In [1]:

    

import math
import meep as mp
from meep import mpb

num_bands = 8
resolution = 32
geometry_lattice = mp.Lattice(size=mp.Vector3(1, 1),
                              basis1=mp.Vector3(math.sqrt(3) / 2, 0.5),
                              basis2=mp.Vector3(math.sqrt(3) / 2, -0.5))
geometry = [mp.Cylinder(0.2, material=mp.Medium(epsilon=12))]
k_points = [
    mp.Vector3(),               # Gamma
    mp.Vector3(y=0.5),          # M
    mp.Vector3(1 / -3, 1 / 3),  # K
    mp.Vector3(),               # Gamma
]
k_points = mp.interpolate(4, k_points)

ms = mpb.ModeSolver(
    geometry=geometry,
    geometry_lattice=geometry_lattice,
    k_points=k_points,
    resolution=resolution,
    num_bands=num_bands
)
ms.run_tm(mpb.output_at_kpoint(mp.Vector3(1 / -3, 1 / 3), mpb.fix_efield_phase,
          mpb.output_efield_z))
tm_freqs = ms.all_freqs
tm_gaps = ms.gap_list
ms.run_te()
te_freqs = ms.all_freqs
te_gaps = ms.gap_list


    

    




Initializing eigensolver data
Computing 8 bands with 1e-07 tolerance
16 k-points
  Vector3<0.0, 0.0, 0.0>
  Vector3<0.0, 0.1, 0.0>
  Vector3<0.0, 0.2, 0.0>
  Vector3<0.0, 0.30000000000000004, 0.0>
  Vector3<0.0, 0.4, 0.0>
  Vector3<0.0, 0.5, 0.0>
  Vector3<-0.06666666666666667, 0.4666666666666667, 0.0>
  Vector3<-0.13333333333333333, 0.43333333333333335, 0.0>
  Vector3<-0.2, 0.39999999999999997, 0.0>
  Vector3<-0.26666666666666666, 0.36666666666666664, 0.0>
  Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
  Vector3<-0.26666666666666666, 0.26666666666666666, 0.0>
  Vector3<-0.19999999999999998, 0.19999999999999998, 0.0>
  Vector3<-0.1333333333333333, 0.1333333333333333, 0.0>
  Vector3<-0.06666666666666665, 0.06666666666666665, 0.0>
  Vector3<0.0, 0.0, 0.0>
elapsed time for initialization: 0.004124641418457031
Outputting epsilon.h5...
elapsed time for k point: 0.09382939338684082
elapsed time for k point: 0.05579042434692383
elapsed time for k point: 0.06534004211425781
elapsed time for k point: 0.0724802017211914
elapsed time for k point: 0.08039641380310059
elapsed time for k point: 0.04375576972961426
elapsed time for k point: 0.050567626953125
elapsed time for k point: 0.06316757202148438
elapsed time for k point: 0.039211273193359375
elapsed time for k point: 0.03944277763366699
elapsed time for k point: 0.03663754463195801
Outputting fields to e.k11.b01.z.tm.h5...
Outputting fields to e.k11.b02.z.tm.h5...
Outputting fields to e.k11.b03.z.tm.h5...
Outputting fields to e.k11.b04.z.tm.h5...
Outputting fields to e.k11.b05.z.tm.h5...
Outputting fields to e.k11.b06.z.tm.h5...
Outputting fields to e.k11.b07.z.tm.h5...
Outputting fields to e.k11.b08.z.tm.h5...
elapsed time for k point: 0.05170464515686035
elapsed time for k point: 0.04603934288024902
elapsed time for k point: 0.05076241493225098
elapsed time for k point: 0.06884884834289551
elapsed time for k point: 0.07752251625061035
Band 1 range: 0.0 at Vector3<0.0, 0.0, 0.0> to 0.2746902260167482 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 2 range: 0.4453310810690987 at Vector3<0.0, 0.5, 0.0> to 0.5605181463869627 at Vector3<0.0, 0.0, 0.0>
Band 3 range: 0.49023891496896765 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 0.5605607990535272 at Vector3<0.0, 0.0, 0.0>
Band 4 range: 0.5932960878698785 at Vector3<0.0, 0.0, 0.0> to 0.7907195975678281 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 5 range: 0.7908320764965159 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 0.8374511179880573 at Vector3<0.0, 0.0, 0.0>
Band 6 range: 0.8375948534062025 at Vector3<0.0, 0.0, 0.0> to 0.8672009266363844 at Vector3<-0.2, 0.39999999999999997, 0.0>
Band 7 range: 0.8691349976044138 at Vector3<-0.13333333333333333, 0.43333333333333335, 0.0> to 0.9941291198691656 at Vector3<0.0, 0.0, 0.0>
Band 8 range: 0.8992499096210421 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 1.0983183609808018 at Vector3<0.0, 0.0, 0.0>
