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 =  0.9845910272336134
f = 0.49379310344827587 (normalized)
T =  0.999934151365913
f = 0.4975862068965517 (normalized)
T =  0.9769428878610282
f = 0.5013793103448275 (normalized)
T =  0.8767335476260507
f = 0.5051724137931034 (normalized)
T =  0.6819614986551562
f = 0.5089655172413793 (normalized)
T =  0.4394491849179022
f = 0.5127586206896552 (normalized)
T =  0.23067729350589558
f = 0.516551724137931 (normalized)
T =  0.09636651755608697
f = 0.5203448275862069 (normalized)
T =  0.028114503756718923
f = 0.5241379310344827 (normalized)
T =  0.002735842698371845
f = 0.5279310344827586 (normalized)
T =  0.0016544384044463556
f = 0.5317241379310345 (normalized)
T =  0.013646566599987376
f = 0.5355172413793103 (normalized)
T =  0.032666306647300525
f = 0.5393103448275862 (normalized)
T =  0.05566628849274647
f = 0.5431034482758621 (normalized)
T =  0.08122997733050324
f = 0.5468965517241379 (normalized)
T =  0.1088189514923115
f = 0.5506896551724138 (normalized)
T =  0.13837707657474108
f = 0.5544827586206896 (normalized)
T =  0.17012550144133787
f = 0.5582758620689655 (normalized)
T =  0.2044566756314227
f = 0.5620689655172414 (normalized)
T =  0.24187831456810083
f = 0.5658620689655172 (normalized)
T =  0.2829801207010243
f = 0.569655172413793 (normalized)
T =  0.32840613269578084
f = 0.5734482758620689 (normalized)
T =  0.3788188498300245
f = 0.5772413793103448 (normalized)
T =  0.43484014003051263
f = 0.5810344827586207 (normalized)
T =  0.4969494445833941
f = 0.5848275862068966 (normalized)
T =  0.5653129003258696
f = 0.5886206896551724 (normalized)
T =  0.6395103701923289
f = 0.5924137931034482 (normalized)
T =  0.7181288136206129
f = 0.5962068965517241 (normalized)
T =  0.7982190259324845
f = 0.6 (normalized)
T =  0.87470606838694
f = 0.4994827586206896 (normalized)
T =  0.9387028078218748
f = 0.5032758620689655 (normalized)
T =  0.7899333972193125
f = 0.5146551724137931 (normalized)
T =  0.15399576894363654
f = 0.518448275862069 (normalized)
T =  0.055429433411073314
f = 0.5004310344827585 (normalized)
T =  0.9108490724807533

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 =  0.9445045989618308
f = 0.49379310344827587 (normalized)
T =  0.9997682511298721
f = 0.4975862068965517 (normalized)
T =  0.9540820015845084
f = 0.5013793103448275 (normalized)
T =  0.8771839203171815
f = 0.5051724137931034 (normalized)
T =  0.9375406178769251
f = 0.5089655172413793 (normalized)
T =  0.7360778228380718
f = 0.5127586206896552 (normalized)
T =  0.07334923968441065
f = 0.516551724137931 (normalized)
T =  0.005324445907031337
f = 0.5203448275862069 (normalized)
T =  0.000262572524505627
f = 0.5241379310344827 (normalized)
T =  3.8523680381370365e-07
f = 0.5279310344827586 (normalized)
T =  7.032026241637712e-09
f = 0.5317241379310345 (normalized)
T =  3.8371562117925214e-05
f = 0.5355172413793103 (normalized)
T =  0.00025529407426389775
f = 0.5393103448275862 (normalized)
T =  0.0008130193282537066
f = 0.5431034482758621 (normalized)
T =  0.0019237711141285474
f = 0.5468965517241379 (normalized)
T =  0.0039359198277736426
f = 0.5506896551724138 (normalized)
T =  0.0074871083098308425
f = 0.5544827586206896 (normalized)
T =  0.01381946570906397
f = 0.5582758620689655 (normalized)
T =  0.025499922857494195
f = 0.5620689655172414 (normalized)
T =  0.04819892570151394
f = 0.5658620689655172 (normalized)
T =  0.09534185503418034
f = 0.569655172413793 (normalized)
T =  0.19997940722052182
f = 0.5734482758620689 (normalized)
T =  0.4324649251771101
f = 0.5772413793103448 (normalized)
T =  0.8135247574027491
f = 0.5810344827586207 (normalized)
T =  0.9993088714501577
f = 0.5848275862068966 (normalized)
T =  0.8689863537800553
f = 0.5886206896551724 (normalized)
T =  0.7215289601199876
f = 0.5924137931034482 (normalized)
T =  0.6483288067496557
f = 0.5962068965517241 (normalized)
T =  0.6435929053520996
f = 0.6 (normalized)
T =  0.6998666814085511
f = 0.49189655172413793 (normalized)
