Note

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Two photonic crystal slabs#

Mechanically tunable photonic crystal structure consisting of coupled photonic crystal slabs.

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np

import nannos as nn

We will code the structures studied in [Suh2003].

nh = 51
L1 = [1.0, 0]
L2 = [0, 1.0]
theta = 0.0 * np.pi / 180
phi = 0.0 * np.pi / 180
psi = 0.0 * np.pi / 180

Nx = 2**8
Ny = 2**8

lattice = nn.Lattice((L1, L2), (Nx, Ny))

epsgrid = lattice.ones() * 12.0
hole = lattice.circle((0.5, 0.5), 0.4)
epsgrid[hole] = 1.0

Define the problem

sup = lattice.Layer("Superstrate", epsilon=1.0)
phc_slab = lattice.Layer("PC slab", thickness=0.55)
sub = lattice.Layer("Substrate", epsilon=1.0)
phc_slab.epsilon = epsgrid
stack = [sup, phc_slab, sub]

Fig 2 (a) from [Suh2003].

def compute_transmission(fn):
    pw = nn.PlaneWave(wavelength=1 / fn, angles=(0, 0, 0))
    sim = nn.Simulation(stack, pw, nh)
    R, T = sim.diffraction_efficiencies()
    print(f"f = {fn} (normalized)")
    print("T = ", T)
    return T


#
freqs_norma = np.linspace(0.49, 0.6, 30)
freqs_adapted, transmission = nn.adaptive_sampler(
    compute_transmission,
    freqs_norma,
)


plt.figure()
plt.plot(freqs_adapted, transmission, c="#be4c83")
plt.xlim(freqs_norma[0], freqs_norma[-1])
plt.ylim(0, 1)
plt.xlabel(r"frequency ($2\pi c / a$)")
plt.ylabel("Transmission")
plt.tight_layout()
plot double phc
f = 0.49 (normalized)
T =  0.9845910272335945
f = 0.49379310344827587 (normalized)
T =  0.9999341513659242
f = 0.4975862068965517 (normalized)
T =  0.9769428878609822
f = 0.5013793103448275 (normalized)
T =  0.8767335476261352
f = 0.5051724137931034 (normalized)
T =  0.6819614986551429
f = 0.5089655172413793 (normalized)
T =  0.43944918491786866
f = 0.5127586206896552 (normalized)
T =  0.2306772935059035
f = 0.516551724137931 (normalized)
T =  0.09636651755607521
f = 0.5203448275862069 (normalized)
T =  0.028114503756722753
f = 0.5241379310344827 (normalized)
T =  0.0027358426983668535
f = 0.5279310344827586 (normalized)
T =  0.001654438404444963
f = 0.5317241379310345 (normalized)
T =  0.013646566599984077
f = 0.5355172413793103 (normalized)
T =  0.032666306647299206
f = 0.5393103448275862 (normalized)
T =  0.05566628849274519
f = 0.5431034482758621 (normalized)
T =  0.08122997733051333
f = 0.5468965517241379 (normalized)
T =  0.10881895149231749
f = 0.5506896551724138 (normalized)
T =  0.13837707657473472
f = 0.5544827586206896 (normalized)
T =  0.17012550144132393
f = 0.5582758620689655 (normalized)
T =  0.2044566756314275
f = 0.5620689655172414 (normalized)
T =  0.2418783145681079
f = 0.5658620689655172 (normalized)
T =  0.2829801207010157
f = 0.569655172413793 (normalized)
T =  0.3284061326957633
f = 0.5734482758620689 (normalized)
T =  0.37881884983002556
f = 0.5772413793103448 (normalized)
T =  0.4348401400305144
f = 0.5810344827586207 (normalized)
T =  0.4969494445833787
f = 0.5848275862068966 (normalized)
T =  0.565312900325856
f = 0.5886206896551724 (normalized)
T =  0.6395103701923202
f = 0.5924137931034482 (normalized)
T =  0.7181288136205825
f = 0.5962068965517241 (normalized)
T =  0.798219025932501
f = 0.6 (normalized)
T =  0.8747060683869687
f = 0.4994827586206896 (normalized)
T =  0.9387028078218619
f = 0.5032758620689655 (normalized)
T =  0.7899333972194305
f = 0.5146551724137931 (normalized)
T =  0.1539957689435605
f = 0.518448275862069 (normalized)
T =  0.05542943341106391
f = 0.5004310344827585 (normalized)
T =  0.9108490724806971

Figs 2 (b-c) from [Suh2003].

phc_slab_top = lattice.Layer("PC slab top", thickness=0.55)
phc_slab_top.epsilon = epsgrid
phc_slab_bot = phc_slab_top.copy("PC slab bottom")

plt.figure()

seps = [1.35, 1.1, 0.95, 0.85, 0.75, 0.65, 0.55]
colors = plt.cm.turbo(np.linspace(0, 1, len(seps)))

for i, sep in enumerate(seps):
    spacer = lattice.Layer("Spacer", epsilon=1, thickness=sep)
    stack = [sup, phc_slab_top, spacer, phc_slab_bot, sub]

    def compute_transmission(fn):
        pw = nn.PlaneWave(wavelength=1 / fn, angles=(0, 0, 0))
        sim = nn.Simulation(stack, pw, nh)
        R, T = sim.diffraction_efficiencies()
        print(f"f = {fn} (normalized)")
        print("T = ", T)
        return T

