Waveguide in PC slabs (Triangular lattice)

Nils Jensen <[email protected]>
Newsgroups gmane.comp.science.photonic-bands
Message-ID <[email protected]>
Dear Steven and MPB’s users,
   I would like to study the reduced and increased index waveguides in PC slabs (Triangular lattice). The waveguide is formed by decreasing/increasing the radii of a line of nearest-neighbor rods/holes, respectively. (According to the paper: Phys. Rev. B 62, 8212 (2000)). 
   First of all, I define the structure: PC slab with triangular lattice of air holes, the reduced index hole slab waveguide is formed by increasing the radii of a line nearest-neighbor holes. 
   The second, I have some MPB’s command as below to calculate the projected band structure. 

(set! geometry-lattice (make lattice (size 7 7 4))
                        (basis1 (/ (sqrt 3) 2) 0.5)
                        (basis2 (/ (sqrt 3) 2) -0.5))
(define-param h 0.5) ; the thickness of the slab
(define-param supercell 4) ; the thickness of the slab
(define-param eps 12) ; the dielectric constant of the slab
(define-param r 0.3) ; the hole radius in the bulk crystal
(define-param ra 0.4) ; the hole radius in the line defect
(set! geometry (append
    (list 
       (make block (center 0 0 0) (size 7 7 4) (material air))
       (make block (center 0 0 0) (size 7 7 0.5)
                   (material (make dielectric (epsilon eps))))
    );list
    (geometric-object-duplicates (vector3 1 0 0) 0 7
      (make cylinder (center -2 -3 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 6
      (make cylinder (center -2 -2 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 7
      (make cylinder (center -3 -1 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 6
      (make cylinder (center -3 0 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 7
      (make cylinder (center -4 1 0) (radius ra) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 6
      (make cylinder (center -4 2 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 7
      (make cylinder (center -5 3 0) (radius r) (height supercell) 
                     (material air)))
    (geometric-object-duplicates (vector3 1 0 0) 0 6
      (make cylinder (center -5 4 0) (radius r) (height supercell) 
                     (material air)))
  );append
)
(define Gamma (vector3 0 0 0))
(define K' (lattice->reciprocal (vector3 0 0.5 0))) ; edge of Brillouin zone
(define-param only-K' false)
(define-param k-interp 8)
(if only-K'
  (set! k-points (list K'))
  (set! k-points (interpolate k-interp (list Gamma K'))))
(set-param! resolution 16)
(set-param! num-bands 8)
(run-zeven (output-at-kpoint K' output-hfield-z))
(run-zodd (output-at-kpoint K' output-efield-z))
(display-eigensolver-stats)
 
My epsilon file is wright, but I don’t understand why my result is wrong - projected band (according to PRB 62, 8212). Could you help me to bug my *.ctl file?
 
I thank you in advance,
Nils Jensen

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