T =  0.9825860355851618
f = 0.4994827586206896 (normalized)
T =  0.9096763681399997
f = 0.5032758620689655 (normalized)
T =  0.8799935661336875
f = 0.5070689655172413 (normalized)
T =  0.9992690233576417
f = 0.5108620689655172 (normalized)
T =  0.26780567061481547
f = 0.5146551724137931 (normalized)
T =  0.019855637450113827
f = 0.518448275862069 (normalized)
T =  0.0013149290969173394
f = 0.5677586206896551 (normalized)
T =  0.1370767802322608
f = 0.571551724137931 (normalized)
T =  0.29461019139463135
f = 0.5753448275862069 (normalized)
T =  0.6154027675814336
f = 0.5791379310344827 (normalized)
T =  0.9587902863584032
f = 0.5829310344827586 (normalized)
T =  0.9521336285500404
f = 0.5867241379310345 (normalized)
T =  0.7870626814950827
f = 0.5943103448275862 (normalized)
T =  0.6380670577849138
f = 0.598103448275862 (normalized)
T =  0.6642908999787747
f = 0.5042241379310344 (normalized)
T =  0.9015525795953991
f = 0.5080172413793103 (normalized)
T =  0.9332460535904661
f = 0.5099137931034483 (normalized)
T =  0.47635913942481245
f = 0.5118103448275861 (normalized)
T =  0.1413245571715032
f = 0.5137068965517242 (normalized)
T =  0.03810350689414524
f = 0.515603448275862 (normalized)
T =  0.010330932299682589
f = 0.5687068965517241 (normalized)
T =  0.16529231069653286
f = 0.570603448275862 (normalized)
T =  0.24256837322297015
f = 0.5725 (normalized)
T =  0.3575771202710204
f = 0.5800862068965518 (normalized)
T =  0.9926715731749228
f = 0.5838793103448277 (normalized)
T =  0.9121317534161507
f = 0.5905172413793103 (normalized)
T =  0.6755990384777404
f = 0.5061206896551724 (normalized)
T =  0.9799769971380518
f = 0.5084913793103447 (normalized)
T =  0.8499114242546674
f = 0.5113362068965517 (normalized)
T =  0.19535189718856635
f = 0.5122844827586206 (normalized)
T =  0.10186250401798312
f = 0.5132327586206897 (normalized)
T =  0.05284115156949477
f = 0.5781896551724137 (normalized)
T =  0.8973780311619269
f = 0.5876724137931035 (normalized)
T =  0.7518832012557874
f = 0.5075431034482758 (normalized)
T =  0.9814982068826035
f = 0.5103879310344828 (normalized)
T =  0.3615866672886648
f = 0.5796120689655173 (normalized)
T =  0.979280858296842
f = 0.5082543103448275 (normalized)
T =  0.8959279226820606
f = 0.5786637931034482 (normalized)
T =  0.9313277126219506
f = 0.49 (normalized)
T =  0.9509248374803391
f = 0.49379310344827587 (normalized)
T =  0.9995958662377167
f = 0.4975862068965517 (normalized)
T =  0.9152284351914067
f = 0.5013793103448275 (normalized)
T =  0.6361891294503885
f = 0.5051724137931034 (normalized)
T =  0.3607660883108921
f = 0.5089655172413793 (normalized)
T =  0.2049106376284187
f = 0.5127586206896552 (normalized)
T =  0.1486487526868567
f = 0.516551724137931 (normalized)
T =  0.3955303767043202
f = 0.5203448275862069 (normalized)
T =  0.0073629107988528696
f = 0.5241379310344827 (normalized)
T =  4.104572568226298e-07
f = 0.5279310344827586 (normalized)
T =  1.4214339479610377e-06
f = 0.5317241379310345 (normalized)
T =  7.565338837678795e-05
f = 0.5355172413793103 (normalized)
T =  0.0004424786470618033
f = 0.5393103448275862 (normalized)
T =  0.0011512978159342311
f = 0.5431034482758621 (normalized)
T =  0.002223758163276067
f = 0.5468965517241379 (normalized)
T =  0.0037200953904934714
f = 0.5506896551724138 (normalized)
T =  0.005766695683960672
f = 0.5544827586206896 (normalized)
T =  0.008586796495484791
f = 0.5582758620689655 (normalized)
T =  0.012555047685519821
f = 0.5620689655172414 (normalized)
T =  0.018300362539768508
f = 0.5658620689655172 (normalized)
T =  0.02690324285592966
f = 0.569655172413793 (normalized)
T =  0.040284195212689194
f = 0.5734482758620689 (normalized)
T =  0.06198844857942234
f = 0.5772413793103448 (normalized)
T =  0.0987826347376843
f = 0.5810344827586207 (normalized)
T =  0.16371036172637113
f = 0.5848275862068966 (normalized)
T =  0.280237013149135
f = 0.5886206896551724 (normalized)
T =  0.4777606871525176
f = 0.5924137931034482 (normalized)
