Dear Steven, dear MEEP users.
I try to compute the band structure of the 2D triangular lattice of
dielectric rods. I have defined the supercell as was recommended by
Steve and put also the 5 sources shifted with the Bloch phase exp(i k*r)
into the computation cell in order to unfold the band structure. I am
calculating the band structure for the rectangular grid in the k-space,
and make a contour plot. I have expected that I will see the signature
of the symmetry of the triangular lattice, but I saw again the
rectangular one.
I guess that I made a mistake in the defining of the sources, but I
can't find it. My ctl file is giving below.
(define-param eps 12);
(define-param sx (sqrt 3) )
(define-param sy 1 )
(define-param a sy)
(define-param r (* a 0.3) ) ; radius of holes
(define Nx 10); number of computation points in k-space
(define Ny 10)
(define kxMax 1 ); size of grid in k-space
(define kyMax 1.7)
(define-param stepX (/ (* 2 kxMax) (- Nx 1) )); step in k-space
(define-param stepY (/ (* 2 kyMax) (- Nx 1) ) )
(define-param p1Vector (vector3 (/ sx 2 ) -0.5 ) ); basis vectors of
triangular lattice
(define-param p2Vector (vector3 (/ sx 2 ) 0.5) )
(define-param p3Vector (vector3 (/ sx -2 ) 0.5) )
(define-param p4Vector (vector3 (/ sx -2 ) -0.5) )
(define-param sVector (vector3 0.1 0.1)); position of the central source
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! geometry
(list
(make cylinder (center 0 0) (radius r) (height
infinity) (material(make dielectric (epsilon eps)))
)
(make cylinder (center (/ sx 2) (/ sy 2)) (radius r) (height
infinity) (material(make dielectric (epsilon eps)))
)
(make cylinder (center (/ sx -2) (/ sy 2)) (radius r)
(height infinity) (material(make dielectric (epsilon eps)))
)
(make cylinder (center (/ sx 2) (/ sy -2)) (radius r)
(height infinity) (material(make dielectric (epsilon eps)))
)
(make cylinder (center (/ sx -2) (/ sy -2)) (radius r)
(height infinity) (material(make dielectric (epsilon eps)))
)
)
)
(set-param! resolution 10)
(define-param fcen 0.31) ; pulse center frequency
(define-param df 1.5) ; pulse freq. width:
( do ((i 0 (1+ i)))
((> i (- Nx 1)))
(
do ((k 0 (1+ k)))
((> k (- Ny 1)))
(set! k-point (vector3 (+ (- kxMax) (* k stepX) ) (+
(- kyMax) (* i stepY) ) 0) )
(set! sources (list
(make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ez) (center sVector)
)
(make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ez) (center (vector3+ sVector
p1Vector))
(amplitude (exp (* 0+1i (vector3* k-point
p1Vector))) )
)
(make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ez) (center (vector3+ sVector
p2Vector))
(amplitude (exp (* 0+1i (vector3* k-point
p2Vector))) )
)
(make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ez) (center (vector3+ sVector
p3Vector))
(amplitude (exp (* 0+1i (vector3* k-point
p3Vector))) )
)
(make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ez) (center (vector3+ sVector
p4Vector))
(amplitude (exp (* 0+1i (vector3* k-point
p4Vector))) )
)
)
)
(run-k-point 300 k-point)
)
)
Maksim Miski-Oglu
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