Gap from band 1 (0.2746902260167482) to band 2 (0.4453310810690987), 47.39883483253789%
Gap from band 3 (0.5605607990535272) to band 4 (0.5932960878698785), 5.6740639480231065%
Gap from band 4 (0.7907195975678281) to band 5 (0.7908320764965159), 0.014223870207005853%
Gap from band 5 (0.8374511179880573) to band 6 (0.8375948534062025), 0.017161966966868752%
Gap from band 6 (0.8672009266363844) to band 7 (0.8691349976044138), 0.22277612770986174%
total elapsed time for run: 0.9940049648284912
done
Initializing eigensolver data
Computing 8 bands with 1e-07 tolerance
16 k-points
  Vector3<0.0, 0.0, 0.0>
  Vector3<0.0, 0.1, 0.0>
  Vector3<0.0, 0.2, 0.0>
  Vector3<0.0, 0.30000000000000004, 0.0>
  Vector3<0.0, 0.4, 0.0>
  Vector3<0.0, 0.5, 0.0>
  Vector3<-0.06666666666666667, 0.4666666666666667, 0.0>
  Vector3<-0.13333333333333333, 0.43333333333333335, 0.0>
  Vector3<-0.2, 0.39999999999999997, 0.0>
  Vector3<-0.26666666666666666, 0.36666666666666664, 0.0>
  Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
  Vector3<-0.26666666666666666, 0.26666666666666666, 0.0>
  Vector3<-0.19999999999999998, 0.19999999999999998, 0.0>
  Vector3<-0.1333333333333333, 0.1333333333333333, 0.0>
  Vector3<-0.06666666666666665, 0.06666666666666665, 0.0>
  Vector3<0.0, 0.0, 0.0>
elapsed time for initialization: 0.0069427490234375
Outputting epsilon.h5...
elapsed time for k point: 0.15627694129943848
elapsed time for k point: 0.10107564926147461
elapsed time for k point: 0.08211708068847656
elapsed time for k point: 0.11973714828491211
elapsed time for k point: 0.08047056198120117
elapsed time for k point: 0.06789278984069824
elapsed time for k point: 0.0987086296081543
elapsed time for k point: 0.1209416389465332
elapsed time for k point: 0.11307835578918457
elapsed time for k point: 0.11387443542480469
elapsed time for k point: 0.06750798225402832
elapsed time for k point: 0.07093214988708496
elapsed time for k point: 0.08395576477050781
elapsed time for k point: 0.08612966537475586
elapsed time for k point: 0.11862421035766602
elapsed time for k point: 0.15810346603393555
Band 1 range: 0.0 at Vector3<0.0, 0.0, 0.0> to 0.4912358164155131 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 2 range: 0.4730722398043351 at Vector3<0.0, 0.5, 0.0> to 0.5631059454933676 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 3 range: 0.5631505237340275 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 0.7939289511462972 at Vector3<0.0, 0.0, 0.0>
Band 4 range: 0.7676614802374466 at Vector3<0.0, 0.5, 0.0> to 0.8214230165372104 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 5 range: 0.8651948161669857 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 1.0334130378837394 at Vector3<0.0, 0.0, 0.0>
Band 6 range: 0.8652308007806785 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 1.0334231152950073 at Vector3<0.0, 0.0, 0.0>
Band 7 range: 1.0213677201228073 at Vector3<0.0, 0.5, 0.0> to 1.1159671684231738 at Vector3<0.0, 0.0, 0.0>
Band 8 range: 1.1086627112265839 at Vector3<-0.26666666666666666, 0.26666666666666666, 0.0> to 1.1168108652006026 at Vector3<0.0, 0.0, 0.0>
Gap from band 2 (0.5631059454933676) to band 3 (0.5631505237340275), 0.007916179285617626%
Gap from band 4 (0.8214230165372104) to band 5 (0.8651948161669857), 5.190482251642612%
total elapsed time for run: 1.6683986186981201
done

In [2]:

    

print('TM gaps')
for gap in tm_gaps:
    print(gap)
print('TE gaps')
for gap in te_gaps:
    print(gap)


    

    




TM gaps
(47.39883483253789, 0.2746902260167482, 0.4453310810690987)
(5.6740639480231065, 0.5605607990535272, 0.5932960878698785)
(0.014223870207005853, 0.7907195975678281, 0.7908320764965159)
(0.017161966966868752, 0.8374511179880573, 0.8375948534062025)
(0.22277612770986174, 0.8672009266363844, 0.8691349976044138)
TE gaps
(0.007916179285617626, 0.5631059454933676, 0.5631505237340275)
(5.190482251642612, 0.8214230165372104, 0.8651948161669857)