T =  0.7419767134052556
f = 0.5962068965517241 (normalized)
T =  0.9460523569702242
f = 0.6 (normalized)
T =  0.999998482395298
f = 0.49189655172413793 (normalized)
T =  0.9814438284227042
f = 0.4994827586206896 (normalized)
T =  0.7909855418134859
f = 0.5070689655172413 (normalized)
T =  0.26840057444532184
f = 0.5108620689655172 (normalized)
T =  0.16538740350442224
f = 0.5146551724137931 (normalized)
T =  0.1693786645776413
f = 0.518448275862069 (normalized)
T =  0.22522971176775827
f = 0.5791379310344827 (normalized)
T =  0.12654903916770951
f = 0.5829310344827586 (normalized)
T =  0.21359700342457982
f = 0.5867241379310345 (normalized)
T =  0.36763233670269263
f = 0.598103448275862 (normalized)
T =  0.9892040598510204
f = 0.4956896551724138 (normalized)
T =  0.9842074974950007
f = 0.5032758620689655 (normalized)
T =  0.4853088496544494
f = 0.5080172413793103 (normalized)
T =  0.23338141762003958
f = 0.5099137931034483 (normalized)
T =  0.18237857174795985
f = 0.515603448275862 (normalized)
T =  0.2213283668235582
f = 0.5175000000000001 (normalized)
T =  0.9888374561052327
f = 0.5222413793103449 (normalized)
T =  0.0003570505547114964
f = 0.5943103448275862 (normalized)
T =  0.8615839315844568
f = 0.49474137931034484 (normalized)
T =  0.9975547298991475
f = 0.49853448275862067 (normalized)
T =  0.8590042098697993
f = 0.5137068965517242 (normalized)
T =  0.15175678191564265
f = 0.5160775862068965 (normalized)
T =  0.2801485808104315
f = 0.5170258620689656 (normalized)
T =  0.6405887319973774
f = 0.5193965517241379 (normalized)
T =  0.0343696197696485
f = 0.521293103448276 (normalized)
T =  0.0017152213943377285
f = 0.5971551724137931 (normalized)
T =  0.9725140300290361
f = 0.4966379310344827 (normalized)
T =  0.957158982330416
f = 0.5151293103448276 (normalized)
T =  0.18857096636799783
f = 0.5163146551724138 (normalized)
T =  0.3275456488002487
f = 0.5167887931034483 (normalized)
T =  0.4952012950637656
f = 0.5179741379310345 (normalized)
T =  0.6462897867010219
f = 0.5189224137931034 (normalized)
T =  0.08268845116747653
f = 0.5198706896551724 (normalized)
T =  0.015535354230467159
f = 0.5952586206896551 (normalized)
T =  0.9090013158952452
f = 0.5158405172413792 (normalized)
T =  0.24621622133520155
f = 0.5161961206896551 (normalized)
T =  0.30179765538794523
f = 0.5166702586206897 (normalized)
T =  0.440538591999583
f = 0.5169073275862069 (normalized)
T =  0.5614096459804441
f = 0.5177370689655173 (normalized)
T =  0.923522093636168
f = 0.5186853448275862 (normalized)
T =  0.13415990895785332
f = 0.5191594827586207 (normalized)
T =  0.05261220833468111
f = 0.5172629310344828 (normalized)
T =  0.8317699897154066
f = 0.517855603448276 (normalized)
T =  0.7961463499904654
f = 0.5182112068965518 (normalized)
T =  0.3869756056190055
f = 0.5188038793103449 (normalized)
T =  0.10487766931492838
f = 0.519040948275862 (normalized)
T =  0.06571701759532998
f = 0.5176185344827586 (normalized)
T =  0.9929925859924635
f = 0.5183297413793104 (normalized)
T =  0.2948987539569648
f = 0.5185668103448275 (normalized)
T =  0.1731189242472478
f = 0.5173814655172415 (normalized)
T =  0.9254205541766944
f = 0.5176778017241379 (normalized)
T =  0.9672046432148269
f = 0.5177963362068967 (normalized)
T =  0.8650226170920106
f = 0.5173221982758622 (normalized)
T =  0.8805966089714987
f = 0.5175592672413794 (normalized)
T =  0.9998373985263624
f = 0.5171443965517242 (normalized)
T =  0.7323457347934617
f = 0.5174407327586208 (normalized)
T =  0.9627906262867785
f = 0.49 (normalized)
T =  0.9759429670513536
f = 0.49379310344827587 (normalized)
T =  0.9995052954555079
f = 0.4975862068965517 (normalized)
T =  0.9356654651891876
f = 0.5013793103448275 (normalized)
T =  0.6332299492326957
f = 0.5051724137931034 (normalized)
T =  0.2858009488744194
f = 0.5089655172413793 (normalized)
T =  0.10511337880936193
f = 0.5127586206896552 (normalized)
T =  0.0358226257202248
f = 0.516551724137931 (normalized)
T =  0.011039980174733508
