band structure of line defect waveguide
Tomofumi Kise <kise <at> yokoken.furukawa.co.jp>
2003-11-10 04:37:19 GMT
Dear Steven,
I calculated the band structure of line defect waveguide
with air-hole triangular lattice slab structure (air-bridge type).
I attached my ctl. file below.
My question is as follows,
Introducing a line defect, there arise many new bands.
I can identify the "guided mode" among them by judging
from whether the output field is localized in the line defect region,
but the band structure of that guided mode is different from those
calculated by FDTD method, especially in the area near and above
the so called "light line".
(see for example, IEEE J. Quantum. Electron. v.38, p.743, 2002, Fig. 4(a) .
My calculated parameters are the same as in this paper.)
Is this due to the calculation method itself? MPB cannot solve in principle
the modes above the light line and it's not correct in that region?
In addition, there also exist new additional bands by MPB, which do not
appear by FDTD.
Does this caused by the assumed boundary conditions or something?
If you have any idea to reproduce or approach the band structures
which widely reported by FDTD, could you comment?
(For example, the size of the supercell, etc.)
Or is there anything wrong in my ctl. file?
Sincerely,
Tomofumi Kise
my attached ctl. file
-------------------------------------------------------
(define-param h 0.571) ; the thickness of the slab
(define-param eps 12.25) ; the dielectric constant of the slab
(define-param loweps 1.0) ; the dielectric constant of the clad
(define-param r 0.312) ; the radius of the holes
(define-param supercell-y 7) ; the (odd) number of lateral supercell periods
(define-param supercell-h 4) ; height of the supercell
; triangular lattice with supercell:
(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 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 cylinder (material air)
(center 0) (radius r) (height supercell-h))))
(set! geometry
(append
; duplicate the bulk crystal rods over the supercell:
(geometric-objects-lattice-duplicates geometry 1 1 4)
; add a rod of slab, to erase a row of air rods and form a waveguide:
(list
(make cylinder (center 0) (radius r) (height h)
(material (make dielectric (epsilon eps)))))))
(define Gamma (vector3 0 0 0 ))
(define K' (lattice->reciprocal (vector3 0.5 0 0))) ; edge of Brillouin
zone.
(set! k-points (interpolate 4 (list Gamma K')))
(set! num-bands 20)
(set-param! resolution (vector3 16 16 8))
(run-zeven
(output-at-kpoint (list-ref k-points (quotient (length k-points) 2))
fix-hfield-phase output-hfield-z))
(display-eigensolver-stats)
-----------------------------------------------------
END
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