# [MPB-discuss] Band diagram of photonic crystal slabs on insulator

```Hi,

I am trying to obtain the band diagram of a photonic crystal slab with
triangular hole lattice on insulator.When I simulated it , The corners
of the every band graph enters to inside of light cone and this
situation causes all gaps disappear.When I simulated same design as
airbridged without insulator,this situation has gone and I could
determine the gaps. I am attaching the graph I obtained and the code I
am using below.Especially Professor Johnson, if you can help me I will
be grateful.
Thank you
```

(define-param h 0.5755) ; the thickness of the slab
(define-param h_sub 2.4) ; the thickness of the oxide
(define-param eps 12.0) ; the dielectric constant of the slab
(define-param eps_sub 2.25) ; the dielectric constant of the slab
(define-param loweps 1.0) ; the dielectric constant of the substrate
(define-param r 0.419) ; the radius of the holes
(define-param supercell-h 6) ; height of the supercell

; triangular lattice with vertical supercell:
(set! geometry-lattice (make lattice (size 1 1 supercell-h)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)))

(set! geometry
(list (make block (material (make dielectric (epsilon loweps)))
(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))
(make block (material (make dielectric (epsilon eps_sub)))
(center 0 0 (- 0 (/ (+ h h_sub) 2))) (size infinity infinity
h_sub))
(make cylinder (material air)
(center 0) (radius r) (height h))))

; 1st Brillouin zone of a triangular lattice:
(define Gamma (vector3 0 0 0))
(define M (vector3 0 0.5 0))
(define K (vector3 (/ -3) (/ 3) 0))

(define-param only-K false) ; run with only-K=true to only do this k-point
(define-param k-interp 32)   ; the number of k points to interpolate
(if only-K
(set! k-points (list K))
(set! k-points (interpolate k-interp (list Gamma M K Gamma))))

(set-param! resolution (vector3 32 32 16))
(set-param! num-bands 9)

; Run even and odd bands, outputting fields only at the K point:
(if (= loweps 1.0)
(begin ; we only have even/odd classification for symmetric structure
(run-zeven (output-at-kpoint K output-hfield-z))
(run-zodd (output-at-kpoint K output-dfield-z)))
(run (output-at-kpoint K output-hfield-z) display-zparities))

(display-eigensolver-stats)

--
Murat Can Sarıhan
Electrical - Electronics Engineering Junior Student
Middle East Technical University / Ankara, Turkey
Phone: +90 545 454 38 38
Mail : mcansari...@gmail.com

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