    freqs_norma = np.linspace(0.49, 0.6, 30)
    freqs_adapted, transmission = nn.adaptive_sampler(
        compute_transmission,
        freqs_norma,
    )

    plt.plot(freqs_adapted, transmission, c=colors[i], label=rf"$d = {sep}a$")
    plt.xlim(freqs_norma[0], freqs_norma[-1])
    plt.ylim(0, 1)
    plt.xlabel(r"frequency ($2\pi c / a$)")
    plt.ylabel("Transmission")
    plt.tight_layout()
    plt.pause(0.1)


plt.legend(loc=(1.05, 0.3))
plt.tight_layout()
plt.show()
plot double phc
f = 0.49 (normalized)
T =  0.9445045989617572
f = 0.49379310344827587 (normalized)
T =  0.9997682511298966
f = 0.4975862068965517 (normalized)
T =  0.9540820015844338
f = 0.5013793103448275 (normalized)
T =  0.8771839203172163
f = 0.5051724137931034 (normalized)
T =  0.9375406178769523
f = 0.5089655172413793 (normalized)
T =  0.7360778228379331
f = 0.5127586206896552 (normalized)
T =  0.0733492396844188
f = 0.516551724137931 (normalized)
T =  0.005324445907029933
f = 0.5203448275862069 (normalized)
T =  0.0002625725245057063
f = 0.5241379310344827 (normalized)
T =  3.8523680381043914e-07
f = 0.5279310344827586 (normalized)
T =  7.032026241518729e-09
f = 0.5317241379310345 (normalized)
T =  3.837156211790377e-05
f = 0.5355172413793103 (normalized)
T =  0.0002552940742638741
f = 0.5393103448275862 (normalized)
T =  0.0008130193282536823
f = 0.5431034482758621 (normalized)
T =  0.0019237711141290828
f = 0.5468965517241379 (normalized)
T =  0.003935919827774125
f = 0.5506896551724138 (normalized)
T =  0.007487108309830092
f = 0.5544827586206896 (normalized)
T =  0.013819465709060865
f = 0.5582758620689655 (normalized)
T =  0.025499922857495486
f = 0.5620689655172414 (normalized)
T =  0.04819892570151984
f = 0.5658620689655172 (normalized)
T =  0.09534185503417059
f = 0.569655172413793 (normalized)
T =  0.19997940722048405
f = 0.5734482758620689 (normalized)
T =  0.4324649251771105
f = 0.5772413793103448 (normalized)
T =  0.8135247574027733
f = 0.5810344827586207 (normalized)
T =  0.9993088714501756
f = 0.5848275862068966 (normalized)
T =  0.8689863537800575
f = 0.5886206896551724 (normalized)
T =  0.7215289601199887
f = 0.5924137931034482 (normalized)
T =  0.6483288067496507
f = 0.5962068965517241 (normalized)
T =  0.6435929053521046
f = 0.6 (normalized)
T =  0.6998666814086062
f = 0.49189655172413793 (normalized)
T =  0.982586035585161
f = 0.4994827586206896 (normalized)
T =  0.9096763681399945
f = 0.5032758620689655 (normalized)
T =  0.8799935661336793
f = 0.5070689655172413 (normalized)
T =  0.9992690233576268
f = 0.5108620689655172 (normalized)
T =  0.26780567061457033
f = 0.5146551724137931 (normalized)
T =  0.019855637450086807
f = 0.518448275862069 (normalized)
T =  0.001314929096916804
f = 0.5677586206896551 (normalized)
T =  0.1370767802323062
f = 0.571551724137931 (normalized)
T =  0.2946101913946141
f = 0.5753448275862069 (normalized)
T =  0.6154027675815811
f = 0.5791379310344827 (normalized)
T =  0.9587902863584552
f = 0.5829310344827586 (normalized)
T =  0.9521336285500672
f = 0.5867241379310345 (normalized)
T =  0.7870626814951046
f = 0.5943103448275862 (normalized)
T =  0.6380670577848827
f = 0.598103448275862 (normalized)
T =  0.6642908999787571
f = 0.5042241379310344 (normalized)
T =  0.9015525795953905
f = 0.5080172413793103 (normalized)
T =  0.9332460535905899
f = 0.5099137931034483 (normalized)
T =  0.4763591394245981
f = 0.5118103448275861 (normalized)
T =  0.14132455717161563
f = 0.5137068965517242 (normalized)
T =  0.03810350689412983
f = 0.515603448275862 (normalized)
T =  0.01033093229967879
f = 0.5687068965517241 (normalized)
T =  0.16529231069653022
f = 0.570603448275862 (normalized)
T =  0.24256837322295335
f = 0.5725 (normalized)
T =  0.3575771202709166
f = 0.5800862068965518 (normalized)
T =  0.9926715731748755
f = 0.5838793103448277 (normalized)
T =  0.9121317534161231
f = 0.5905172413793103 (normalized)
T =  0.6755990384777427
f = 0.5061206896551724 (normalized)
T =  0.9799769971380159
f = 0.5084913793103447 (normalized)
T =  0.8499114242550205
f = 0.5113362068965517 (normalized)
T =  0.19535189718864213
f = 0.5122844827586206 (normalized)
T =  0.10186250401793377
f = 0.5132327586206897 (normalized)
T =  0.05284115156948757
f = 0.5781896551724137 (normalized)
T =  0.897378031161913
f = 0.5876724137931035 (normalized)