In [5]:

    

import matplotlib.pyplot as plt
%matplotlib inline

fig, ax = plt.subplots(figsize=(10,8))
x = range(len(tm_freqs))
# Plot bands
# Scatter plot for multiple y values, see https://stackoverflow.com/a/34280815/2261298
for xz, tmz, tez in zip(x, tm_freqs, te_freqs):
    ax.scatter([xz]*len(tmz), tmz, color='blue')
    ax.scatter([xz]*len(tez), tez, color='red', facecolors='none')
ax.plot(tm_freqs, color='blue')
ax.plot(te_freqs, color='red')
ax.set_ylim([0, 1])
ax.set_xlim([x[0], x[-1]])

# Plot gaps
for gap in tm_gaps:
    if gap[0] > 1:
        ax.fill_between(x, gap[1], gap[2], color='blue', alpha=0.2)

for gap in te_gaps:
    if gap[0] > 1:
        ax.fill_between(x, gap[1], gap[2], color='red', alpha=0.2)


# Plot labels
ax.text(12, 0.04, 'TM bands', color='blue', size=15)
ax.text(13.05, 0.235, 'TE bands', color='red', size=15)
        
points_in_between = (len(tm_freqs) - 4) / 3
tick_locs = [i*points_in_between+i for i in range(4)]
tick_labs = ['Γ', 'X', 'M', 'Γ']
ax.set_xticks(tick_locs)
ax.set_xticklabels(tick_labs, size=16)
ax.set_ylabel('frequency (c/a)', size=16)
ax.grid(True)

#fig.savefig('tri-rods-bands.gif')
#plt.show()


    

In [5]:

    

te_freqs


    

    
Out[5]:





array([[0.        , 0.56122868, 0.79392895, 0.79465884, 1.03341305,
        1.0334231 , 1.11596707, 1.11681108],
       [0.10186545, 0.55980488, 0.7914598 , 0.79325781, 0.99212584,
        1.0284481 , 1.09798768, 1.11509623],
       [0.2026617 , 0.55513296, 0.78426545, 0.78493177, 0.92532786,
        1.01803714, 1.06979283, 1.11297591],
       [0.30075563, 0.54500319, 0.75283567, 0.7766037 , 0.88152751,
        1.00851179, 1.04494018, 1.11169802],
       [0.39275648, 0.52157674, 0.70557127, 0.77010985, 0.8686497 ,
        1.0025144 , 1.02766389, 1.11107007],
       [0.46842838, 0.47307224, 0.68322508, 0.76766148, 0.86698733,
        1.00051654, 1.02136772, 1.11088069],
       [0.47265399, 0.4741968 , 0.67604016, 0.77269512, 0.86687897,
        0.96981271, 1.05066191, 1.11080832],
       [0.47743248, 0.48508093, 0.65726584, 0.78480239, 0.86657691,
        0.93293272, 1.08111767, 1.11058686],
       [0.4823197 , 0.50500991, 0.6305842 , 0.79974512, 0.86612592,
        0.90046485, 1.0993589 , 1.11024462],
       [0.48785247, 0.53142658, 0.59815121, 0.8142077 , 0.86561691,
        0.87564315, 1.10710779, 1.10982757],
       [0.49123582, 0.56310595, 0.56315052, 0.82142302, 0.86519482,
        0.8652308 , 1.10922671, 1.10941284],
       [0.44612608, 0.5321911 , 0.63701185, 0.80665388, 0.86614037,
        0.89319761, 1.10593097, 1.10866271],
       [0.34526693, 0.54288202, 0.71339633, 0.79502239, 0.87581445,
        0.93882146, 1.09707327, 1.10903623],
       [0.2334793 , 0.55326918, 0.76871943, 0.79219628, 0.91276616,
        0.98720251, 1.08918698, 1.11097852],
       [0.1175561 , 0.55932303, 0.7897356 , 0.79357592, 0.98304335,
        1.0237432 , 1.09660717, 1.11448234],
       [0.        , 0.56122866, 0.79392895, 0.79465884, 1.03341301,
        1.03342312, 1.11596722, 1.11681075]])

In [18]:

    

ms.gap_list


    

    
Out[18]:





[(0.007916179281161635, 0.5631059454934042, 0.5631505237340391),
 (5.190482251647822, 0.8214230165371806, 0.8651948161669994)]

In [ ]: