triangular lattice

"Kai Lin Woon" <[email protected]>
Newsgroups gmane.comp.science.photonic-bands
Message-ID <[email protected]>
Hi all

I am learning to use the programme. I dont know whether I have input my parameter correctly. Worst still I dont know how to interpret the output data. My structure is basically a triangular lattice air hole array slab.

with radius of 0.2a, thickness of 3a and dielectric constant of 2.05.

I got results of

Band 1 range: 0.0 at #(0 0 0) to 0.483367541415775 at #(-0.333333333333333 0.333333333333333 0)
Band 2 range: 0.157720410628411 at #(0 0 0) to 0.483748773255701 at #(-0.333333333333333 0.333333333333333 0)
Band 3 range: 0.157839351869381 at #(0 0 0) to 0.510293008785601 at #(-0.333333333333333 0.333333333333333 0)
Band 4 range: 0.334102866446129 at #(0 0 0) to 0.536196307498935 at #(-0.266666666666667 0.266666666666667 0.0)

Can someone translate into human language of what does it mean? Describing graphically.

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hole-air-slabs.txt (application/octet-stream, 1.4 KB)
(define-param h 3) ; the thickness of the slab
(define-param eps 2.05) ; the dielectric constant of the slab
(define-param loweps 1.0) ; the dielectric constant of the substrate
(define-param r 0.2) ; the radius of the holes
(define-param supercell-h 5) ; 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 eps)))
		  (center 0 0 0) (size infinity infinity h))
	    (make cylinder (material air)
		  (center 0 0 0) (radius r) (height supercell-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 4)   ; 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 8 8 4))
(set-param! num-bands 4)

; Run even and odd bands, outputting fields only at the K point:
(run-zeven (output-at-kpoint K output-hfield-z))
(run-zodd (output-at-kpoint K output-dfield-z))

(display-eigensolver-stats)
results.txt (application/octet-stream, 11.9 KB)
init-params: initializing eigensolver data
Computing 4 bands with 1.000000e-07 tolerance.
Working in 3 dimensions.
Grid size is 8 x 8 x 20.
Solving for 4 bands at a time.
Creating Maxwell data...
Allocating fields...
Mesh size is 3.
Lattice vectors:
     (0.866025, 0.5, 0)
     (0.866025, -0.5, 0)
     (0, 0, 5)
Cell volume = 4.33013
Reciprocal lattice vectors (/ 2 pi):
     (0.57735, 1, -0)
     (0.57735, -1, 0)
     (-0, 0, 0.2)
Geometric objects:
     block, center = (0,0,0)
          size (1e+20,1e+20,3)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon = 2.05
     cylinder, center = (0,0,0)
          radius 0.2, height 5, axis (0, 0, 1)
          dielectric constant epsilon = 1
Geometric object tree has depth 3 and 14 object nodes (vs. 2 actual objects)
Initializing dielectric function...
16 k-points:
     (0,0,0)
     (0,0.1,0)
     (0,0.2,0)
     (0,0.3,0)
     (0,0.4,0)
     (0,0.5,0)
     (-0.0666667,0.466667,0)
     (-0.133333,0.433333,0)
     (-0.2,0.4,0)
     (-0.266667,0.366667,0)
     (-0.333333,0.333333,0)
     (-0.266667,0.266667,0)
     (-0.2,0.2,0)
     (-0.133333,0.133333,0)
     (-0.0666667,0.0666667,0)
     (0,0,0)
Solving for band polarization: zeven.
Initializing fields to random numbers...
elapsed time for initialization: 0 seconds.
epsilon: 1-2.05, mean 1.53484, harm. mean 1.38064, 61.9531% > 1, 50.9375% "fill"
Outputting epsilon...
solve_kpoint (0,0,0):
zevenfreqs:, k index, k1, k2, k3, kmag/2pi, zeven band 1, zeven band 2, zeven band 3, zeven band 4
Solving for bands 2 to 4...
Finished solving for bands 2 to 4 after 19 iterations.
zevenfreqs:, 1, 0, 0, 0, 0, 0, 0.171371, 0.171462, 0.322361
elapsed time for k point: 2 seconds.
solve_kpoint (0,0.1,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 11 iterations.
zevenfreqs:, 2, 0, 0.1, 0, 0.11547, 0.0931444, 0.194428, 0.199261, 0.336242
elapsed time for k point: 2 seconds.
solve_kpoint (0,0.2,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 9 iterations.
zevenfreqs:, 3, 0, 0.2, 0, 0.23094, 0.182263, 0.249937, 0.266859, 0.375277
elapsed time for k point: 1 seconds.
solve_kpoint (0,0.3,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zevenfreqs:, 4, 0, 0.3, 0, 0.34641, 0.267532, 0.319333, 0.350026, 0.435759
elapsed time for k point: 1 seconds.
solve_kpoint (0,0.4,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 34 iterations.
zevenfreqs:, 5, 0, 0.4, 0, 0.46188, 0.350774, 0.39368, 0.433001, 0.507788
elapsed time for k point: 4 seconds.
solve_kpoint (0,0.5,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 21 iterations.
zevenfreqs:, 6, 0, 0.5, 0, 0.57735, 0.419536, 0.452585, 0.462952, 0.478216
elapsed time for k point: 2 seconds.
solve_kpoint (-0.0666667,0.466667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zevenfreqs:, 7, -0.0666667, 0.466667, 0, 0.581187, 0.422564, 0.45503, 0.465347, 0.480862
elapsed time for k point: 2 seconds.
solve_kpoint (-0.133333,0.433333,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zevenfreqs:, 8, -0.133333, 0.433333, 0, 0.592546, 0.431496, 0.462286, 0.472461, 0.488649
elapsed time for k point: 0 seconds.
solve_kpoint (-0.2,0.4,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zevenfreqs:, 9, -0.2, 0.4, 0, 0.61101, 0.445857, 0.474121, 0.484075, 0.501061
elapsed time for k point: 1 seconds.
solve_kpoint (-0.266667,0.366667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 7 iterations.
zevenfreqs:, 10, -0.266667, 0.366667, 0, 0.635959, 0.464648, 0.490143, 0.499737, 0.516551
elapsed time for k point: 1 seconds.
solve_kpoint (-0.333333,0.333333,0):
Solving for bands 1 to 4...
    iteration   42: trace = 1.020463494705046 (8.97323e-05% change)
Finished solving for bands 1 to 4 after 44 iterations.
zevenfreqs:, 11, -0.333333, 0.333333, 0, 0.666667, 0.481027, 0.508374, 0.509078, 0.521029
elapsed time for k point: 4 seconds.
Outputting fields to h.k11.b01.z.zeven...
Outputting fields to h.k11.b02.z.zeven...
Outputting fields to h.k11.b03.z.zeven...
Outputting fields to h.k11.b04.z.zeven...
solve_kpoint (-0.266667,0.266667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 29 iterations.
zevenfreqs:, 12, -0.266667, 0.266667, 0, 0.533333, 0.402506, 0.440337, 0.482402, 0.552162
elapsed time for k point: 4 seconds.
solve_kpoint (-0.2,0.2,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 8 iterations.
zevenfreqs:, 13, -0.2, 0.2, 0, 0.4, 0.306595, 0.353452, 0.389295, 0.469223
elapsed time for k point: 1 seconds.
solve_kpoint (-0.133333,0.133333,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 7 iterations.
zevenfreqs:, 14, -0.133333, 0.133333, 0, 0.266667, 0.209014, 0.270489, 0.291892, 0.394853
elapsed time for k point: 0 seconds.
solve_kpoint (-0.0666667,0.0666667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 4 iterations.
zevenfreqs:, 15, -0.0666667, 0.0666667, 0, 0.133333, 0.107267, 0.201441, 0.207817, 0.341887
elapsed time for k point: 1 seconds.
solve_kpoint (0,0,0):
Solving for bands 2 to 4...
Finished solving for bands 2 to 4 after 4 iterations.
zevenfreqs:, 16, 0, 0, 0, 0, 0, 0.171371, 0.171462, 0.322613
elapsed time for k point: 0 seconds.
Band 1 range: 0.0 at #(0 0 0) to 0.48102747806562 at #(-0.333333333333333 0.333333333333333 0)
Band 2 range: 0.171371054687285 at #(0 0 0) to 0.508373940532307 at #(-0.333333333333333 0.333333333333333 0)
Band 3 range: 0.171462407767288 at #(0 0 0) to 0.509078282410883 at #(-0.333333333333333 0.333333333333333 0)
Band 4 range: 0.322361394526113 at #(0 0 0) to 0.552161796584612 at #(-0.266666666666667 0.266666666666667 0.0)
total elapsed time for run: 28 seconds.
done.
init-params: initializing eigensolver data
Computing 4 bands with 1.000000e-07 tolerance.
Working in 3 dimensions.
Grid size is 8 x 8 x 20.
Solving for 4 bands at a time.
Creating Maxwell data...
Mesh size is 3.
Lattice vectors:
     (0.866025, 0.5, 0)
     (0.866025, -0.5, 0)
     (0, 0, 5)
Cell volume = 4.33013
Reciprocal lattice vectors (/ 2 pi):
     (0.57735, 1, -0)
     (0.57735, -1, 0)
     (-0, 0, 0.2)
Geometric objects:
     block, center = (0,0,0)
          size (1e+20,1e+20,3)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon = 2.05
     cylinder, center = (0,0,0)
          radius 0.2, height 5, axis (0, 0, 1)
          dielectric constant epsilon = 1
Geometric object tree has depth 3 and 14 object nodes (vs. 2 actual objects)
Initializing dielectric function...
16 k-points:
     (0,0,0)
     (0,0.1,0)
     (0,0.2,0)
     (0,0.3,0)
     (0,0.4,0)
     (0,0.5,0)
     (-0.0666667,0.466667,0)
     (-0.133333,0.433333,0)
     (-0.2,0.4,0)
     (-0.266667,0.366667,0)
     (-0.333333,0.333333,0)
     (-0.266667,0.266667,0)
     (-0.2,0.2,0)
     (-0.133333,0.133333,0)
     (-0.0666667,0.0666667,0)
     (0,0,0)
Solving for band polarization: zodd.
Initializing fields to random numbers...
elapsed time for initialization: 1 seconds.
epsilon: 1-2.05, mean 1.53484, harm. mean 1.38064, 61.9531% > 1, 50.9375% "fill"
Outputting epsilon...
solve_kpoint (0,0,0):
zoddfreqs:, k index, k1, k2, k3, kmag/2pi, zodd band 1, zodd band 2, zodd band 3, zodd band 4
Solving for bands 2 to 4...
Finished solving for bands 2 to 4 after 18 iterations.
zoddfreqs:, 1, 0, 0, 0, 0, 0, 0.15772, 0.157839, 0.33411
elapsed time for k point: 2 seconds.
solve_kpoint (0,0.1,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 23 iterations.
zoddfreqs:, 2, 0, 0.1, 0, 0.11547, 0.0964696, 0.181865, 0.186686, 0.346734
elapsed time for k point: 2 seconds.
solve_kpoint (0,0.2,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 10 iterations.