T =  0.7518832012557842
f = 0.5075431034482758 (normalized)
T =  0.9814982068825374
f = 0.5103879310344828 (normalized)
T =  0.36158666728842775
f = 0.5796120689655173 (normalized)
T =  0.979280858296875
f = 0.5082543103448275 (normalized)
T =  0.8959279226824611
f = 0.5786637931034482 (normalized)
T =  0.931327712621857
f = 0.49 (normalized)
T =  0.9509248374802818
f = 0.49379310344827587 (normalized)
T =  0.9995958662377392
f = 0.4975862068965517 (normalized)
T =  0.9152284351912737
f = 0.5013793103448275 (normalized)
T =  0.6361891294505823
f = 0.5051724137931034 (normalized)
T =  0.360766088310873
f = 0.5089655172413793 (normalized)
T =  0.2049106376283984
f = 0.5127586206896552 (normalized)
T =  0.14864875268685895
f = 0.516551724137931 (normalized)
T =  0.3955303767042962
f = 0.5203448275862069 (normalized)
T =  0.007362910798856318
f = 0.5241379310344827 (normalized)
T =  4.104572568131442e-07
f = 0.5279310344827586 (normalized)
T =  1.4214339479643943e-06
f = 0.5317241379310345 (normalized)
T =  7.565338837674164e-05
f = 0.5355172413793103 (normalized)
T =  0.000442478647061771
f = 0.5393103448275862 (normalized)
T =  0.001151297815934178
f = 0.5431034482758621 (normalized)
T =  0.0022237581632766398
f = 0.5468965517241379 (normalized)
T =  0.003720095390493919
f = 0.5506896551724138 (normalized)
T =  0.005766695683960173
f = 0.5544827586206896 (normalized)
T =  0.008586796495483294
f = 0.5582758620689655 (normalized)
T =  0.01255504768552035
f = 0.5620689655172414 (normalized)
T =  0.01830036253976991
f = 0.5658620689655172 (normalized)
T =  0.026903242855927705
f = 0.569655172413793 (normalized)
T =  0.040284195212683664
f = 0.5734482758620689 (normalized)
T =  0.06198844857942305
f = 0.5772413793103448 (normalized)
T =  0.0987826347376846
f = 0.5810344827586207 (normalized)
T =  0.163710361726353
f = 0.5848275862068966 (normalized)
T =  0.28023701314911265
f = 0.5886206896551724 (normalized)
T =  0.4777606871524989
f = 0.5924137931034482 (normalized)
T =  0.741976713405179
f = 0.5962068965517241 (normalized)
T =  0.9460523569702636
f = 0.6 (normalized)
T =  0.9999984823953091
f = 0.49189655172413793 (normalized)
T =  0.981443828422702
f = 0.4994827586206896 (normalized)
T =  0.7909855418134241
f = 0.5070689655172413 (normalized)
T =  0.2684005744452798
f = 0.5108620689655172 (normalized)
T =  0.16538740350437497
f = 0.5146551724137931 (normalized)
T =  0.16937866457764594
f = 0.518448275862069 (normalized)
T =  0.22522971176754603
f = 0.5791379310344827 (normalized)
T =  0.126549039167722
f = 0.5829310344827586 (normalized)
T =  0.21359700342457844
f = 0.5867241379310345 (normalized)
T =  0.3676323367026518
f = 0.598103448275862 (normalized)
T =  0.9892040598510357
f = 0.4956896551724138 (normalized)
T =  0.9842074974949965
f = 0.5032758620689655 (normalized)
T =  0.48530884965462384
f = 0.5080172413793103 (normalized)
T =  0.23338141762003045
f = 0.5099137931034483 (normalized)
T =  0.18237857174794983
f = 0.515603448275862 (normalized)
T =  0.22132836682351964
f = 0.5175000000000001 (normalized)
T =  0.9888374561046552
f = 0.5222413793103449 (normalized)
T =  0.00035705055471149454
f = 0.5943103448275862 (normalized)
T =  0.8615839315843989
f = 0.49474137931034484 (normalized)
T =  0.9975547298991163
f = 0.49853448275862067 (normalized)
T =  0.8590042098698207
f = 0.5137068965517242 (normalized)
T =  0.15175678191564057
f = 0.5160775862068965 (normalized)
T =  0.28014858081026733
f = 0.5170258620689656 (normalized)
T =  0.6405887319968087
f = 0.5193965517241379 (normalized)
T =  0.034369619769684584
f = 0.521293103448276 (normalized)
T =  0.001715221394336946
f = 0.5971551724137931 (normalized)
T =  0.9725140300290479
f = 0.4966379310344827 (normalized)
T =  0.9571589823303683
f = 0.5151293103448276 (normalized)
T =  0.18857096636796414
f = 0.5163146551724138 (normalized)
T =  0.32754564880027426
f = 0.5167887931034483 (normalized)
T =  0.49520129506358473
f = 0.5179741379310345 (normalized)
T =  0.6462897867011063
f = 0.5189224137931034 (normalized)
T =  0.08268845116760686
f = 0.5198706896551724 (normalized)
T =  0.015535354230513923
f = 0.5952586206896551 (normalized)
T =  0.9090013158953406
f = 0.5158405172413792 (normalized)
T =  0.24621622133523974
f = 0.5161961206896551 (normalized)
T =  0.30179765538781494
