Angular Reflectance Spectrum of a Planar Interface

We turn to a similar but slightly different example for which there exists an analytic solution via the Fresnel equations: computing the broadband reflectance spectrum of a planar air-dielectric interface for an incident planewave over a range of angles. Similar to the previous example, we will need to run two simulations: (1) an empty cell with air/vacuum ($n$=1) everywhere to obtain the incident flux, and (2) with the dielectric ($n$=3.5) interface to obtain the reflected flux. For each angle of the incident planewave, a separate simulation is necessary.

A 1d cell must be used since a higher-dimensional cell will introduce artificial modes due to band folding. We will use a Gaussian source spanning visible wavelengths of 0.4 to 0.8 μm. Unlike a continuous-wave (CW) source, a pulsed source turns off. This enables a termination condition of when there are no fields remaining in the cell (due to absorption by the PMLs) via the run function stop_when_fields_decayed, similar to the previous example.

Creating an oblique planewave source typically requires specifying two parameters: (1) for periodic structures, the Bloch-periodic wavevector $\vec{k}$ via k_point, and (2) the source amplitude function amp_func for setting the $e^{i\vec{k} \cdot \vec{r}}$ spatial dependence ($\vec{r}$ is the position vector). Since we have a 1d cell and the source is at a single point, it is not necessary to specify the source amplitude (see this 2d example for how this is done). The magnitude of the Bloch-periodic wavevector is specified according to the dispersion relation formula for a planewave in homogeneous media with index $n$: $ω=c|\vec{k}|/n$. As the source in this example is incident from air, $|\vec{k}|$ is simply equal to the frequency $ω$ (the minimum frequency of the pulse which excludes the 2π factor). Note that a fixed wavevector only applies to a single frequency. Any broadband source is therefore incident at a specified angle for only a single frequency. This is described in more detail in Section 4.5 ("Efficient Frequency-Angle Coverage") in Chapter 4 ("Electromagnetic Wave Source Conditions") of the book Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology.

In this example, the plane of incidence which contains $\vec{k}$ and the surface normal vector is $xz$. The source angle θ is defined in degrees in the counterclockwise (CCW) direction around the $y$ axis with 0 degrees along the +$z$ axis. In Meep, a 1d cell is defined along the $z$ direction. When $\vec{k}$ is not set, only the $E_x$ and $H_y$ field components are permitted. A non-zero $\vec{k}$ results in a 3d simulation where all field components are allowed and are complex (the fields are real, by default). A current source with $E_x$ polarization lies in the plane of incidence and corresponds to the convention of $\mathcal{P}$-polarization. In order to model the $\mathcal{S}$-polarization, we must use an $E_y$ source. This example involves just the $\mathcal{P}$-polarization.

In [1]:
import meep as mp
import math
import numpy as np
import numpy.matlib
import matplotlib.pyplot as plt

resolution = 50                 # pixels/um

dpml = 1.0                      # PML thickness
sz = 10 + 2*dpml
cell_size = mp.Vector3(z=sz)
pml_layers = [mp.PML(dpml)]

wvl_min = 0.4                   # min wavelength
wvl_max = 0.8                   # max wavelength
fmin = 1/wvl_max                # min frequency
fmax = 1/wvl_min                # max frequency
fcen = 0.5*(fmin+fmax)          # center frequency
df = fmax-fmin                  # frequency width
nfreq = 50                      # number of frequency bins

def planar_reflectance(theta):    
    # rotation angle (in degrees) of source: CCW around Y axis, 0 degrees along +Z axis
    theta_r = math.radians(theta)

    # plane of incidence is XZ; rotate counter clockwise (CCW) about y-axis
    k = mp.Vector3(z=fmin).rotate(mp.Vector3(y=1), theta_r)
    
    # if normal incidence, force number of dimensions to be 1
    if theta_r == 0:
        dimensions = 1
    else:
        dimensions = 3
    
    sources = [mp.Source(mp.GaussianSource(fcen,fwidth=df), component=mp.Ex, center=mp.Vector3(z=-0.5*sz+dpml))]

    sim = mp.Simulation(cell_size=cell_size,
                        boundary_layers=pml_layers,
                        sources=sources,
                        k_point=k,
                        dimensions=dimensions,
                        resolution=resolution)

    refl_fr = mp.FluxRegion(center=mp.Vector3(z=-0.25*sz))
    refl = sim.add_flux(fcen, df, nfreq, refl_fr)
    
    sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ex, mp.Vector3(z=-0.5*sz+dpml), 1e-9))

    empty_flux = mp.get_fluxes(refl)
    empty_data = sim.get_flux_data(refl)

    sim.reset_meep()

    # add a block with n=3.5 for the air-dielectric interface
    geometry = [mp.Block(mp.Vector3(mp.inf,mp.inf,0.5*sz), center=mp.Vector3(z=0.25*sz), material=mp.Medium(index=3.5))]

    sim = mp.Simulation(cell_size=cell_size,
                        geometry=geometry,
                        boundary_layers=pml_layers,
                        sources=sources,
                        k_point=k,
                        dimensions=dimensions,
                        resolution=resolution)

    refl = sim.add_flux(fcen, df, nfreq, refl_fr)
    sim.load_minus_flux_data(refl, empty_data)

    sim.run(until_after_sources=mp.stop_when_fields_decayed(50, mp.Ex, mp.Vector3(z=-0.5*sz+dpml), 1e-9))

    refl_flux = mp.get_fluxes(refl)
    freqs = mp.get_flux_freqs(refl)

    wvls = np.empty(nfreq)
    theta_out = np.empty(nfreq)
    R = np.empty(nfreq)
    for i in range(nfreq):
        wvls[i] = 1/freqs[i]
        theta_out[i] = math.degrees(math.asin(k.x/freqs[i]))
        R[i] = -refl_flux[i]/empty_flux[i]
        print("refl:, {}, {}, {}, {}".format(k.x,wvls[i],theta_out[i],R[i]))
        
    return k.x*np.ones(nfreq), wvls, theta_out, R 

The function planar_reflectance computes the reflectance at each frequency as well as the wavevector component $k_x$ and the corresponding angle for the ($k_x$, ω) pair. For those frequencies not equal to the minimum frequency of the source, this is not the same as the specified angle of the incident planewave, but rather sin-1(kx/ω).