f = 0.5203448275862069 (normalized)
T =  0.002601546072316472
f = 0.5241379310344827 (normalized)
T =  0.000257548156022708
f = 0.5279310344827586 (normalized)
T =  0.006838160624989917
f = 0.5317241379310345 (normalized)
T =  0.0016066043751388915
f = 0.5355172413793103 (normalized)
T =  0.002977328978819519
f = 0.5393103448275862 (normalized)
T =  0.004622408750718087
f = 0.5431034482758621 (normalized)
T =  0.0064803243307489595
f = 0.5468965517241379 (normalized)
T =  0.008598932172927827
f = 0.5506896551724138 (normalized)
T =  0.011087869075854616
f = 0.5544827586206896 (normalized)
T =  0.014117892331974803
f = 0.5582758620689655 (normalized)
T =  0.017942134358908502
f = 0.5620689655172414 (normalized)
T =  0.0229408366650338
f = 0.5658620689655172 (normalized)
T =  0.02970264981346046
f = 0.569655172413793 (normalized)
T =  0.03917148342481505
f = 0.5734482758620689 (normalized)
T =  0.05291770762071236
f = 0.5772413793103448 (normalized)
T =  0.0736510857558964
f = 0.5810344827586207 (normalized)
T =  0.1061989443891071
f = 0.5848275862068966 (normalized)
T =  0.15929488354106594
f = 0.5886206896551724 (normalized)
T =  0.24820946953667467
f = 0.5924137931034482 (normalized)
T =  0.39498097608854454
f = 0.5962068965517241 (normalized)
T =  0.6102178383573703
f = 0.6 (normalized)
T =  0.8387889313295136
f = 0.49189655172413793 (normalized)
T =  0.989038665151238
f = 0.4994827586206896 (normalized)
T =  0.8130454797766983
f = 0.5070689655172413 (normalized)
T =  0.17564835404073623
f = 0.5108620689655172 (normalized)
T =  0.06186456128223033
f = 0.5146551724137931 (normalized)
T =  0.020264968704026866
f = 0.5829310344827586 (normalized)
T =  0.1294096066297822
f = 0.5867241379310345 (normalized)
T =  0.19800125803572308
f = 0.5943103448275862 (normalized)
T =  0.495197341312602
f = 0.4956896551724138 (normalized)
T =  0.9905076198220873
f = 0.5004310344827585 (normalized)
T =  0.7278778043692485
f = 0.5032758620689655 (normalized)
T =  0.4428998532150581
f = 0.5080172413793103 (normalized)
T =  0.13621106163423588
f = 0.5099137931034483 (normalized)
T =  0.08079054816079026
f = 0.5905172413793103 (normalized)
T =  0.3129572942188051
f = 0.49474137931034484 (normalized)
T =  0.9989268356789286
f = 0.49853448275862067 (normalized)
T =  0.8832250947798942
f = 0.5061206896551724 (normalized)
T =  0.2250454163058699
f = 0.4966379310344827 (normalized)
T =  0.9706035692695473
f = 0.4980603448275862 (normalized)
T =  0.9117126440132834
f = 0.49 (normalized)
T =  0.9909512116769181
f = 0.49379310344827587 (normalized)
T =  0.9993313770031051
f = 0.4975862068965517 (normalized)
T =  0.9629748115461775
f = 0.5013793103448275 (normalized)
T =  0.6964734046133447
f = 0.5051724137931034 (normalized)
T =  0.3011537487013509
f = 0.5089655172413793 (normalized)
T =  0.09468942169359906
f = 0.5127586206896552 (normalized)
T =  0.026623737073822262
f = 0.516551724137931 (normalized)
T =  0.006722660287408535
f = 0.5203448275862069 (normalized)
T =  0.001380677538271978
f = 0.5241379310344827 (normalized)
T =  0.00023821668041096943
f = 0.5279310344827586 (normalized)
T =  0.00019926067721356876
f = 0.5317241379310345 (normalized)
T =  0.0023802446251422246
f = 0.5355172413793103 (normalized)
T =  0.08831428897229382
f = 0.5393103448275862 (normalized)
T =  0.16723902214188388
f = 0.5431034482758621 (normalized)
T =  0.05201338540834612
f = 0.5468965517241379 (normalized)
T =  0.03729976257434579
f = 0.5506896551724138 (normalized)
T =  0.03370226435607493
f = 0.5544827586206896 (normalized)
T =  0.033708591932276155
f = 0.5582758620689655 (normalized)
T =  0.03574349724249767
f = 0.5620689655172414 (normalized)
T =  0.03949667814679142
f = 0.5658620689655172 (normalized)
T =  0.04516100871287221
f = 0.569655172413793 (normalized)
T =  0.0533097847061248
f = 0.5734482758620689 (normalized)
T =  0.0649899525936409
f = 0.5772413793103448 (normalized)
T =  0.08199592447528752
f = 0.5810344827586207 (normalized)
T =  0.10741748022254015
