) 2) -0.5 0)
                         (basis3 0 0 1)
                         ))
(set! resolution resol)
(set! num-bands nb)
(set! mesh-size mesh)

(set! k-points (list (vector3 0 0 0)          ; Gamma
                     (vector3 0 0.5 0)        ; M
                     (vector3 (/ -3) (/ 3) 0) ; K
                     (vector3 0 0 0)))        ; Gamma

(set! k-points (interpolate 96 k-points))

(set! default-material (make dielectric (index nout)))
(set! geometry (list
                (make block
                  (center 0 0 0) (size 1 1 sthk)
                  (material (make dielectric (index n))))
                (make cylinder
                       (center 0 0 0) (radius r) (height sthk)
                       (material (make dielectric (index rodn))))
                ))

(run-zeven)