The reflectance spectrum is generated over the angular range of 0$^\circ$ to 80$^\circ$ in increments of 5$^\circ$.

In [2]:
theta_in = np.arange(0,85,5)
wvl = np.empty(nfreq)
kxs = np.empty((nfreq,theta_in.size))
thetas = np.empty((nfreq,theta_in.size))
Rmeep = np.empty((nfreq,theta_in.size))

for j in range(theta_in.size):
  kxs[:,j], wvl, thetas[:,j], Rmeep[:,j] = planar_reflectance(theta_in[j])

# create a 2d matrix for the wavelength by repeating the column vector for each angle
wvls = np.transpose(np.matlib.repmat(wvl,theta_in.size,1))
-----------
Initializing structure...
time for choose_chunkdivision = 0.000254154 s
Working in 1D dimensions.
Computational cell is 0 x 0 x 12 with resolution 50
time for set_epsilon = 0.000342131 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.25332329653323415 / 0.25332329653323415 = 1.0
field decay(t = 100.01): 6.806395978139867e-16 / 0.25332329653323415 = 2.6868417043700194e-15
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108004 s
Working in 1D dimensions.
Computational cell is 0 x 0 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.000371933 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.25332329652480207 / 0.25332329652480207 = 1.0
field decay(t = 100.01): 1.9736380723733672e-11 / 0.25332329652480207 = 7.790985272371642e-11
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.0, 0.8, 0.0, 0.29476330384323207
refl:, 0.0, 0.784, 0.0, 0.29416578611798405
refl:, 0.0, 0.7686274509803922, 0.0, 0.2935560666132851
refl:, 0.0, 0.7538461538461539, 0.0, 0.29293290546540196
refl:, 0.0, 0.739622641509434, 0.0, 0.2922951429790378
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refl:, 0.0, 0.7127272727272727, 0.0, 0.29097731021514417
refl:, 0.0, 0.7, 0.0, 0.29029575759541565
refl:, 0.0, 0.6877192982456141, 0.0, 0.2895975033066778
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refl:, 0.0, 0.56, 0.0, 0.27904384994339343
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refl:, 0.0, 0.49, 0.0, 0.26890977948431494
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refl:, 0.0, 0.47804878048780486, 0.0, 0.26664234270279846
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refl:, 0.0, 0.4307692307692308, 0.0, 0.25532959438320507
refl:, 0.0, 0.4260869565217391, 0.0, 0.2539529088676918
refl:, 0.0, 0.421505376344086, 0.0, 0.2525520862693137
refl:, 0.0, 0.41702127659574467, 0.0, 0.2511282531123407
refl:, 0.0, 0.4126315789473684, 0.0, 0.24967934554669954
refl:, 0.0, 0.4083333333333333, 0.0, 0.24820404444956207
refl:, 0.0, 0.4041237113402062, 0.0, 0.24670386250022297
refl:, 0.0, 0.4, 0.0, 0.24517862401765392
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00770998 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.25242167342001043 / 0.25242167342001043 = 1.0
field decay(t = 100.01): 1.8867425254108467e-14 / 0.25242167342001043 = 7.474566267815881e-14
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.026345 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.2524216734361254 / 0.2524216734361254 = 1.0
field decay(t = 100.01): 2.0310851043564926e-11 / 0.2524216734361254 = 8.046397429777174e-11
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.1089446784345727, 0.8, 5.0, 0.2934227118859898
refl:, 0.1089446784345727, 0.784, 4.899752997934953, 0.29287850682357097
refl:, 0.1089446784345727, 0.7686274509803922, 4.803451415694315, 0.2923194417293526
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refl:, 0.1089446784345727, 0.4083333333333333, 2.549686797979975, 0.2478653741944476
refl:, 0.1089446784345727, 0.4041237113402062, 2.5233842703240543, 0.24637235281997996
refl:, 0.1089446784345727, 0.4, 2.4976190449198983, 0.2448541987123429
-----------
Initializing structure...
time for choose_chunkdivision = 0.00011611 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00750589 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.24974540035413878 / 0.24974540035413878 = 1.0
field decay(t = 100.01): 6.006906595531682e-14 / 0.24974540035413878 = 2.40521210281106e-13
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0191441 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.24974540044608928 / 0.24974540044608928 = 1.0
field decay(t = 100.01): 2.1519308385946042e-11 / 0.24974540044608928 = 8.61649838095467e-11
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.2170602220836629, 0.8, 10.0, 0.2893781746253207
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refl:, 0.2170602220836629, 0.56, 6.981780911561047, 0.2764449243213644
refl:, 0.2170602220836629, 0.552112676056338, 6.882966732780441, 0.2755914805667849
refl:, 0.2170602220836629, 0.5444444444444444, 6.786917113194022, 0.27471697321444166
refl:, 0.2170602220836629, 0.536986301369863, 6.693517371228444, 0.27382008373306266
refl:, 0.2170602220836629, 0.5297297297297298, 6.602659095992853, 0.2729019522035499
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refl:, 0.2170602220836629, 0.5157894736842105, 6.428162147069652, 0.27100303851505764
refl:, 0.2170602220836629, 0.509090909090909, 6.3443343580501015, 0.27001939086671356
refl:, 0.2170602220836629, 0.5025641025641026, 6.262669115245526, 0.26901406912439724
refl:, 0.2170602220836629, 0.4962025316455696, 6.1830836393232005, 0.2679876733928022
