

In [1]:

    
import meep as mp
from meep import mpb
import math

num_bands = 8

k_points = [mp.Vector3(),
            mp.Vector3(0., 0.5),
            mp.Vector3(-1/3, 1/3),
            mp.Vector3()]

k_points = mp.interpolate(10, k_points)

geometry = [mp.Cylinder(0.25, material=mp.Medium(epsilon=12.96))]

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))

default_material = mp.Medium(epsilon=2.4)

resolution = 32

ms = mpb.ModeSolver(num_bands=num_bands,
                    k_points=k_points,
                    geometry=geometry,
                    geometry_lattice=geometry_lattice,
                    resolution=resolution,
                    default_material=default_material)

result = ms.run_tm()









    



Initializing eigensolver data
Computing 8 bands with 1e-07 tolerance
34 k-points
  Vector3<0.0, 0.0, 0.0>
  Vector3<0.0, 0.045454545454545456, 0.0>
  Vector3<0.0, 0.09090909090909091, 0.0>
  Vector3<0.0, 0.13636363636363635, 0.0>
  Vector3<0.0, 0.18181818181818182, 0.0>
  Vector3<0.0, 0.2272727272727273, 0.0>
  Vector3<0.0, 0.2727272727272727, 0.0>
  Vector3<0.0, 0.3181818181818182, 0.0>
  Vector3<0.0, 0.36363636363636365, 0.0>
  Vector3<0.0, 0.4090909090909091, 0.0>
  Vector3<0.0, 0.4545454545454546, 0.0>
  Vector3<0.0, 0.5, 0.0>
  Vector3<-0.0303030303030303, 0.48484848484848486, 0.0>
  Vector3<-0.0606060606060606, 0.46969696969696967, 0.0>
  Vector3<-0.0909090909090909, 0.45454545454545453, 0.0>
  Vector3<-0.1212121212121212, 0.4393939393939394, 0.0>
  Vector3<-0.1515151515151515, 0.4242424242424242, 0.0>
  Vector3<-0.1818181818181818, 0.40909090909090906, 0.0>
  Vector3<-0.2121212121212121, 0.3939393939393939, 0.0>
  Vector3<-0.2424242424242424, 0.3787878787878788, 0.0>
  Vector3<-0.2727272727272727, 0.36363636363636365, 0.0>
  Vector3<-0.303030303030303, 0.34848484848484845, 0.0>
  Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
  Vector3<-0.30303030303030304, 0.30303030303030304, 0.0>
  Vector3<-0.2727272727272727, 0.2727272727272727, 0.0>
  Vector3<-0.24242424242424243, 0.24242424242424243, 0.0>
  Vector3<-0.2121212121212121, 0.2121212121212121, 0.0>
  Vector3<-0.18181818181818182, 0.18181818181818182, 0.0>
  Vector3<-0.15151515151515152, 0.15151515151515152, 0.0>
  Vector3<-0.12121212121212122, 0.12121212121212122, 0.0>
  Vector3<-0.09090909090909091, 0.09090909090909091, 0.0>
  Vector3<-0.06060606060606061, 0.06060606060606061, 0.0>
  Vector3<-0.03030303030303033, 0.03030303030303033, 0.0>
  Vector3<0.0, 0.0, 0.0>
elapsed time for initialization: 0.0048296451568603516
Outputting epsilon.h5...
elapsed time for k point: 0.07717466354370117
elapsed time for k point: 0.044971466064453125
elapsed time for k point: 0.04034829139709473
elapsed time for k point: 0.043203115463256836
elapsed time for k point: 0.06350564956665039
elapsed time for k point: 0.03676939010620117
elapsed time for k point: 0.04258251190185547
elapsed time for k point: 0.04217195510864258
elapsed time for k point: 0.04337930679321289
elapsed time for k point: 0.058980703353881836
elapsed time for k point: 0.03945183753967285
elapsed time for k point: 0.03976583480834961
elapsed time for k point: 0.06740498542785645
elapsed time for k point: 0.05871224403381348
elapsed time for k point: 0.039623260498046875
elapsed time for k point: 0.041029930114746094
elapsed time for k point: 0.036249399185180664
elapsed time for k point: 0.03565359115600586
elapsed time for k point: 0.05867934226989746
elapsed time for k point: 0.03459286689758301
elapsed time for k point: 0.03743577003479004
elapsed time for k point: 0.03988361358642578
elapsed time for k point: 0.034384727478027344
elapsed time for k point: 0.03908705711364746
elapsed time for k point: 0.05443859100341797
elapsed time for k point: 0.04035758972167969
elapsed time for k point: 0.03983664512634277
elapsed time for k point: 0.039566993713378906
elapsed time for k point: 0.0443418025970459
elapsed time for k point: 0.04936099052429199
elapsed time for k point: 0.06439900398254395
elapsed time for k point: 0.05106520652770996
elapsed time for k point: 0.050637245178222656
elapsed time for k point: 0.0414736270904541
Band 1 range: 0.0 at Vector3<0.0, 0.0, 0.0> to 0.22878697388087121 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 2 range: 0.3066223040599163 at Vector3<0.0, 0.5, 0.0> to 0.4367426627292241 at Vector3<0.0, 0.0, 0.0>
Band 3 range: 0.3467698802437271 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 0.43684934468726316 at Vector3<0.0, 0.0, 0.0>
Band 4 range: 0.4603794511991463 at Vector3<0.0, 0.0, 0.0> to 0.5787586659725432 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0>
Band 5 range: 0.5646992054451095 at Vector3<-0.2121212121212121, 0.2121212121212121, 0.0> to 0.6151179218789232 at Vector3<0.0, 0.5, 0.0>
Band 6 range: 0.6028005040819665 at Vector3<0.0, 0.0, 0.0> to 0.6577746481135313 at Vector3<-0.1212121212121212, 0.4393939393939394, 0.0>
Band 7 range: 0.659279276108018 at Vector3<-0.1212121212121212, 0.4393939393939394, 0.0> to 0.7390354806790289 at Vector3<-0.12121212121212122, 0.12121212121212122, 0.0>
Band 8 range: 0.6929572075806846 at Vector3<-0.3333333333333333, 0.3333333333333333, 0.0> to 0.7846797749994332 at Vector3<0.0, 0.0, 0.0>
Gap from band 1 (0.22878697388087121) to band 2 (0.3066223040599163), 29.075077099300145%
Gap from band 3 (0.43684934468726316) to band 4 (0.4603794511991463), 5.245062713047852%
Gap from band 6 (0.6577746481135313) to band 7 (0.659279276108018), 0.22848388616677381%
total elapsed time for run: 1.6017587184906006
done



In [2]:

    
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline

def resolve_crossovers(frequencies, crossovers):
    freqs = np.copy(frequencies)
    for i in range(len(crossovers)):
        if crossovers[i] != 0:
            for co in crossovers[i]:
                temp = np.copy(freqs[co:, i+1])
                freqs[co:, i+1] = freqs[co:, i]
                freqs[co:, i] = temp
    return freqs

def plot_photonic_bands(frequencies, num_bands=4):
    points_in_between = (len(frequencies) - 4) / 3
    tick_locs = [i*points_in_between+i for i in range(4)]
    tick_labs = ['Γ', 'X', 'M', 'Γ']
    fig, ax = plt.subplots()

    ax.plot(frequencies[:, :num_bands])
    ax.set_xticks(tick_locs)
    ax.set_xticklabels(tick_labs)

new_freqs = resolve_crossovers(ms.all_freqs, crossovers=[0, [23]])
plot_photonic_bands(new_freqs, num_bands=3)