zoddfreqs:, 3, 0, 0.2, 0, 0.23094, 0.186028, 0.239243, 0.258399, 0.382493
elapsed time for k point: 1 seconds.
solve_kpoint (0,0.3,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 5 iterations.
zoddfreqs:, 4, 0, 0.3, 0, 0.34641, 0.269335, 0.310704, 0.348518, 0.437617
elapsed time for k point: 1 seconds.
solve_kpoint (0,0.4,0):
Solving for bands 1 to 4...
    iteration   41: trace = 0.7241096238200005 (0.000269782% change)
Finished solving for bands 1 to 4 after 82 iterations.
zoddfreqs:, 5, 0, 0.4, 0, 0.46188, 0.350648, 0.387015, 0.438627, 0.504522
elapsed time for k point: 9 seconds.
solve_kpoint (0,0.5,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 20 iterations.
zoddfreqs:, 6, 0, 0.5, 0, 0.57735, 0.422469, 0.443017, 0.451275, 0.484908
elapsed time for k point: 2 seconds.
solve_kpoint (-0.0666667,0.466667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zoddfreqs:, 7, -0.0666667, 0.466667, 0, 0.581187, 0.425078, 0.445731, 0.4542, 0.487209
elapsed time for k point: 1 seconds.
solve_kpoint (-0.133333,0.433333,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zoddfreqs:, 8, -0.133333, 0.433333, 0, 0.592546, 0.432812, 0.453706, 0.462823, 0.494051
elapsed time for k point: 0 seconds.
solve_kpoint (-0.2,0.4,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 6 iterations.
zoddfreqs:, 9, -0.2, 0.4, 0, 0.61101, 0.445411, 0.466359, 0.476682, 0.505239
elapsed time for k point: 1 seconds.
solve_kpoint (-0.266667,0.366667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 9 iterations.
zoddfreqs:, 10, -0.266667, 0.366667, 0, 0.635959, 0.462474, 0.481784, 0.494772, 0.52036
elapsed time for k point: 1 seconds.
solve_kpoint (-0.333333,0.333333,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 19 iterations.
zoddfreqs:, 11, -0.333333, 0.333333, 0, 0.666667, 0.483368, 0.483749, 0.510293, 0.523579
elapsed time for k point: 2 seconds.
Outputting fields to d.k11.b01.z.zodd...
Outputting fields to d.k11.b02.z.zodd...
Outputting fields to d.k11.b03.z.zodd...
Outputting fields to d.k11.b04.z.zodd...
solve_kpoint (-0.266667,0.266667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 28 iterations.
zoddfreqs:, 12, -0.266667, 0.266667, 0, 0.533333, 0.400525, 0.435822, 0.489648, 0.536196
elapsed time for k point: 4 seconds.
solve_kpoint (-0.2,0.2,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 12 iterations.
zoddfreqs:, 13, -0.2, 0.2, 0, 0.4, 0.307181, 0.346077, 0.391083, 0.469659
elapsed time for k point: 2 seconds.
solve_kpoint (-0.133333,0.133333,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 5 iterations.
zoddfreqs:, 14, -0.133333, 0.133333, 0, 0.266667, 0.212225, 0.260506, 0.285312, 0.401158
elapsed time for k point: 1 seconds.
solve_kpoint (-0.0666667,0.0666667,0):
Solving for bands 1 to 4...
Finished solving for bands 1 to 4 after 5 iterations.
zoddfreqs:, 15, -0.0666667, 0.0666667, 0, 0.133333, 0.110877, 0.189209, 0.195596, 0.352337
elapsed time for k point: 1 seconds.
solve_kpoint (0,0,0):
Solving for bands 2 to 4...
Finished solving for bands 2 to 4 after 5 iterations.
zoddfreqs:, 16, 0, 0, 0, 0, 0, 0.15772, 0.157839, 0.334103
elapsed time for k point: 1 seconds.
Band 1 range: 0.0 at #(0 0 0) to 0.483367541415775 at #(-0.333333333333333 0.333333333333333 0)
Band 2 range: 0.157720410628411 at #(0 0 0) to 0.483748773255701 at #(-0.333333333333333 0.333333333333333 0)
Band 3 range: 0.157839351869381 at #(0 0 0) to 0.510293008785601 at #(-0.333333333333333 0.333333333333333 0)
Band 4 range: 0.334102866446129 at #(0 0 0) to 0.536196307498935 at #(-0.266666666666667 0.266666666666667 0.0)
total elapsed time for run: 33 seconds.
done.
eigensolver iterations for 32 k-points: 3.0-82.0, mean = 14.640625, median = 8.5
mean flops per iteration = 973725.993596585
mean time per iteration = 0.130202774813234 s
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