f = 0.5848275862068966 (normalized)
T =  0.1466662540912248
f = 0.5886206896551724 (normalized)
T =  0.20923287283613876
f = 0.5924137931034482 (normalized)
T =  0.3107572713047467
f = 0.5962068965517241 (normalized)
T =  0.4706082775139156
f = 0.6 (normalized)
T =  0.6874315118314127
f = 0.4994827586206896 (normalized)
T =  0.8678461795983079
f = 0.5032758620689655 (normalized)
T =  0.4863179594586758
f = 0.5070689655172413 (normalized)
T =  0.17250361384734308
f = 0.5108620689655172 (normalized)
T =  0.05072204877769642
f = 0.5146551724137931 (normalized)
T =  0.013624666279924482
f = 0.5336206896551724 (normalized)
T =  0.011529337553681589
f = 0.5412068965517242 (normalized)
T =  0.0762335862615568
f = 0.5867241379310345 (normalized)
T =  0.17421924280540446
f = 0.5943103448275862 (normalized)
T =  0.3824324923759103
f = 0.4956896551724138 (normalized)
T =  0.9962320895158363
f = 0.5004310344827585 (normalized)
T =  0.7906883646829626
f = 0.5061206896551724 (normalized)
T =  0.22956146429327612
f = 0.5080172413793103 (normalized)
T =  0.12829160212991483
f = 0.5099137931034483 (normalized)
T =  0.06947817994662425
f = 0.5345689655172414 (normalized)
T =  0.028967362789484315
f = 0.5374137931034483 (normalized)
T =  0.9600834900618395
f = 0.5421551724137932 (normalized)
T =  0.06111073445069267
f = 0.5905172413793103 (normalized)
T =  0.2538897414762962
f = 0.49853448275862067 (normalized)
T =  0.9249719401259994
f = 0.534094827586207 (normalized)
T =  0.017966675455679648
f = 0.5364655172413793 (normalized)
T =  0.3812440927699068
f = 0.5383620689655173 (normalized)
T =  0.35648243686880465
f = 0.5402586206896551 (normalized)
T =  0.10438529907711583
f = 0.4980603448275862 (normalized)
T =  0.9461879091634776
f = 0.5350431034482759 (normalized)
T =  0.04894869753207547
f = 0.5359913793103448 (normalized)
T =  0.17432977886412207
f = 0.5369396551724137 (normalized)
T =  0.8088700047785868
f = 0.5378879310344828 (normalized)
T =  0.6038792638965913
f = 0.5397844827586207 (normalized)
T =  0.1287814454230476
f = 0.5407327586206896 (normalized)
T =  0.08791096233212281
f = 0.5357543103448276 (normalized)
T =  0.12249829510574158
f = 0.536228448275862 (normalized)
T =  0.25491003741010787
f = 0.5367025862068965 (normalized)
T =  0.5709721292325634
f = 0.537176724137931 (normalized)
T =  0.9834335633830084
f = 0.5376508620689655 (normalized)
T =  0.7893230162319231
f = 0.5388362068965518 (normalized)
T =  0.2329358572533347
f = 0.5358728448275862 (normalized)
T =  0.14564249671433585
f = 0.5361099137931034 (normalized)
T =  0.2101038642458538
f = 0.5363469827586207 (normalized)
T =  0.31109537618264105
f = 0.5365840517241378 (normalized)
T =  0.46763432122001114
f = 0.5370581896551724 (normalized)
T =  0.9148878087373152
f = 0.537532327586207 (normalized)
T =  0.8836918002479226
f = 0.5381250000000001 (normalized)
T =  0.45923797455195814
f = 0.5385991379310345 (normalized)
T =  0.28436226174785345
f = 0.539073275862069 (normalized)
T =  0.1953721360827341
f = 0.5395474137931034 (normalized)
T =  0.1456698513765396
f = 0.5371174568965518 (normalized)
T =  0.9551555114822327
f = 0.5372952586206896 (normalized)
T =  0.9984203499039872
f = 0.5384806034482759 (normalized)
T =  0.3172896944316181
f = 0.5374730603448277 (normalized)
T =  0.9253695122962673
f = 0.49 (normalized)
T =  0.9989480015948943
f = 0.49379310344827587 (normalized)
T =  0.9988209287528684
f = 0.4975862068965517 (normalized)
T =  0.9892786754900735
f = 0.5013793103448275 (normalized)
T =  0.808910384164826
f = 0.5051724137931034 (normalized)
T =  0.3747757184208607
f = 0.5089655172413793 (normalized)
T =  0.10869962785954312
f = 0.5127586206896552 (normalized)
T =  0.0278660655993925
f = 0.516551724137931 (normalized)
T =  0.006963413270117528
f = 0.5203448275862069 (normalized)
T =  0.0017471063896595121
f = 0.5241379310344827 (normalized)
T =  0.0005556750078363116
f = 0.5279310344827586 (normalized)
T =  0.0004357956957829354