f = 0.5166702586206897 (normalized)
T =  0.4405385919992656
f = 0.5169073275862069 (normalized)
T =  0.5614096459804669
f = 0.5177370689655173 (normalized)
T =  0.9235220936355232
f = 0.5186853448275862 (normalized)
T =  0.13415990895811378
f = 0.5191594827586207 (normalized)
T =  0.05261220833475896
f = 0.5172629310344828 (normalized)
T =  0.8317699897148881
f = 0.517855603448276 (normalized)
T =  0.7961463499912715
f = 0.5182112068965518 (normalized)
T =  0.38697560561892563
f = 0.5188038793103449 (normalized)
T =  0.10487766931491997
f = 0.519040948275862 (normalized)
T =  0.06571701759526145
f = 0.5176185344827586 (normalized)
T =  0.992992585992344
f = 0.5183297413793104 (normalized)
T =  0.294898753957315
f = 0.5185668103448275 (normalized)
T =  0.17311892424749678
f = 0.5173814655172415 (normalized)
T =  0.9254205541770595
f = 0.5176778017241379 (normalized)
T =  0.9672046432147671
f = 0.5177963362068967 (normalized)
T =  0.865022617090895
f = 0.5173221982758622 (normalized)
T =  0.8805966089718591
f = 0.5175592672413794 (normalized)
T =  0.9998373985261682
f = 0.5171443965517242 (normalized)
T =  0.7323457347931537
f = 0.5174407327586208 (normalized)
T =  0.9627906262867728
f = 0.49 (normalized)
T =  0.9759429670513314
f = 0.49379310344827587 (normalized)
T =  0.999505295455531
f = 0.4975862068965517 (normalized)
T =  0.9356654651890655
f = 0.5013793103448275 (normalized)
T =  0.6332299492329224
f = 0.5051724137931034 (normalized)
T =  0.2858009488743998
f = 0.5089655172413793 (normalized)
T =  0.10511337880934746
f = 0.5127586206896552 (normalized)
T =  0.03582262572022687
f = 0.516551724137931 (normalized)
T =  0.011039980174731031
f = 0.5203448275862069 (normalized)
T =  0.0026015460723169174
f = 0.5241379310344827 (normalized)
T =  0.00025754815602224224
f = 0.5279310344827586 (normalized)
T =  0.006838160624992474
f = 0.5317241379310345 (normalized)
T =  0.0016066043751386044
f = 0.5355172413793103 (normalized)
T =  0.0029773289788195064
f = 0.5393103448275862 (normalized)
T =  0.004622408750717773
f = 0.5431034482758621 (normalized)
T =  0.006480324330750494
f = 0.5468965517241379 (normalized)
T =  0.008598932172928772
f = 0.5506896551724138 (normalized)
T =  0.011087869075853754
f = 0.5544827586206896 (normalized)
T =  0.014117892331972874
f = 0.5582758620689655 (normalized)
T =  0.017942134358909262
f = 0.5620689655172414 (normalized)
T =  0.022940836665035026
f = 0.5658620689655172 (normalized)
T =  0.029702649813458645
f = 0.569655172413793 (normalized)
T =  0.03917148342481058
f = 0.5734482758620689 (normalized)
T =  0.05291770762071289
f = 0.5772413793103448 (normalized)
T =  0.07365108575589673
f = 0.5810344827586207 (normalized)
T =  0.10619894438909751
f = 0.5848275862068966 (normalized)
T =  0.1592948835410554
f = 0.5886206896551724 (normalized)
T =  0.24820946953666304
f = 0.5924137931034482 (normalized)
T =  0.3949809760884822
f = 0.5962068965517241 (normalized)
T =  0.6102178383574179
f = 0.6 (normalized)
T =  0.8387889313295763
f = 0.49189655172413793 (normalized)
T =  0.9890386651512434
f = 0.4994827586206896 (normalized)
T =  0.8130454797766422
f = 0.5070689655172413 (normalized)
T =  0.17564835404069004
f = 0.5108620689655172 (normalized)
T =  0.061864561282197514
f = 0.5146551724137931 (normalized)
T =  0.020264968704011496
f = 0.5829310344827586 (normalized)
T =  0.12940960662978201
f = 0.5867241379310345 (normalized)
T =  0.19800125803569968
f = 0.5943103448275862 (normalized)
T =  0.49519734131252174
f = 0.4956896551724138 (normalized)
T =  0.990507619822078
f = 0.5004310344827585 (normalized)
T =  0.7278778043690856
f = 0.5032758620689655 (normalized)
T =  0.4428998532152694
f = 0.5080172413793103 (normalized)
T =  0.13621106163422314
f = 0.5099137931034483 (normalized)
T =  0.08079054816077605
f = 0.5905172413793103 (normalized)
T =  0.31295729421874563
f = 0.49474137931034484 (normalized)
T =  0.998926835678898
f = 0.49853448275862067 (normalized)
T =  0.8832250947799054
f = 0.5061206896551724 (normalized)
T =  0.22504541630593153
f = 0.4966379310344827 (normalized)
T =  0.9706035692695151
f = 0.4980603448275862 (normalized)
T =  0.9117126440132012
f = 0.49 (normalized)
T =  0.9909512116769185
f = 0.49379310344827587 (normalized)
T =  0.9993313770031285
f = 0.4975862068965517 (normalized)
T =  0.9629748115460786
f = 0.5013793103448275 (normalized)
T =  0.6964734046135677
f = 0.5051724137931034 (normalized)
T =  0.30115374870132927
f = 0.5089655172413793 (normalized)
T =  0.09468942169358469
f = 0.5127586206896552 (normalized)
T =  0.026623737073824056
f = 0.516551724137931 (normalized)
T =  0.006722660287407142
f = 0.5203448275862069 (normalized)
T =  0.0013806775382721893
f = 0.5241379310344827 (normalized)
T =  0.00023821668041079793
f = 0.5279310344827586 (normalized)
T =  0.00019926067721351122
f = 0.5317241379310345 (normalized)
T =  0.0023802446251408285
f = 0.5355172413793103 (normalized)
T =  0.08831428897225167
f = 0.5393103448275862 (normalized)
T =  0.1672390221418549
f = 0.5431034482758621 (normalized)
T =  0.05201338540835283
f = 0.5468965517241379 (normalized)
T =  0.037299762574348444
f = 0.5506896551724138 (normalized)
T =  0.03370226435607302
f = 0.5544827586206896 (normalized)
T =  0.033708591932273387
f = 0.5582758620689655 (normalized)
T =  0.035743497242499
f = 0.5620689655172414 (normalized)
T =  0.03949667814679222
f = 0.5658620689655172 (normalized)
T =  0.04516100871287019
f = 0.569655172413793 (normalized)
T =  0.05330978470611978
f = 0.5734482758620689 (normalized)
T =  0.0649899525936414
f = 0.5772413793103448 (normalized)
T =  0.08199592447528788
f = 0.5810344827586207 (normalized)
T =  0.10741748022253242
f = 0.5848275862068966 (normalized)
T =  0.14666625409121686
f = 0.5886206896551724 (normalized)
T =  0.20923287283612868
f = 0.5924137931034482 (normalized)
T =  0.3107572713047007
f = 0.5962068965517241 (normalized)
T =  0.4706082775139502
f = 0.6 (normalized)
T =  0.687431511831489
f = 0.4994827586206896 (normalized)
T =  0.8678461795982714
f = 0.5032758620689655 (normalized)
T =  0.4863179594589169
f = 0.5070689655172413 (normalized)
T =  0.17250361384729224
f = 0.5108620689655172 (normalized)
T =  0.05072204877766681
f = 0.5146551724137931 (normalized)
T =  0.013624666279913286
f = 0.5336206896551724 (normalized)
T =  0.011529337553683624
f = 0.5412068965517242 (normalized)
T =  0.07623358626155224
f = 0.5867241379310345 (normalized)
T =  0.17421924280538484
f = 0.5943103448275862 (normalized)
T =  0.38243249237584226
f = 0.4956896551724138 (normalized)
T =  0.9962320895158222
f = 0.5004310344827585 (normalized)
T =  0.790688364682816
f = 0.5061206896551724 (normalized)
T =  0.2295614642933457
f = 0.5080172413793103 (normalized)
T =  0.12829160212990165
f = 0.5099137931034483 (normalized)
T =  0.06947817994660903
f = 0.5345689655172414 (normalized)
T =  0.02896736278949059
f = 0.5374137931034483 (normalized)
T =  0.9600834900617309
f = 0.5421551724137932 (normalized)
T =  0.06111073445069382
f = 0.5905172413793103 (normalized)
T =  0.2538897414762512
f = 0.49853448275862067 (normalized)
T =  0.9249719401259945
f = 0.534094827586207 (normalized)
T =  0.017966675455685328
f = 0.5364655172413793 (normalized)
T =  0.3812440927700815
f = 0.5383620689655173 (normalized)
T =  0.3564824368688049
f = 0.5402586206896551 (normalized)
T =  0.1043852990771133
f = 0.4980603448275862 (normalized)
T =  0.9461879091634096
f = 0.5350431034482759 (normalized)
T =  0.048948697532073
f = 0.5359913793103448 (normalized)
T =  0.1743297788640408
f = 0.5369396551724137 (normalized)
T =  0.8088700047783898
f = 0.5378879310344828 (normalized)
T =  0.6038792638969905
f = 0.5397844827586207 (normalized)
T =  0.1287814454230355
f = 0.5407327586206896 (normalized)
T =  0.0879109623321255
f = 0.5357543103448276 (normalized)
T =  0.12249829510584127
f = 0.536228448275862 (normalized)
T =  0.25491003741023144
f = 0.5367025862068965 (normalized)
T =  0.5709721292329759
f = 0.537176724137931 (normalized)
T =  0.9834335633825997
f = 0.5376508620689655 (normalized)
T =  0.7893230162315313
f = 0.5388362068965518 (normalized)
T =  0.2329358572533173
f = 0.5358728448275862 (normalized)
T =  0.1456424967143598
f = 0.5361099137931034 (normalized)
T =  0.21010386424600652
f = 0.5363469827586207 (normalized)
T =  0.31109537618268124
f = 0.5365840517241378 (normalized)
T =  0.4676343212204067
f = 0.5370581896551724 (normalized)
T =  0.9148878087374318
f = 0.537532327586207 (normalized)
T =  0.8836918002481243
f = 0.5381250000000001 (normalized)
T =  0.4592379745525562
f = 0.5385991379310345 (normalized)
T =  0.2843622617479375
f = 0.539073275862069 (normalized)