refl:, 0.2170602220836629, 0.49, 6.105499330654852, 0.2669381026643071
refl:, 0.2170602220836629, 0.4839506172839506, 6.029841508312739, 0.265864537999668
refl:, 0.2170602220836629, 0.47804878048780486, 5.956039168418179, 0.26476870360049726
refl:, 0.2170602220836629, 0.47228915662650606, 5.884024760185935, 0.26365066570667506
refl:, 0.2170602220836629, 0.4666666666666667, 5.813733978168244, 0.26250810411848724
refl:, 0.2170602220836629, 0.4611764705882353, 5.745105569345401, 0.26134058873292715
refl:, 0.2170602220836629, 0.4558139534883721, 5.678081153837623, 0.26014984735445634
refl:, 0.2170602220836629, 0.4505747126436782, 5.612605058127373, 0.25893548643505515
refl:, 0.2170602220836629, 0.4454545454545454, 5.5486241597837695, 0.2576951510120501
refl:, 0.2170602220836629, 0.44044943820224725, 5.486087742772728, 0.2564288095400968
refl:, 0.2170602220836629, 0.43555555555555553, 5.424947362519055, 0.2551382775804875
refl:, 0.2170602220836629, 0.4307692307692308, 5.365156719961124, 0.25382296989852066
refl:, 0.2170602220836629, 0.4260869565217391, 5.306671543905553, 0.25248068938520546
refl:, 0.2170602220836629, 0.421505376344086, 5.249449481049872, 0.2511120329000034
refl:, 0.2170602220836629, 0.41702127659574467, 5.19344999309547, 0.2497191778959394
refl:, 0.2170602220836629, 0.4126315789473684, 5.138634260422533, 0.2483012320567707
refl:, 0.2170602220836629, 0.4083333333333333, 5.08496509184317, 0.2468560224651321
refl:, 0.2170602220836629, 0.4041237113402062, 5.032406839989342, 0.24538435149961998
refl:, 0.2170602220836629, 0.4, 4.980925321928872, 0.2438873823711191
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00942492 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.24537918139687384 / 0.24537918139687384 = 1.0
field decay(t = 100.01): 1.2755953357084837e-13 / 0.24537918139687384 = 5.198466016745522e-13
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000109911 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.015625 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.24537918161848085 / 0.24537918161848085 = 1.0
field decay(t = 100.01): 2.2796495621609012e-11 / 0.24537918161848085 = 9.290313657111033e-11
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.3235238063781509, 0.8, 14.999999999999998, 0.28256373042287475
refl:, 0.3235238063781509, 0.784, 14.693171512000124, 0.28247093802487827
refl:, 0.3235238063781509, 0.7686274509803922, 14.398780921441814, 0.28233355058613946
refl:, 0.3235238063781509, 0.7538461538461539, 14.116078899389818, 0.2821545309608155
refl:, 0.3235238063781509, 0.739622641509434, 13.844375746673084, 0.2819358770069733
refl:, 0.3235238063781509, 0.7259259259259259, 13.583035518835887, 0.2816776835689441
refl:, 0.3235238063781509, 0.7127272727272727, 13.331470838933798, 0.28138133257604653
refl:, 0.3235238063781509, 0.7, 13.089138305160036, 0.281049646363028
refl:, 0.3235238063781509, 0.6877192982456141, 12.855534414514684, 0.28068351331308133
refl:, 0.3235238063781509, 0.6758620689655173, 12.630191935533823, 0.28028281405469785
refl:, 0.3235238063781509, 0.664406779661017, 12.412676672931594, 0.2798495314094937
refl:, 0.3235238063781509, 0.6533333333333333, 12.202584575236058, 0.27938611173524625
refl:, 0.3235238063781509, 0.6426229508196721, 11.999539143408532, 0.2788927304404999
refl:, 0.3235238063781509, 0.632258064516129, 11.803189104258525, 0.27836932361278227
refl:, 0.3235238063781509, 0.6222222222222222, 11.613206317390016, 0.27781781071798484
refl:, 0.3235238063781509, 0.6124999999999999, 11.429283888592414, 0.27723982281143944
refl:, 0.3235238063781509, 0.6030769230769231, 11.25113446614539, 0.27663483656101373
refl:, 0.3235238063781509, 0.593939393939394, 11.078488699542484, 0.2760025164435567
refl:, 0.3235238063781509, 0.5850746268656717, 10.91109384273803, 0.27534443882671783
refl:, 0.3235238063781509, 0.5764705882352942, 10.748712486253877, 0.2746616477877146
refl:, 0.3235238063781509, 0.5681159420289855, 10.591121404404543, 0.2739530013321228
refl:, 0.3235238063781509, 0.56, 10.438110505558328, 0.27321798287921667
refl:, 0.3235238063781509, 0.552112676056338, 10.289481874787974, 0.2724582796019277
refl:, 0.3235238063781509, 0.5444444444444444, 10.145048899510067, 0.27167450266463894
refl:, 0.3235238063781509, 0.536986301369863, 10.004635469795673, 0.2708649570485523
refl:, 0.3235238063781509, 0.5297297297297298, 9.868075245978739, 0.27002944005333146
refl:, 0.3235238063781509, 0.5226666666666667, 9.735210987013529, 0.2691698987799361
refl:, 0.3235238063781509, 0.5157894736842105, 9.60589393375409, 0.26828628327229254
refl:, 0.3235238063781509, 0.509090909090909, 9.479983241961918, 0.2673766390145325
refl:, 0.3235238063781509, 0.5025641025641026, 9.3573454604044, 0.266441343276572
refl:, 0.3235238063781509, 0.4962025316455696, 9.237854049896542, 0.2654822435375998
refl:, 0.3235238063781509, 0.49, 9.121388939570695, 0.26449858196569564
refl:, 0.3235238063781509, 0.4839506172839506, 9.00783611704105, 0.2634884799544352
refl:, 0.3235238063781509, 0.47804878048780486, 8.897087249467761, 0.26245270185974406
refl:, 0.3235238063781509, 0.47228915662650606, 8.789039332825531, 0.26139274110511584
refl:, 0.3235238063781509, 0.4666666666666667, 8.683594366947904, 0.26030735036150837
refl:, 0.3235238063781509, 0.4611764705882353, 8.5806590541555, 0.2591947457863499
refl:, 0.3235238063781509, 0.4558139534883721, 8.480144519487721, 0.25805589551088276
refl:, 0.3235238063781509, 0.4505747126436782, 8.381966050745921, 0.256892047194308
refl:, 0.3235238063781509, 0.4454545454545454, 8.286042856724524, 0.2557015480946698
refl:, 0.3235238063781509, 0.44044943820224725, 8.192297842157469, 0.2544827165503608
refl:, 0.3235238063781509, 0.43555555555555553, 8.100657398042404, 0.25323697315876975
refl:, 0.3235238063781509, 0.4307692307692308, 8.011051206126568, 0.25196549708688976
refl:, 0.3235238063781509, 0.4260869565217391, 7.923412056447124, 0.2506663282693837
refl:, 0.3235238063781509, 0.421505376344086, 7.837675676917115, 0.2493383700330171
refl:, 0.3235238063781509, 0.41702127659574467, 7.753780574036344, 0.24798388324916928
refl:, 0.3235238063781509, 0.4126315789473684, 7.671667883886533, 0.24660386238549814
refl:, 0.3235238063781509, 0.4083333333333333, 7.591281232641979, 0.2451961050843521
refl:, 0.3235238063781509, 0.4041237113402062, 7.512566605892175, 0.2437600099079589
refl:, 0.3235238063781509, 0.4, 7.435472226131853, 0.24229747168145319
-----------
Initializing structure...
time for choose_chunkdivision = 0.000112772 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.007622 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.23946072431081186 / 0.23946072431081186 = 1.0
field decay(t = 100.01): 2.143367304660103e-13 / 0.23946072431081186 = 8.950809410724429e-13
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000111818 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0173719 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.23946072470582727 / 0.23946072470582727 = 1.0
field decay(t = 100.01): 2.2924410648414684e-11 / 0.23946072470582727 = 9.573348897434795e-11
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.4275251791570859, 0.8, 20.0, 0.27287026974445927
refl:, 0.4275251791570859, 0.784, 19.583468236198428, 0.2732024101218738
refl:, 0.4275251791570859, 0.7686274509803922, 19.184283570762837, 0.2734622444200681
refl:, 0.4275251791570859, 0.7538461538461539, 18.80136282780684, 0.27365329059595683
refl:, 0.4275251791570859, 0.739622641509434, 18.433712921276232, 0.27378076185161915
refl:, 0.4275251791570859, 0.7259259259259259, 18.080421505473552, 0.27384851240423785
refl:, 0.4275251791570859, 0.7127272727272727, 17.74064878668832, 0.2738584846379507
refl:, 0.4275251791570859, 0.7, 17.413620328364388, 0.27381376974644933
refl:, 0.4275251791570859, 0.6877192982456141, 17.098620709730763, 0.27371850538265774
refl:, 0.4275251791570859, 0.6758620689655173, 16.794987920274295, 0.2735750966910372
refl:, 0.4275251791570859, 0.664406779661017, 16.50210839086207, 0.2733847949229058
refl:, 0.4275251791570859, 0.6533333333333333, 16.21941257752279, 0.2731503266875855
refl:, 0.4275251791570859, 0.6426229508196721, 15.946371026493122, 0.2728749017452174
refl:, 0.4275251791570859, 0.632258064516129, 15.682490859619808, 0.2725596258354739
refl:, 0.4275251791570859, 0.6222222222222222, 15.427312627971409, 0.2722049153191827
refl:, 0.4275251791570859, 0.6124999999999999, 15.18040748886694, 0.2718130795196188
refl:, 0.4275251791570859, 0.6030769230769231, 14.941374667722823, 0.2713863599041548
refl:, 0.4275251791570859, 0.593939393939394, 14.709839171355561, 0.2709245158308668
refl:, 0.4275251791570859, 0.5850746268656717, 14.485449723819883, 0.2704275378957415
refl:, 0.4275251791570859, 0.5764705882352942, 14.267876899642369, 0.26989771202120866
refl:, 0.4275251791570859, 0.5681159420289855, 14.056811432538773, 0.26933628796739983
refl:, 0.4275251791570859, 0.56, 13.851962680467771, 0.26874214027712073
refl:, 0.4275251791570859, 0.552112676056338, 13.653057230248155, 0.2681155761222093
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refl:, 0.4275251791570859, 0.536986301369863, 13.272061215531336, 0.2667723151469476
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refl:, 0.4275251791570859, 0.509090909090909, 12.570995568032437, 0.2637242645202348
refl:, 0.4275251791570859, 0.5025641025641026, 12.407244014521105, 0.2628885752055156
refl:, 0.4275251791570859, 0.4962025316455696, 12.247737102692609, 0.26202377900308255
refl:, 0.4275251791570859, 0.49, 12.092310629857906, 0.2611315306153532
refl:, 0.4275251791570859, 0.4839506172839506, 11.94080881933422, 0.2602107728685866
refl:, 0.4275251791570859, 0.47804878048780486, 11.793083782798943, 0.25926014291141586
refl:, 0.4275251791570859, 0.47228915662650606, 11.648995023590732, 0.25828106391345235
refl:, 0.4275251791570859, 0.4666666666666667, 11.508408977339421, 0.25727477704208235
refl:, 0.4275251791570859, 0.4611764705882353, 11.37119858666983, 0.2562395153461572
refl:, 0.4275251791570859, 0.4558139534883721, 11.23724290704701, 0.2551740956437644
refl:, 0.4275251791570859, 0.4505747126436782, 11.106426741117268, 0.2540803028372474
refl:, 0.4275251791570859, 0.4454545454545454, 10.978640299154753, 0.25295873317085843
refl:, 0.4275251791570859, 0.44044943820224725, 10.853778883451254, 0.2518070732573948
refl:, 0.4275251791570859, 0.43555555555555553, 10.731742594690267, 0.2506247305646683