f = 0.5317241379310345 (normalized)
T =  0.0010127429170739856
f = 0.5355172413793103 (normalized)
T =  0.0036114321618713726
f = 0.5393103448275862 (normalized)
T =  0.014408014737828073
f = 0.5431034482758621 (normalized)
T =  0.06876330828661623
f = 0.5468965517241379 (normalized)
T =  0.4938027800537688
f = 0.5506896551724138 (normalized)
T =  0.7244278703406323
f = 0.5544827586206896 (normalized)
T =  0.27126699409471977
f = 0.5582758620689655 (normalized)
T =  0.1616016296549879
f = 0.5620689655172414 (normalized)
T =  0.12409778481698952
f = 0.5658620689655172 (normalized)
T =  0.10966813625680893
f = 0.569655172413793 (normalized)
T =  0.10616434503079893
f = 0.5734482758620689 (normalized)
T =  0.10998366144837633
f = 0.5772413793103448 (normalized)
T =  0.12057484692028055
f = 0.5810344827586207 (normalized)
T =  0.13922336611671543
f = 0.5848275862068966 (normalized)
T =  0.1691604867490638
f = 0.5886206896551724 (normalized)
T =  0.21649811057108356
f = 0.5924137931034482 (normalized)
T =  0.2918979283340779
f = 0.5962068965517241 (normalized)
T =  0.4116373566428743
f = 0.6 (normalized)
T =  0.5900734061433816
f = 0.4994827586206896 (normalized)
T =  0.9385613956955664
f = 0.5032758620689655 (normalized)
T =  0.5980671227714899
f = 0.5070689655172413 (normalized)
T =  0.20825226579261544
f = 0.5108620689655172 (normalized)
T =  0.05530407074545667
f = 0.5146551724137931 (normalized)
T =  0.013964427613244077
f = 0.5412068965517242 (normalized)
T =  0.030370610283594054
f = 0.5487931034482758 (normalized)
T =  0.9897381536867785
f = 0.5525862068965517 (normalized)
T =  0.41527263229382944
f = 0.5563793103448276 (normalized)
T =  0.20048082132287498
f = 0.5601724137931035 (normalized)
T =  0.13847691297378562
f = 0.5867241379310345 (normalized)
T =  0.19011752383702019
f = 0.5943103448275862 (normalized)
T =  0.34505731030857717
f = 0.598103448275862 (normalized)
T =  0.49340676670972844
f = 0.4956896551724138 (normalized)
T =  0.9998536500857548
f = 0.5004310344827585 (normalized)
T =  0.8854111202741729
f = 0.5023275862068965 (normalized)
T =  0.7106632631877975
f = 0.5080172413793103 (normalized)
T =  0.15119751922556174
f = 0.5099137931034483 (normalized)
T =  0.07767525459776033
f = 0.5118103448275861 (normalized)
T =  0.039287576320619924
f = 0.5449999999999999 (normalized)
T =  0.1743490940872042
f = 0.5497413793103447 (normalized)
T =  0.9280522858408803
f = 0.5535344827586206 (normalized)
T =  0.32968510248007976
f = 0.5554310344827587 (normalized)
T =  0.23020867400710404
f = 0.5573275862068965 (normalized)
T =  0.17838526128975166
f = 0.5905172413793103 (normalized)
T =  0.2497952575688066
f = 0.49853448275862067 (normalized)
T =  0.9714390729827066
f = 0.500905172413793 (normalized)
T =  0.8501144172480344
f = 0.5061206896551724 (normalized)
T =  0.2824960435578992
f = 0.5421551724137932 (normalized)
T =  0.04518235674039613
f = 0.5459482758620688 (normalized)
T =  0.291776612605588
f = 0.5478448275862069 (normalized)
T =  0.7808126388916721
f = 0.5502155172413792 (normalized)
T =  0.8300347957963542
f = 0.5516379310344828 (normalized)
T =  0.5426228843651772
f = 0.5540086206896551 (normalized)
T =  0.29780121364704015
f = 0.5549568965517242 (normalized)
T =  0.2490140280349218
f = 0.49995689655172404 (normalized)
T =  0.9147943154600092
f = 0.544051724137931 (normalized)
T =  0.10767332220181276
f = 0.5464224137931033 (normalized)
T =  0.38019904257954573
f = 0.5473706896551724 (normalized)
T =  0.6315317558213216
f = 0.5492672413793103 (normalized)
T =  0.9912623894404028
f = 0.5511637931034483 (normalized)
T =  0.6267070308271371
f = 0.5530603448275861 (normalized)
T =  0.36827784368229244
f = 0.5445258620689655 (normalized)
T =  0.1364132834558327
f = 0.5454741379310344 (normalized)
T =  0.2247429420770286
f = 0.5483189655172414 (normalized)
T =  0.9126067907573646
f = 0.5495043103448275 (normalized)
T =  0.9660339880169869
f = 0.549978448275862 (normalized)
T =  0.881446270034494
f = 0.5485560344827586 (normalized)