T =  0.19537213608272982
f = 0.5395474137931034 (normalized)
T =  0.14566985137649713
f = 0.5371174568965518 (normalized)
T =  0.9551555114823437
f = 0.5372952586206896 (normalized)
T =  0.9984203499037756
f = 0.5384806034482759 (normalized)
T =  0.3172896944315999
f = 0.5374730603448277 (normalized)
T =  0.9253695122963327
f = 0.49 (normalized)
T =  0.9989480015949032
f = 0.49379310344827587 (normalized)
T =  0.9988209287528945
f = 0.4975862068965517 (normalized)
T =  0.9892786754900099
f = 0.5013793103448275 (normalized)
T =  0.8089103841650028
f = 0.5051724137931034 (normalized)
T =  0.3747757184208355
f = 0.5089655172413793 (normalized)
T =  0.10869962785952571
f = 0.5127586206896552 (normalized)
T =  0.027866065599394294
f = 0.516551724137931 (normalized)
T =  0.006963413270116342
f = 0.5203448275862069 (normalized)
T =  0.0017471063896597192
f = 0.5241379310344827 (normalized)
T =  0.0005556750078361085
f = 0.5279310344827586 (normalized)
T =  0.0004357956957829003
f = 0.5317241379310345 (normalized)
T =  0.001012742917073757
f = 0.5355172413793103 (normalized)
T =  0.0036114321618710104
f = 0.5393103448275862 (normalized)
T =  0.014408014737828082
f = 0.5431034482758621 (normalized)
T =  0.06876330828663971
f = 0.5468965517241379 (normalized)
T =  0.49380278005383377
f = 0.5506896551724138 (normalized)
T =  0.7244278703406862
f = 0.5544827586206896 (normalized)
T =  0.27126699409475963
f = 0.5582758620689655 (normalized)
T =  0.1616016296549924
f = 0.5620689655172414 (normalized)
T =  0.12409778481698412
f = 0.5658620689655172 (normalized)
T =  0.10966813625680694
f = 0.569655172413793 (normalized)
T =  0.10616434503079247
f = 0.5734482758620689 (normalized)
T =  0.10998366144837779
f = 0.5772413793103448 (normalized)
T =  0.120574846920281
f = 0.5810344827586207 (normalized)
T =  0.13922336611670788
f = 0.5848275862068966 (normalized)
T =  0.16916048674905662
f = 0.5886206896551724 (normalized)
T =  0.2164981105710727
f = 0.5924137931034482 (normalized)
T =  0.29189792833404005
f = 0.5962068965517241 (normalized)
T =  0.41163735664289824
f = 0.6 (normalized)
T =  0.5900734061434523
f = 0.4994827586206896 (normalized)
T =  0.9385613956955614
f = 0.5032758620689655 (normalized)
T =  0.5980671227717588
f = 0.5070689655172413 (normalized)
T =  0.2082522657925508
f = 0.5108620689655172 (normalized)
T =  0.05530407074542346
f = 0.5146551724137931 (normalized)
T =  0.013964427613232933
f = 0.5412068965517242 (normalized)
T =  0.03037061028359012
f = 0.5487931034482758 (normalized)
T =  0.9897381536866512
f = 0.5525862068965517 (normalized)
T =  0.41527263229385064
f = 0.5563793103448276 (normalized)
T =  0.20048082132288159
f = 0.5601724137931035 (normalized)
T =  0.13847691297379247
f = 0.5867241379310345 (normalized)
T =  0.19011752383700287
f = 0.5943103448275862 (normalized)
T =  0.34505731030851944
f = 0.598103448275862 (normalized)
T =  0.49340676670974964
f = 0.4956896551724138 (normalized)
T =  0.9998536500857332
f = 0.5004310344827585 (normalized)
T =  0.8854111202740687
f = 0.5023275862068965 (normalized)
T =  0.7106632631878159
f = 0.5080172413793103 (normalized)
T =  0.15119751922554583
f = 0.5099137931034483 (normalized)
T =  0.07767525459774115
f = 0.5118103448275861 (normalized)
T =  0.039287576320637375
f = 0.5449999999999999 (normalized)
T =  0.1743490940871135
f = 0.5497413793103447 (normalized)
T =  0.9280522858408071
f = 0.5535344827586206 (normalized)
T =  0.32968510248014127
f = 0.5554310344827587 (normalized)
T =  0.2302086740071206
f = 0.5573275862068965 (normalized)
T =  0.17838526128975082
f = 0.5905172413793103 (normalized)
T =  0.24979525756876805
f = 0.49853448275862067 (normalized)
T =  0.9714390729826834
f = 0.500905172413793 (normalized)
T =  0.8501144172479922
f = 0.5061206896551724 (normalized)
T =  0.28249604355798813
f = 0.5421551724137932 (normalized)
T =  0.045182356740402
f = 0.5459482758620688 (normalized)
T =  0.2917766126056365
f = 0.5478448275862069 (normalized)
T =  0.7808126388914379
f = 0.5502155172413792 (normalized)
T =  0.8300347957961827
f = 0.5516379310344828 (normalized)
T =  0.5426228843650903
f = 0.5540086206896551 (normalized)
T =  0.2978012136470479
f = 0.5549568965517242 (normalized)
T =  0.24901402803492012
f = 0.49995689655172404 (normalized)
T =  0.914794315460146
f = 0.544051724137931 (normalized)
T =  0.10767332220182031
f = 0.5464224137931033 (normalized)
T =  0.3801990425794359
f = 0.5473706896551724 (normalized)
T =  0.6315317558215611
f = 0.5492672413793103 (normalized)
T =  0.9912623894404193
f = 0.5511637931034483 (normalized)
T =  0.626707030827106
f = 0.5530603448275861 (normalized)
T =  0.3682778436822184
f = 0.5445258620689655 (normalized)
T =  0.13641328345575873
f = 0.5454741379310344 (normalized)
T =  0.22474294207727563
f = 0.5483189655172414 (normalized)
T =  0.9126067907573696
f = 0.5495043103448275 (normalized)
T =  0.9660339880168214
f = 0.549978448275862 (normalized)
T =  0.8814462700347429
f = 0.5485560344827586 (normalized)
T =  0.9600091241578813
f = 0.549030172413793 (normalized)
T =  0.9999936091949825
f = 0.49 (normalized)
T =  0.9995399957487939
f = 0.49379310344827587 (normalized)
T =  0.9972363782541634
f = 0.4975862068965517 (normalized)
T =  0.9999094600447491
f = 0.5013793103448275 (normalized)
T =  0.9384767633144488
f = 0.5051724137931034 (normalized)
T =  0.5407833885446208
f = 0.5089655172413793 (normalized)
T =  0.1591981133272824
f = 0.5127586206896552 (normalized)
T =  0.03952466316905206
f = 0.516551724137931 (normalized)
T =  0.010612623102606848
f = 0.5203448275862069 (normalized)
T =  0.0033949704912945044
f = 0.5241379310344827 (normalized)
T =  0.001529346381578212
f = 0.5279310344827586 (normalized)
T =  0.0011854170000144045
f = 0.5317241379310345 (normalized)
T =  0.0015640901058667437
f = 0.5355172413793103 (normalized)
T =  0.0028171402710999655
f = 0.5393103448275862 (normalized)
T =  0.00576998180086611
f = 0.5431034482758621 (normalized)
T =  0.012499045721325649
f = 0.5468965517241379 (normalized)
T =  0.028484889772338443
f = 0.5506896551724138 (normalized)
T =  0.07031207562553478
f = 0.5544827586206896 (normalized)
T =  0.1966312268704179
f = 0.5582758620689655 (normalized)
T =  0.5945645218549849
f = 0.5620689655172414 (normalized)
T =  0.9963414590944641
f = 0.5658620689655172 (normalized)
T =  0.664529667371532
f = 0.569655172413793 (normalized)
T =  0.4208409112044243
f = 0.5734482758620689 (normalized)
T =  0.312665993618026
f = 0.5772413793103448 (normalized)
T =  0.2653591306716487
f = 0.5810344827586207 (normalized)
T =  0.24931024177906275
f = 0.5848275862068966 (normalized)
T =  0.2545490759432534
f = 0.5886206896551724 (normalized)
T =  0.27985404113609685
f = 0.5924137931034482 (normalized)
T =  0.32998304948194596
f = 0.5962068965517241 (normalized)
T =  0.41579147310981046
f = 0.6 (normalized)
T =  0.5526114380508425
f = 0.4994827586206896 (normalized)
T =  0.9925550012082404
f = 0.5032758620689655 (normalized)
T =  0.7849333444609335
f = 0.5108620689655172 (normalized)
T =  0.07914888635429247
f = 0.5146551724137931 (normalized)
T =  0.020164149344788426
f = 0.5525862068965517 (normalized)
T =  0.1154892697215839
f = 0.5563793103448276 (normalized)
T =  0.34460161403502615
f = 0.5601724137931035 (normalized)
T =  0.8913283756926887
f = 0.571551724137931 (normalized)
T =  0.3558931500220915
f = 0.5753448275862069 (normalized)
T =  0.2839394883190957
f = 0.5867241379310345 (normalized)
T =  0.2645310151876739
f = 0.5943103448275862 (normalized)
T =  0.36750472780524757
f = 0.598103448275862 (normalized)
T =  0.4769464185630474
f = 0.5004310344827585 (normalized)
T =  0.9748016378548766
f = 0.5023275862068965 (normalized)
T =  0.8763257293868418
f = 0.5042241379310344 (normalized)
T =  0.6688012465347837
f = 0.5070689655172413 (normalized)
T =  0.30947164063370675
f = 0.5118103448275861 (normalized)
T =  0.055824297360035045
f = 0.5535344827586206 (normalized)
T =  0.15001754334676692
f = 0.5554310344827587 (normalized)
T =  0.25973396739659627
f = 0.5573275862068965 (normalized)
T =  0.4560423699167162
f = 0.5611206896551724 (normalized)
T =  0.9817149851911617
f = 0.5639655172413793 (normalized)
T =  0.8551236019715526
f = 0.5677586206896551 (normalized)
T =  0.5189407202056499
f = 0.5725 (normalized)
T =  0.3320993021398809
f = 0.5905172413793103 (normalized)
T =  0.30128704721673005
f = 0.5018534482758621 (normalized)
T =  0.9109875724140282
f = 0.5080172413793103 (normalized)
T =  0.22374155025352338
f = 0.5099137931034483 (normalized)
T =  0.11237979012832042
f = 0.5592241379310345 (normalized)
T =  0.749221710987455