refl:, 0.4275251791570859, 0.4307692307692308, 10.61243605852877, 0.249413825082604
refl:, 0.4275251791570859, 0.4260869565217391, 10.495768170772996, 0.2481743775271508
refl:, 0.4275251791570859, 0.421505376344086, 10.381651859681224, 0.24690419443990608
refl:, 0.4275251791570859, 0.41702127659574467, 10.270003864057921, 0.2456037441531416
refl:, 0.4275251791570859, 0.4126315789473684, 10.160744525922071, 0.24427554305470142
refl:, 0.4275251791570859, 0.4083333333333333, 10.053797596639106, 0.2429193465329389
refl:, 0.4275251791570859, 0.4041237113402062, 9.949090055502005, 0.24153322642643202
refl:, 0.4275251791570859, 0.4, 9.846551939834079, 0.2401180039660742
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00934601 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.23217567515545764 / 0.23217567515545764 = 1.0
field decay(t = 100.01): 3.1895846890533654e-13 / 0.23217567515545764 = 1.3737807317315728e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.016118 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.23217567572617967 / 0.23217567572617967 = 1.0
field decay(t = 100.01): 2.511386584143695e-11 / 0.23217567572617967 = 1.0816751480484724e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.5282728271758743, 0.8, 25.0, 0.2601481976279196
refl:, 0.5282728271758743, 0.784, 24.46679999189225, 0.2610696372423531
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refl:, 0.5282728271758743, 0.6877192982456141, 21.303209386217617, 0.26473707694833154
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refl:, 0.5282728271758743, 0.5025641025641026, 15.396127712651408, 0.25840617419006323
refl:, 0.5282728271758743, 0.4962025316455696, 15.196505081970068, 0.2576643632602327
refl:, 0.5282728271758743, 0.49, 15.002054761894165, 0.2568889467859571
refl:, 0.5282728271758743, 0.4839506172839506, 14.81257590751694, 0.2560818324629057
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refl:, 0.5282728271758743, 0.47228915662650606, 14.44778048381156, 0.25436772779199046
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refl:, 0.5282728271758743, 0.4505747126436782, 13.770084777392734, 0.25055182001671567
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refl:, 0.5282728271758743, 0.44044943820224725, 13.454757018141454, 0.24845117408859577
refl:, 0.5282728271758743, 0.43555555555555553, 13.30249792861589, 0.24735169966979012
refl:, 0.5282728271758743, 0.4307692307692308, 13.153677679016674, 0.2462187296769865
refl:, 0.5282728271758743, 0.4260869565217391, 13.008180017272103, 0.24505436171970374
refl:, 0.5282728271758743, 0.421505376344086, 12.865893919575512, 0.24385825418409707
refl:, 0.5282728271758743, 0.41702127659574467, 12.726713297162874, 0.2426284381212972
refl:, 0.5282728271758743, 0.4126315789473684, 12.590536722774571, 0.24136614460408662
refl:, 0.5282728271758743, 0.4083333333333333, 12.457267175263851, 0.24007405600657153
refl:, 0.5282728271758743, 0.4041237113402062, 12.326811800951434, 0.238751417728497
refl:, 0.5282728271758743, 0.4, 12.199081690448809, 0.2373967326334257
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108004 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00868416 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.22375100718842 / 0.22375100718842 = 1.0
field decay(t = 100.01): 4.4054832270861915e-13 / 0.22375100718842 = 1.9689221883038714e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0171471 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.22375100783149995 / 0.22375100783149995 = 1.0
field decay(t = 100.01): 2.604590852088861e-11 / 0.22375100783149995 = 1.1640577074183724e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.6249999999999999, 0.8, 29.999999999999993, 0.2442050337697129
refl:, 0.6249999999999999, 0.784, 29.34058157502373, 0.24592026654412946
refl:, 0.6249999999999999, 0.7686274509803922, 28.711017527148794, 0.2474593095717218
refl:, 0.6249999999999999, 0.7538461538461539, 28.10922128260952, 0.24883736533494075
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refl:, 0.6249999999999999, 0.7259259259259259, 26.98155921981659, 0.25116546178265714
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refl:, 0.6249999999999999, 0.7, 25.944479772370002, 0.2529918131418104
refl:, 0.6249999999999999, 0.6877192982456141, 25.45642688540588, 0.2537410511682661
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refl:, 0.6249999999999999, 0.6426229508196721, 23.680701877992792, 0.25580383669879514
refl:, 0.6249999999999999, 0.632258064516129, 23.276033704033082, 0.2561140687592272
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refl:, 0.6249999999999999, 0.6124999999999999, 22.508004555237044, 0.2565208309064006
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refl:, 0.6249999999999999, 0.593939393939394, 21.79039137167391, 0.25666334314703
refl:, 0.6249999999999999, 0.5850746268656717, 21.448922527676533, 0.256643740595326
refl:, 0.6249999999999999, 0.5764705882352942, 21.118259889941786, 0.25656730578199227
refl:, 0.6249999999999999, 0.5681159420289855, 20.797885581592283, 0.25643465337781024
refl:, 0.6249999999999999, 0.56, 20.487315114722662, 0.256248873599916
refl:, 0.6249999999999999, 0.552112676056338, 20.186094678183196, 0.25601329709669296
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refl:, 0.6249999999999999, 0.536986301369863, 19.610027594036424, 0.255394616552182
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refl:, 0.6249999999999999, 0.5226666666666667, 19.066580100655866, 0.25459252830565576
refl:, 0.6249999999999999, 0.5157894736842105, 18.806217577124535, 0.25412542518907427
refl:, 0.6249999999999999, 0.509090909090909, 18.553004535020655, 0.2536152551480315
refl:, 0.6249999999999999, 0.5025641025641026, 18.306644915884704, 0.2530647648651237
refl:, 0.6249999999999999, 0.4962025316455696, 18.066859089603533, 0.25247451149799194
refl:, 0.6249999999999999, 0.49, 17.833382709813034, 0.251843602956665
refl:, 0.6249999999999999, 0.4839506172839506, 17.605965665348197, 0.25117351956545597
refl:, 0.6249999999999999, 0.47804878048780486, 17.38437111831227, 0.2504665488589744
refl:, 0.6249999999999999, 0.47228915662650606, 17.168374620396104, 0.2497220477831976
refl:, 0.6249999999999999, 0.4666666666666667, 16.957763300004142, 0.24893902021832587
refl:, 0.6249999999999999, 0.4611764705882353, 16.752335113553887, 0.24811948817045582
refl:, 0.6249999999999999, 0.4558139534883721, 16.551898155026578, 0.24726486187036864
refl:, 0.6249999999999999, 0.4505747126436782, 16.35627001847215, 0.24637335126615545
refl:, 0.6249999999999999, 0.4454545454545454, 16.165277208722518, 0.24544445758208924
refl:, 0.6249999999999999, 0.44044943820224725, 15.978754596053776, 0.24448044797494067
refl:, 0.6249999999999999, 0.43555555555555553, 15.796544910968182, 0.24348141406546195
refl:, 0.6249999999999999, 0.4307692307692308, 15.618498275648548, 0.24244508607372425
refl:, 0.6249999999999999, 0.4260869565217391, 15.44447176897603, 0.24137187009594935
refl:, 0.6249999999999999, 0.421505376344086, 15.274329022304034, 0.2402639528246127
refl:, 0.6249999999999999, 0.41702127659574467, 15.107939843449019, 0.23912065251888115
refl:, 0.6249999999999999, 0.4126315789473684, 14.94517986659885, 0.23794038016947253
refl:, 0.6249999999999999, 0.4083333333333333, 14.78593022605342, 0.23672496742401775
refl:, 0.6249999999999999, 0.4041237113402062, 14.630077251904048, 0.23547697979370008
refl:, 0.6249999999999999, 0.4, 14.477512185929921, 0.23419574038931623
-----------
Initializing structure...
time for choose_chunkdivision = 0.000112057 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00802183 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.2144470639002981 / 0.2144470639002981 = 1.0
field decay(t = 100.01): 5.749510870152026e-13 / 0.2144470639002981 = 2.6810863089387505e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.016397 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.21444706445458073 / 0.21444706445458073 = 1.0
field decay(t = 100.01): 2.737725032991902e-11 / 0.21444706445458073 = 1.276643744205575e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.7169705454388076, 0.8, 35.0, 0.22482605012853205
refl:, 0.7169705454388076, 0.784, 34.201491482224874, 0.2275879297659293
refl:, 0.7169705454388076, 0.7686274509803922, 33.4413597291606, 0.2300861771421993
refl:, 0.7169705454388076, 0.7538461538461539, 32.71669424141867, 0.23234663839124975
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refl:, 0.7169705454388076, 0.7, 30.12441698853809, 0.2394088473062314
refl:, 0.7169705454388076, 0.6877192982456141, 29.542859352190995, 0.24075882698160853
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refl:, 0.7169705454388076, 0.664406779661017, 28.447942424882076, 0.24305087670480616
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refl:, 0.7169705454388076, 0.4558139534883721, 19.07497712952083, 0.2423917032614313
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refl:, 0.7169705454388076, 0.44044943820224725, 18.408468109247096, 0.23998068018388435
refl:, 0.7169705454388076, 0.43555555555555553, 18.196718136035763, 0.23909605307915388
refl:, 0.7169705454388076, 0.4307692307692308, 17.98987056333767, 0.23817255818097147
refl:, 0.7169705454388076, 0.4260869565217391, 17.787754068005896, 0.23720797538105634
refl:, 0.7169705454388076, 0.421505376344086, 17.590205358285754, 0.236202366418755
refl:, 0.7169705454388076, 0.41702127659574467, 17.39706870053973, 0.23515820136339463
refl:, 0.7169705454388076, 0.4126315789473684, 17.20819547960629, 0.2340750107196232
refl:, 0.7169705454388076, 0.4083333333333333, 17.02344378999232, 0.2329510888033509
refl:, 0.7169705454388076, 0.4041237113402062, 16.842678055366356, 0.23178864386805378
refl:, 0.7169705454388076, 0.4, 16.665768674058118, 0.2305906700422077
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00882411 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.20454876789491885 / 0.20454876789491885 = 1.0
field decay(t = 100.01): 7.178635175771892e-13 / 0.20454876789491885 = 3.509498125874663e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108004 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.018625 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.20454876813558592 / 0.20454876813558592 = 1.0
field decay(t = 100.01): 2.8174572450318613e-11 / 0.20454876813558592 = 1.3774012284270024e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.8034845121081741, 0.8, 39.99999999999999, 0.20179462162966672
refl:, 0.8034845121081741, 0.784, 39.04509528455022, 0.2059250719323383
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refl:, 0.8034845121081741, 0.44044943820224725, 20.725693916468796, 0.23505540516189377
refl:, 0.8034845121081741, 0.43555555555555553, 20.48499963280006, 0.23429986728741037
refl:, 0.8034845121081741, 0.4307692307692308, 20.249960190511292, 0.23350021386178307
refl:, 0.8034845121081741, 0.4260869565217391, 20.020374012481035, 0.23265749904183425
refl:, 0.8034845121081741, 0.421505376344086, 19.79604920948226, 0.23176986721335244
refl:, 0.8034845121081741, 0.41702127659574467, 19.576802992091316, 0.23083693098169072
refl:, 0.8034845121081741, 0.4126315789473684, 19.362461125837058, 0.22986107450928206
refl:, 0.8034845121081741, 0.4083333333333333, 19.15285742585141, 0.2288423958877941
refl:, 0.8034845121081741, 0.4041237113402062, 18.9478332876545, 0.22777913143869027
refl:, 0.8034845121081741, 0.4, 18.747237251037504, 0.22667336344348024
-----------
Initializing structure...
time for choose_chunkdivision = 0.000111103 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.006598 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.1943564114319847 / 0.1943564114319847 = 1.0
field decay(t = 100.01): 8.613369505850488e-13 / 0.1943564114319847 = 4.431739319731548e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108004 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0163691 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.1943564112167818 / 0.1943564112167818 = 1.0
field decay(t = 100.01): 2.929219089217826e-11 / 0.1943564112167818 = 1.5071378766870859e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.8838834764831843, 0.8, 44.99999999999999, 0.1749506546010766
refl:, 0.8838834764831843, 0.784, 43.865246854678944, 0.18084614262894314
refl:, 0.8838834764831843, 0.7686274509803922, 42.79498686880298, 0.18616490888473136
refl:, 0.8838834764831843, 0.7538461538461539, 41.78306957363623, 0.1909834896778329
refl:, 0.8838834764831843, 0.739622641509434, 40.82419653278361, 0.1953532231998348
refl:, 0.8838834764831843, 0.7259259259259259, 39.913765803587594, 0.19932045676242707
refl:, 0.8838834764831843, 0.7127272727272727, 39.047751315763335, 0.20293092176670602
refl:, 0.8838834764831843, 0.7, 38.2226079814105, 0.20621465898807328
refl:, 0.8838834764831843, 0.6877192982456141, 37.435196089128915, 0.20920558346668153
refl:, 0.8838834764831843, 0.6758620689655173, 36.682720369951866, 0.21192936258982145
refl:, 0.8838834764831843, 0.664406779661017, 35.962680378531154, 0.2144091185242741
refl:, 0.8838834764831843, 0.6533333333333333, 35.272829708778914, 0.21666666414632094
refl:, 0.8838834764831843, 0.6426229508196721, 34.61114218453038, 0.2187182335956619
refl:, 0.8838834764831843, 0.632258064516129, 33.975783613579615, 0.22058228827610923
refl:, 0.8838834764831843, 0.6222222222222222, 33.36508802077569, 0.22227211810191635
refl:, 0.8838834764831843, 0.6124999999999999, 32.77753751829758, 0.22379917822267162
refl:, 0.8838834764831843, 0.6030769230769231, 32.21174515294742, 0.225178014297656
refl:, 0.8838834764831843, 0.593939393939394, 31.666440208036935, 0.22641701701757366
refl:, 0.8838834764831843, 0.5850746268656717, 31.14045554291693, 0.22752429105750807
refl:, 0.8838834764831843, 0.5764705882352942, 30.6327166347442, 0.22851103000945724
refl:, 0.8838834764831843, 0.5681159420289855, 30.142232050688204, 0.2293833309292736
refl:, 0.8838834764831843, 0.56, 29.66808512880701, 0.23014665030198314
refl:, 0.8838834764831843, 0.552112676056338, 29.20942668547734, 0.2308091072410071
refl:, 0.8838834764831843, 0.5444444444444444, 28.765468598924116, 0.23137604508998047
refl:, 0.8838834764831843, 0.536986301369863, 28.33547814384704, 0.23185120425684555
refl:, 0.8838834764831843, 0.5297297297297298, 27.91877297273401, 0.23223967284122596
refl:, 0.8838834764831843, 0.5226666666666667, 27.514716656212954, 0.23254649427327514
refl:, 0.8838834764831843, 0.5157894736842105, 27.12271470851516, 0.23277497605931805
refl:, 0.8838834764831843, 0.509090909090909, 26.742211035417114, 0.2329274877105852
refl:, 0.8838834764831843, 0.5025641025641026, 26.372684751370738, 0.23300817835325607
refl:, 0.8838834764831843, 0.4962025316455696, 26.013647320299032, 0.23302096475520206
refl:, 0.8838834764831843, 0.49, 25.66463998102006, 0.23296661309174865
refl:, 0.8838834764831843, 0.4839506172839506, 25.32523142370283, 0.2328473819749458
refl:, 0.8838834764831843, 0.47804878048780486, 24.99501568834094, 0.23266777547883646
refl:, 0.8838834764831843, 0.47228915662650606, 24.673610260104642, 0.2324286704369094
refl:, 0.8838834764831843, 0.4666666666666667, 24.360654339720863, 0.23213016162250638
refl:, 0.8838834764831843, 0.4611764705882353, 24.055807269832574, 0.23177609164136181
refl:, 0.8838834764831843, 0.4558139534883721, 23.75874710068368, 0.2313686559958002
refl:, 0.8838834764831843, 0.4505747126436782, 23.46916928052956, 0.23090689658521463
refl:, 0.8838834764831843, 0.4454545454545454, 23.18678545794031, 0.23039248392782377
refl:, 0.8838834764831843, 0.44044943820224725, 22.911322384688706, 0.22982847953509086