T =  0.960009124157852
f = 0.549030172413793 (normalized)
T =  0.9999936091950344
f = 0.49 (normalized)
T =  0.9995399957487886
f = 0.49379310344827587 (normalized)
T =  0.9972363782541372
f = 0.4975862068965517 (normalized)
T =  0.9999094600447822
f = 0.5013793103448275 (normalized)
T =  0.9384767633143779
f = 0.5051724137931034 (normalized)
T =  0.5407833885446461
f = 0.5089655172413793 (normalized)
T =  0.15919811332730865
f = 0.5127586206896552 (normalized)
T =  0.039524663169049595
f = 0.516551724137931 (normalized)
T =  0.010612623102608248
f = 0.5203448275862069 (normalized)
T =  0.003394970491294224
f = 0.5241379310344827 (normalized)
T =  0.0015293463815785613
f = 0.5279310344827586 (normalized)
T =  0.0011854170000144323
f = 0.5317241379310345 (normalized)
T =  0.0015640901058668766
f = 0.5355172413793103 (normalized)
T =  0.002817140271100098
f = 0.5393103448275862 (normalized)
T =  0.005769981800866106
f = 0.5431034482758621 (normalized)
T =  0.012499045721323014
f = 0.5468965517241379 (normalized)
T =  0.028484889772335334
f = 0.5506896551724138 (normalized)
T =  0.07031207562554331
f = 0.5544827586206896 (normalized)
T =  0.19663122687048595
f = 0.5582758620689655 (normalized)
T =  0.5945645218549486
f = 0.5620689655172414 (normalized)
T =  0.9963414590945148
f = 0.5658620689655172 (normalized)
T =  0.6645296673715008
f = 0.569655172413793 (normalized)
T =  0.42084091120440936
f = 0.5734482758620689 (normalized)
T =  0.312665993618027
f = 0.5772413793103448 (normalized)
T =  0.2653591306716473
f = 0.5810344827586207 (normalized)
T =  0.24931024177906566
f = 0.5848275862068966 (normalized)
T =  0.25454907594325943
f = 0.5886206896551724 (normalized)
T =  0.2798540411361076
f = 0.5924137931034482 (normalized)
T =  0.32998304948197876
f = 0.5962068965517241 (normalized)
T =  0.4157914731097948
f = 0.6 (normalized)
T =  0.5526114380507806
f = 0.4994827586206896 (normalized)
T =  0.9925550012082163
f = 0.5032758620689655 (normalized)
T =  0.7849333444606922
f = 0.5108620689655172 (normalized)
T =  0.07914888635433957
f = 0.5146551724137931 (normalized)
T =  0.020164149344803227
f = 0.5525862068965517 (normalized)
T =  0.11548926972158656
f = 0.5563793103448276 (normalized)
T =  0.3446016140350588
f = 0.5601724137931035 (normalized)
T =  0.8913283756928194
f = 0.571551724137931 (normalized)
T =  0.3558931500220879
f = 0.5753448275862069 (normalized)
T =  0.2839394883191045
f = 0.5867241379310345 (normalized)
T =  0.2645310151876909
f = 0.5943103448275862 (normalized)
T =  0.3675047278053002
f = 0.598103448275862 (normalized)
T =  0.476946418563031
f = 0.5004310344827585 (normalized)
T =  0.97480163785491
f = 0.5023275862068965 (normalized)
T =  0.8763257293868075
f = 0.5042241379310344 (normalized)
T =  0.6688012465346715
f = 0.5070689655172413 (normalized)
T =  0.30947164063380234
f = 0.5118103448275861 (normalized)
T =  0.05582429736001007
f = 0.5535344827586206 (normalized)
T =  0.15001754334682027
f = 0.5554310344827587 (normalized)
T =  0.25973396739666105
f = 0.5573275862068965 (normalized)
T =  0.45604236991670277
f = 0.5611206896551724 (normalized)
T =  0.981714985191206
f = 0.5639655172413793 (normalized)
T =  0.8551236019715438
f = 0.5677586206896551 (normalized)
T =  0.5189407202057414
f = 0.5725 (normalized)
T =  0.33209930213984973
f = 0.5905172413793103 (normalized)
T =  0.3012870472167613
f = 0.5018534482758621 (normalized)
T =  0.9109875724140684
f = 0.5080172413793103 (normalized)
T =  0.22374155025354278
f = 0.5099137931034483 (normalized)
T =  0.11237979012835057
f = 0.5592241379310345 (normalized)
T =  0.7492217109874939
f = 0.5615948275862068 (normalized)
T =  0.9987021993424664
f = 0.5630172413793104 (normalized)
T =  0.944242426512959
f = 0.5687068965517241 (normalized)
T =  0.4648505563416428
f = 0.570603448275862 (normalized)
T =  0.385049057918244
f = 0.5606465517241379 (normalized)
T =  0.9451902220256803
f = 0.562543103448276 (normalized)
T =  0.9769576777297039