f = 0.5615948275862068 (normalized)
T =  0.9987021993424349
f = 0.5630172413793104 (normalized)
T =  0.9442424265128956
f = 0.5687068965517241 (normalized)
T =  0.4648505563416617
f = 0.570603448275862 (normalized)
T =  0.385049057918246
f = 0.5606465517241379 (normalized)
T =  0.9451902220257062
f = 0.562543103448276 (normalized)
T =  0.9769576777297204
f = 0.5608836206896551 (normalized)
T =  0.9658115244741778
f = 0.49 (normalized)
T =  0.9971991048843083
f = 0.49379310344827587 (normalized)
T =  0.9920003583208585
f = 0.4975862068965517 (normalized)
T =  0.9793384472657396
f = 0.5013793103448275 (normalized)
T =  0.9998300471122119
f = 0.5051724137931034 (normalized)
T =  0.8216337811633614
f = 0.5089655172413793 (normalized)
T =  0.29760644404191955
f = 0.5127586206896552 (normalized)
T =  0.074356162477423
f = 0.516551724137931 (normalized)
T =  0.021622046725920104
f = 0.5203448275862069 (normalized)
T =  0.008290733135485942
f = 0.5241379310344827 (normalized)
T =  0.0044520955589322335
f = 0.5279310344827586 (normalized)
T =  0.003413561289361597
f = 0.5317241379310345 (normalized)
T =  0.0035369931088034498
f = 0.5355172413793103 (normalized)
T =  0.004492444950379594
f = 0.5393103448275862 (normalized)
T =  0.006428045451064956
f = 0.5431034482758621 (normalized)
T =  0.009850272637558511
f = 0.5468965517241379 (normalized)
T =  0.01580125585561978
f = 0.5506896551724138 (normalized)
T =  0.026390419456524077
f = 0.5544827586206896 (normalized)
T =  0.04611705992450814
f = 0.5582758620689655 (normalized)
T =  0.08528463267032439
f = 0.5620689655172414 (normalized)
T =  0.1690157076671622
f = 0.5658620689655172 (normalized)
T =  0.35636957203577807
f = 0.569655172413793 (normalized)
T =  0.715753193557045
f = 0.5734482758620689 (normalized)
T =  0.996717691249883
f = 0.5772413793103448 (normalized)
T =  0.868692349089276
f = 0.5810344827586207 (normalized)
T =  0.6591193655030622
f = 0.5848275862068966 (normalized)
T =  0.5299400609278236
f = 0.5886206896551724 (normalized)
T =  0.46957910707387873
f = 0.5924137931034482 (normalized)
T =  0.4584867827695601
f = 0.5962068965517241 (normalized)
T =  0.4911288872262469
f = 0.6 (normalized)
T =  0.5738012872324141
f = 0.5032758620689655 (normalized)
T =  0.9718830075307638
f = 0.5070689655172413 (normalized)
T =  0.5480757608964042
f = 0.5108620689655172 (normalized)
T =  0.14845884842242976
f = 0.5146551724137931 (normalized)
T =  0.03890827952953805
f = 0.518448275862069 (normalized)
T =  0.012880171192291762
f = 0.5601724137931035 (normalized)
T =  0.11896620362083893
f = 0.5677586206896551 (normalized)
T =  0.5160643890121311
f = 0.5753448275862069 (normalized)
T =  0.9683524041852151
f = 0.5791379310344827 (normalized)
T =  0.7561491544028892
f = 0.5829310344827586 (normalized)
T =  0.5842720182334118
f = 0.5867241379310345 (normalized)
T =  0.49270193592020406
f = 0.598103448275862 (normalized)
T =  0.5254820848296854
f = 0.5042241379310344 (normalized)
T =  0.9164337392553725
f = 0.5061206896551724 (normalized)
T =  0.692507046055795
f = 0.5099137931034483 (normalized)
T =  0.2109613452684079
f = 0.5118103448275861 (normalized)
T =  0.10466462194588912
f = 0.5137068965517242 (normalized)
T =  0.05342349646471232
f = 0.5611206896551724 (normalized)
T =  0.14147743273259428
f = 0.5639655172413793 (normalized)
T =  0.24419712049360662
f = 0.571551724137931 (normalized)
T =  0.9033177774258861
f = 0.5762931034482759 (normalized)
T =  0.9231767709055613
f = 0.5857758620689655 (normalized)
T =  0.5093908334514293
f = 0.5023275862068965 (normalized)
T =  0.9956251907715209
f = 0.5046982758620688 (normalized)
T =  0.8740095748848147
f = 0.5080172413793103 (normalized)
T =  0.4113705457606692
f = 0.5113362068965517 (normalized)
T =  0.12457136129212283
f = 0.5630172413793104 (normalized)
T =  0.2027815687842287
f = 0.5668103448275861 (normalized)
T =  0.43000763770744577
f = 0.5725 (normalized)
T =  0.9657847297437165
f = 0.5743965517241378 (normalized)
T =  0.9957211553398393
f = 0.5037499999999999 (normalized)
T =  0.9488080392442163
f = 0.570603448275862 (normalized)
T =  0.8162907185816054
f = 0.5720258620689656 (normalized)
T =  0.9381955067722421

Total running time of the script: (0 minutes 29.241 seconds)

Estimated memory usage: 519 MB

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