Hello everyone,
I am using MPB to compute dispersion relations for the diamond lattice
as described by a minimal surface equation:
cos(Z) sin(X+Y) + sin(Z) cos(X-Y) = t
where X = 2 pi x/a; Y = 2 pi y/a; Z = 2 pi z/a. Lower case x, y and z
are the Cartesian coordinates for the surface.
The reference for this equation is: Wilts, B.D., Michielsen, K. et al.
"Hemispherical brillouin zone imaging of a
diamond-type biological photonic crystal", J. R. Soc. Interface,
doi:10.1098/rsif.2011.0730.
I am attempting to compare the band results for this surface with those
of a regular diamond lattice at the same
dielectric filling fraction, 78.5 %.
The band diagrams compare favorably but are not the same. I am unsure
(due to lack of experience)
as to whether or not I have set the calculation up correctly. The
iso-surface plot produced by rote calculation of the
surface looks different than the iso-surface plot produced by viewing
the epsilon.h5 file by using Visit.
My ctl file is shown below. Any help will be appreciated. Thanks very
much.
; diamond lattice - surface equation method test
;
(define pi 3.141592654)
(define a 1.0)
(define twopioa (/ (* 2 pi) a))
(define px 0.0)
(define py 0.0)
(define pz 0.0)
(define fr 0.0)
(define t 0.70)
(define epsc 2.45)
(define epsa 1.0)
(define (eps-func p)
(set! fr 0.0)
(set! px (vector3-x (lattice->cartesian p)))
(set! py (vector3-y (lattice->cartesian p)))
(set! pz (vector3-z (lattice->cartesian p)))
(set! fr (+ (+ (* px twopioa) (* py twopioa)) (* pz twopioa)))
(make dielectric (epsilon
(if (> fr t) epsa epsc ))))
(set! geometry-lattice (make lattice
(basis-size (sqrt 0.5) (sqrt 0.5) (sqrt 0.5))
(basis1 0 1 1)
(basis2 1 0 1)
(basis3 1 1 0)))
(set! k-points (interpolate 4 (list
(vector3 0 0.5 0.5) ; X
(vector3 0 0.625 0.375) ; U
(vector3 0 0.5 0) ; L
(vector3 0 0 0) ; Gamma
(vector3 0 0.5 0.5) ; X
(vector3 0.25 0.75 0.5) ; W
(vector3 0.375 0.75 0.375)))) ; K
(set! default-material (make material-function
(material-func eps-func)))
(set-param! resolution 32)
(set-param! mesh-size 3)
(set-param! num-bands 3)
(run)
Doug Nance
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