f = 0.5608836206896551 (normalized)
T =  0.9658115244742488
f = 0.49 (normalized)
T =  0.9971991048843138
f = 0.49379310344827587 (normalized)
T =  0.9920003583208242
f = 0.4975862068965517 (normalized)
T =  0.9793384472657722
f = 0.5013793103448275 (normalized)
T =  0.9998300471122465
f = 0.5051724137931034 (normalized)
T =  0.8216337811633738
f = 0.5089655172413793 (normalized)
T =  0.297606444041968
f = 0.5127586206896552 (normalized)
T =  0.07435616247741862
f = 0.516551724137931 (normalized)
T =  0.021622046725922456
f = 0.5203448275862069 (normalized)
T =  0.008290733135485376
f = 0.5241379310344827 (normalized)
T =  0.004452095558933035
f = 0.5279310344827586 (normalized)
T =  0.0034135612893615884
f = 0.5317241379310345 (normalized)
T =  0.003536993108803495
f = 0.5355172413793103 (normalized)
T =  0.0044924449503796595
f = 0.5393103448275862 (normalized)
T =  0.006428045451064886
f = 0.5431034482758621 (normalized)
T =  0.009850272637557259
f = 0.5468965517241379 (normalized)
T =  0.01580125585561879
f = 0.5506896551724138 (normalized)
T =  0.026390419456526218
f = 0.5544827586206896 (normalized)
T =  0.04611705992451774
f = 0.5582758620689655 (normalized)
T =  0.08528463267032009
f = 0.5620689655172414 (normalized)
T =  0.16901570766713708
f = 0.5658620689655172 (normalized)
T =  0.35636957203582054
f = 0.569655172413793 (normalized)
T =  0.7157531935571462
f = 0.5734482758620689 (normalized)
T =  0.9967176912498987
f = 0.5772413793103448 (normalized)
T =  0.8686923490892544
f = 0.5810344827586207 (normalized)
T =  0.6591193655030333
f = 0.5848275862068966 (normalized)
T =  0.5299400609278152
f = 0.5886206896551724 (normalized)
T =  0.46957910707388645
f = 0.5924137931034482 (normalized)
T =  0.45848678276958016
f = 0.5962068965517241 (normalized)
T =  0.491128887226242
f = 0.6 (normalized)
T =  0.5738012872323648
f = 0.5032758620689655 (normalized)
T =  0.9718830075306746
f = 0.5070689655172413 (normalized)
T =  0.5480757608965398
f = 0.5108620689655172 (normalized)
T =  0.1484588484225154
f = 0.5146551724137931 (normalized)
T =  0.038908279529564105
f = 0.518448275862069 (normalized)
T =  0.012880171192293347
f = 0.5601724137931035 (normalized)
T =  0.1189662036208616
f = 0.5677586206896551 (normalized)
T =  0.5160643890119624
f = 0.5753448275862069 (normalized)
T =  0.9683524041853008
f = 0.5791379310344827 (normalized)
T =  0.7561491544029108
f = 0.5829310344827586 (normalized)
T =  0.5842720182333913
f = 0.5867241379310345 (normalized)
T =  0.4927019359202087
f = 0.598103448275862 (normalized)
T =  0.5254820848296752
f = 0.5042241379310344 (normalized)
T =  0.9164337392553146
f = 0.5061206896551724 (normalized)
T =  0.6925070460556504
f = 0.5099137931034483 (normalized)
T =  0.21096134526846777
f = 0.5118103448275861 (normalized)
T =  0.10466462194584279
f = 0.5137068965517242 (normalized)
T =  0.053423496464723656
f = 0.5611206896551724 (normalized)
T =  0.14147743273262128
f = 0.5639655172413793 (normalized)
T =  0.24419712049361927
f = 0.571551724137931 (normalized)
T =  0.9033177774259504
f = 0.5762931034482759 (normalized)
T =  0.9231767709055823
f = 0.5857758620689655 (normalized)
T =  0.5093908334514385
f = 0.5023275862068965 (normalized)
T =  0.9956251907714829
f = 0.5046982758620688 (normalized)
T =  0.8740095748849143
f = 0.5080172413793103 (normalized)
T =  0.41137054576068527
f = 0.5113362068965517 (normalized)
T =  0.12457136129209546
f = 0.5630172413793104 (normalized)
T =  0.20278156878418796
f = 0.5668103448275861 (normalized)
T =  0.43000763770749706
f = 0.5725 (normalized)
T =  0.9657847297437614
f = 0.5743965517241378 (normalized)
T =  0.9957211553397974
f = 0.5037499999999999 (normalized)
T =  0.9488080392441327
f = 0.570603448275862 (normalized)
T =  0.8162907185816407
f = 0.5720258620689656 (normalized)
T =  0.9381955067722683

Total running time of the script: (0 minutes 35.171 seconds)

Estimated memory usage: 645 MB

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