> Hi guys i made almost 3 years ago the geometry for the image on pp. 72.
the ctl file was simple:
(define-param eps 8.9) ; the dielectric constant of the spheres
(define m (make dielectric (epsilon eps)))
(set! geometry-lattice (make lattice ( size 1 1 no-size)))
(set! geometry (list (make cylinder (center 0 0 0)(material m)
(radius infinity) (height 0.165) (axis 0 1 0));
checar el ejr\e
(make cylinder (center 0 0 0)(material m)
(radius infinity) (height 0.165) (axis 1 0 0))))
(set! resolution 32)
(run-tm output-efield-z)
(run-te (output-at-kpoint (vector3 0.5 0 0) output-hfield-z output-dpwr))
its been a while since i made it but a remembered that has a little isues
with the axis, but the band structure was right.
I hope this can help you. =)
> Hi centaur,
>
>
>
> Thank you a lot for your explanation. I did the correction Mahmoud
> suggested and I can get numerical results for all k in the Brillouin zone
> now. But plotting the eigenvales doesn't give the correct band structure
> (at least that one depicted in the textbook at page 72 for instance). The
> first 3 bands I get are similar, but the forth one is different. I used a
> 128 grid resolution and here's what I got:
>
>
>
>
>
> init-params: initializing eigensolver data
>
> Computing 8 bands with 1.000000e-07 tolerance.
>
> Working in 2 dimensions.
>
> Grid size is 128 x 128 x 1.
>
> Solving for 8 bands at a time.
>
> Creating Maxwell data...
>
> Allocating fields...
>
> Mesh size is 3.
>
> Lattice vectors:
>
> (1, 0, 0)
>
> (0, 1, 0)
>
> (0, 0, 1)
>
> Cell volume = 1
>
> Reciprocal lattice vectors (/ 2 pi):
>
> (1, -0, 0)
>
> (-0, 1, -0)
>
> (0, -0, 1)
>
> Geometric objects:
>
> block, center = (0,0,0)
>
> size (1,1,0)
>
> axes (1,0,0), (0,1,0), (0,0,1)
>
> dielectric constant epsilon = 8.9
>
> block, center = (0,0,0)
>
> size (0.9175,0.9175,0)
>
> axes (1,0,0), (0,1,0), (0,0,1)
>
> dielectric constant epsilon = 1
>
> Geometric object tree has depth 4 and 19 object nodes (vs. 2 actual
> objects)
>
> Initializing dielectric function...
>
> 16 k-points:
>
> (0,0,0)
>
> (0.1,0,0)
>
> (0.2,0,0)
>
> (0.3,0,0)
>
> (0.4,0,0)
>
> (0.5,0,0)
>
> (0.5,0.1,0)
>
> (0.5,0.2,0)
>
> (0.5,0.3,0)
>
> (0.5,0.4,0)
>
> (0.5,0.5,0)
>
> (0.4,0.4,0)
>
> (0.3,0.3,0)
>
> (0.2,0.2,0)
>
> (0.1,0.1,0)
>
> (0,0,0)
>
> Solving for band polarization: tm.
>
> Initializing fields to random numbers...
>
> elapsed time for initialization: 0 seconds.
>
> epsilon: 1-8.9, mean 2.22403, harm. mean 1.16912, 16.449% > 1, 15.4941%
> "fill"
>
> matrixio: cannot output "epsilon" (compiled without HDF)
>
> Outputting epsilon...
>
> solve_kpoint (0,0,0):
>
> tmfreqs:, k index, k1, k2, k3, kmag/2pi, tm band 1, tm band 2, tm band 3,
> tm band 4, tm band 5, tm band 6, tm band 7, tm band 8
>
> Solving for bands 2 to 8...
>
> Finished solving for bands 2 to 8 after 24 iterations.
>
> tmfreqs:, 1, 0, 0, 0, 0, 0, 0.55462, 0.584893, 0.647329, 0.647329,
> 0.916036, 0.975607, 1.02498
>
> elapsed time for k point: 3 seconds.
>
> solve_kpoint (0.1,0,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 11 iterations.
>
> tmfreqs:, 2, 0.1, 0, 0, 0.1, 0.0669224, 0.540818, 0.576425, 0.648193,
> 0.668831, 0.906108, 0.966719, 1.01149
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.2,0,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 6 iterations.
>
> tmfreqs:, 3, 0.2, 0, 0, 0.2, 0.133004, 0.500709, 0.576419, 0.650482,
> 0.706253, 0.883264, 0.941601, 1.00332
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.3,0,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 7 iterations.
>
> tmfreqs:, 4, 0.3, 0, 0, 0.3, 0.197058, 0.451673, 0.581184, 0.653367,
> 0.74477, 0.858876, 0.909578, 1.00078
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.4,0,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 6 iterations.
