Dear mpb users,
I am trying to get band diagram of hexagonal photonic crytsal without and
with defect(one row rods are removed) in sample figure 1.20 of "Photonic
crystals, Towards Nanoscale Photonic Devices, Jean-Michel Lourtioz's book.
o o
o
o o
o
o o
x
o o
o
o o
o
o o
But, obtained band structure is different. Band gap begin at the same
frequency but upper band gap edge is different.
My code is below. Could you show me where the mistake is?
best regards.
---------------------------------------------------------
;;For hexagonal phc without defect:
(define-param epspoly 13) ; the dielectric constant of the background
(define-param epsair 1) ; holes
(define-param r 0.4) ; the radius of the holes
(define-param supercell-y 31) ; the (odd) number of lateral supercell periods
(set! default-material (make dielectric (epsilon epspoly)))
; triangular lattice with vertical supercell:
(set! geometry-lattice (make lattice (size 1 supercell-y 1)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)))
;;;;;;;;;;;;;;;;;;;;;;;; Geometry
(define-param a 1)
(define-param d (* (/ (sqrt 3) 2) a))
(set! geometry
(append
(geometric-objects-lattice-duplicates
(list
(make cylinder (center 0 0 0) (radius r) (height infinity)
(material (make dielectric (epsilon epsair)))
)
(make cylinder (center (* .5 a) (* -1 d) 0) (radius r)
(height
infinity) (material (make dielectric (epsilon epsair)))
)
)
1 (* a (sqrt 3) a))
))
; 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 only-K false) ; run with only-K=true to only do this k-point
(define-param k-interp 9) ; the number of k points to interpolate
(if only-K
(set! k-points (list K))
(set! k-points (interpolate k-interp (list Gamma K'))))
(define-param res 32)
(set! grid-size (vector3 res (* res supercell-y) 1))
(define-param extra-bands 125)
(set! num-bands (+ supercell-y extra-bands))
(set-param! mesh-size 7)
(run-tm)
-----------------------------------------------------------
;; for hexagonal phc with defect. one row rods are removed
(define-param epspoly 13) ; the dielectric constant of the background
(define-param epsair 1) ; holes
(define-param r 0.4) ; the radius of the holes
(define-param supercell-y 31) ; the (odd) number of lateral supercell periods
(set! default-material (make dielectric (epsilon epspoly)))
; triangular lattice with vertical supercell:
(set! geometry-lattice (make lattice (size 1 supercell-y 1)
(basis1 (/ (sqrt 3) 2) 0.5)
(basis2 (/ (sqrt 3) 2) -0.5)))
;;;;;;;;;;;;;;;;;;;;;;;; Geometry
(define-param a 1)
(define-param d (* (/ (sqrt 3) 2) a))
(set! geometry
(append
(geometric-objects-lattice-duplicates
(list
(make cylinder (center 0 0 0) (radius r) (height infinity)
(material (make dielectric (epsilon epsair)))
)
(make cylinder (center (* .5 a) (* -1 d) 0) (radius r)
(height
infinity) (material (make dielectric (epsilon epsair)))
)
)
1 (* a (sqrt 3) a))
))
(set! geometry (append geometry
(list (make cylinder (center 0 0 0)
(radius r) (height infinity)
(material (make dielectric (epsilon
epspoly))))
)
)
)
; 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 only-K false) ; run with only-K=true to only do this k-point
(define-param k-interp 9) ; the number of k points to interpolate
(if only-K
(set! k-points (list K))
(set! k-points (interpolate k-interp (list Gamma K'))))
(define-param res 32)
(set! grid-size (vector3 res (* res supercell-y) 1))
(define-param extra-bands 125)
(set! num-bands (+ supercell-y extra-bands))
(set-param! mesh-size 7)
;(run-te)
(run-tm)
--------------------------------------------------
Ozgur Onder KARAKILINC
Pamukkale University
Electrical-Electronics Eng.Dept.
20070 Kinikli-Denizli TURKEY
Tel: (+90 258) 296 3213
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