>
> tmfreqs:, 5, 0.4, 0, 0, 0.4, 0.256026, 0.401307, 0.585904, 0.655749,
> 0.780163, 0.840954, 0.877558, 0.999922
>
> elapsed time for k point: 0 seconds.
>
> solve_kpoint (0.5,0,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 5 iterations.
>
> tmfreqs:, 6, 0.5, 0, 0, 0.5, 0.290329, 0.369845, 0.587855, 0.656671,
> 0.799715, 0.83437, 0.859091, 0.999707
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.5,0.1,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 7 iterations.
>
> tmfreqs:, 7, 0.5, 0.1, 0, 0.509902, 0.295654, 0.375827, 0.568536, 0.67548,
> 0.800089, 0.81972, 0.859164, 0.980526
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.5,0.2,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 6 iterations.
>
> tmfreqs:, 8, 0.5, 0.2, 0, 0.538516, 0.3108, 0.392257, 0.533092, 0.709383,
> 0.78517, 0.801307, 0.859364, 0.947961
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.5,0.3,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 6 iterations.
>
> tmfreqs:, 9, 0.5, 0.3, 0, 0.583095, 0.333404, 0.414639, 0.495614,
> 0.743953, 0.745908, 0.804065, 0.859616, 0.913533
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.5,0.4,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 5 iterations.
>
> tmfreqs:, 10, 0.5, 0.4, 0, 0.640312, 0.358894, 0.435299, 0.461556,
> 0.714307, 0.771476, 0.811843, 0.859821, 0.880291
>
> elapsed time for k point: 0 seconds.
>
> solve_kpoint (0.5,0.5,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 5 iterations.
>
> tmfreqs:, 11, 0.5, 0.5, 0, 0.707107, 0.373594, 0.444088, 0.444088, 0.7018,
> 0.781038, 0.823407, 0.859899, 0.859899
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.4,0.4,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 5 iterations.
>
> tmfreqs:, 12, 0.4, 0.4, 0, 0.565685, 0.341631, 0.45163, 0.456954,
> 0.725973, 0.766027, 0.79736, 0.87409, 0.885092
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.3,0.3,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 6 iterations.
>
> tmfreqs:, 13, 0.3, 0.3, 0, 0.424264, 0.271729, 0.472824, 0.483875,
> 0.735067, 0.757502, 0.782055, 0.902434, 0.922019
>
> elapsed time for k point: 0 seconds.
>
> solve_kpoint (0.2,0.2,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 7 iterations.
>
> tmfreqs:, 14, 0.2, 0.2, 0, 0.282843, 0.186379, 0.503616, 0.519534,
> 0.699542, 0.715404, 0.844811, 0.933312, 0.959658
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0.1,0.1,0):
>
> Solving for bands 1 to 8...
>
> Finished solving for bands 1 to 8 after 9 iterations.
>
> tmfreqs:, 15, 0.1, 0.1, 0, 0.141421, 0.0944507, 0.536736, 0.55934,
> 0.665262, 0.673318, 0.895697, 0.961462, 0.996788
>
> elapsed time for k point: 1 seconds.
>
> solve_kpoint (0,0,0):
>
> Solving for bands 2 to 8...
>
> Finished solving for bands 2 to 8 after 14 iterations.
>
> tmfreqs:, 16, 0, 0, 0, 0, 0, 0.55462, 0.584893, 0.647329, 0.647329,
> 0.916036, 0.975607, 1.02498
>
> elapsed time for k point: 2 seconds.
>
> Band 1 range: 0.0 at #(0 0 0) to 0.373593761541658 at #(0.5 0.5 0)
>
> Band 2 range: 0.369845219009963 at #(0.5 0 0) to 0.554619673821229 at #(0
> 0 0)
>
> Band 3 range: 0.44408758157381 at #(0.5 0.5 0) to 0.587854966282244 at
> #(0.5 0 0)
>
> Band 4 range: 0.647329007716348 at #(0 0 0) to 0.743953468761287 at #(0.5
> 0.3 0)
>
> Band 5 range: 0.647329011025346 at #(0 0 0) to 0.80008895291846 at #(0.5
> 0.1 0)
>
> Band 6 range: 0.7820547571181 at #(0.3 0.3 0) to 0.916036167003583 at #(0
> 0 0)
>
> Band 7 range: 0.859091237355604 at #(0.5 0 0) to 0.975607478161245 at #(0
> 0 0)
>
> Band 8 range: 0.859899019931888 at #(0.5 0.5 0) to 1.02498251525285 at #(0
> 0 0)
>
> Gap from band 3 (0.587854966282244) to band 4 (0.647329007716348),
> 9.62998916535034%
>
> total elapsed time for run: 16 seconds.
>
> done.
>
>
>
> Some deprecated features have been used. Set the environment
>
> variable GUILE_WARN_DEPRECATED to "detailed" and rerun the
>
> program to get more information. Set it to "no" to suppress
>
> this message.
>
>
>
>
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