refl:, 0.8838834764831843, 0.43555555555555553, 22.64252090923418, 0.22921468760037644
refl:, 0.8838834764831843, 0.4307692307692308, 22.380135051959574, 0.2285503145110825
refl:, 0.8838834764831843, 0.4260869565217391, 22.123931154313652, 0.22783728199610298
refl:, 0.8838834764831843, 0.421505376344086, 21.873687094881706, 0.22707701516938034
refl:, 0.8838834764831843, 0.41702127659574467, 21.629191566166806, 0.226267933168201
refl:, 0.8838834764831843, 0.4126315789473684, 21.390243406530644, 0.22540929123705422
refl:, 0.8838834764831843, 0.4083333333333333, 21.156650982328358, 0.22450324859888127
refl:, 0.8838834764831843, 0.4041237113402062, 20.928231615787418, 0.2235503997974889
refl:, 0.8838834764831843, 0.4, 20.704811054635428, 0.22254911459777174
-----------
Initializing structure...
time for choose_chunkdivision = 0.000109911 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.006423 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.18417632037527257 / 0.18417632037527257 = 1.0
field decay(t = 100.01): 1.0178427595748204e-12 / 0.18417632037527257 = 5.5264583280895835e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0184629 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.18417631975521828 / 0.18417631975521828 = 1.0
field decay(t = 100.01): 2.8713012611847576e-11 / 0.18417631975521828 = 1.5589958931750262e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 0.9575555538987225, 0.8, 50.0, 0.14429067301668
refl:, 0.9575555538987225, 0.784, 48.6530933185261, 0.15241249489296654
refl:, 0.9575555538987225, 0.7686274509803922, 47.39207738436693, 0.15970237410745958
refl:, 0.9575555538987225, 0.7538461538461539, 46.207396358038395, 0.16628917742963503
refl:, 0.9575555538987225, 0.739622641509434, 45.091066324150106, 0.1722363131532337
refl:, 0.9575555538987225, 0.7259259259259259, 44.036334278275795, 0.1776288135399773
refl:, 0.9575555538987225, 0.7127272727272727, 43.037427456538545, 0.1825236470768417
refl:, 0.9575555538987225, 0.7, 42.089365210987516, 0.1869718164862598
refl:, 0.9575555538987225, 0.6877192982456141, 41.18781524255363, 0.19102552097133876
refl:, 0.9575555538987225, 0.6758620689655173, 40.32898196453324, 0.19471651743120957
refl:, 0.9575555538987225, 0.664406779661017, 39.50951857909891, 0.1980846376246996
refl:, 0.9575555538987225, 0.6533333333333333, 38.726456948394606, 0.20115681830261414
refl:, 0.9575555538987225, 0.6426229508196721, 37.97715101972185, 0.20395988101926588
refl:, 0.9575555538987225, 0.632258064516129, 37.25923071465613, 0.20651807398114963
refl:, 0.9575555538987225, 0.6222222222222222, 36.57056399547784, 0.20884957043569513
refl:, 0.9575555538987225, 0.6124999999999999, 35.909225393217994, 0.21097550520798009
refl:, 0.9575555538987225, 0.6030769230769231, 35.273469693564564, 0.21290924565401623
refl:, 0.9575555538987225, 0.593939393939394, 34.6617097783444, 0.214665416754943
refl:, 0.9575555538987225, 0.5850746268656717, 34.07249784378941, 0.2162593463941121
refl:, 0.9575555538987225, 0.5764705882352942, 33.504509384470694, 0.21769885837479563
refl:, 0.9575555538987225, 0.5681159420289855, 32.95652945897567, 0.2189956192414337
refl:, 0.9575555538987225, 0.56, 32.42744085087325, 0.22016058268759847
refl:, 0.9575555538987225, 0.552112676056338, 31.91621381391884, 0.22119898455404
refl:, 0.9575555538987225, 0.5444444444444444, 31.42189714930561, 0.22211935917204448
refl:, 0.9575555538987225, 0.536986301369863, 30.943610409083956, 0.2229298821236265
refl:, 0.9575555538987225, 0.5297297297297298, 30.480537056602333, 0.22363493657078803
refl:, 0.9575555538987225, 0.5226666666666667, 30.031918444163345, 0.2242400133418431
refl:, 0.9575555538987225, 0.5157894736842105, 29.597048491686717, 0.22475115535497284
refl:, 0.9575555538987225, 0.509090909090909, 29.17526896927061, 0.2251729335780506
refl:, 0.9575555538987225, 0.5025641025641026, 28.76596530209651, 0.22550858491249842
refl:, 0.9575555538987225, 0.4962025316455696, 28.36856282886028, 0.22576196217784258
refl:, 0.9575555538987225, 0.49, 27.982523455399697, 0.22593807040959396
refl:, 0.9575555538987225, 0.4839506172839506, 27.60734265386835, 0.22603917633476883
refl:, 0.9575555538987225, 0.47804878048780486, 27.24254676502359, 0.22606684493527063
refl:, 0.9575555538987225, 0.47228915662650606, 26.88769056722596, 0.22602594884033364
refl:, 0.9575555538987225, 0.4666666666666667, 26.54235508080712, 0.22591913511748662
refl:, 0.9575555538987225, 0.4611764705882353, 26.206145580726076, 0.2257461894573964
refl:, 0.9575555538987225, 0.4558139534883721, 25.878689794039474, 0.2255106337747593
refl:, 0.9575555538987225, 0.4505747126436782, 25.55963626177365, 0.22521611643853037
refl:, 0.9575555538987225, 0.4454545454545454, 25.248652847395146, 0.2248621048576318
refl:, 0.9575555538987225, 0.44044943820224725, 24.945425376307522, 0.2244497571914091
refl:, 0.9575555538987225, 0.43555555555555553, 24.64965639271632, 0.22398274531115286
refl:, 0.9575555538987225, 0.4307692307692308, 24.361064021851533, 0.22346171326862457
refl:, 0.9575555538987225, 0.4260869565217391, 24.079380926958596, 0.22288585592315466
refl:, 0.9575555538987225, 0.421505376344086, 23.804353351700417, 0.22225690920257898
refl:, 0.9575555538987225, 0.41702127659574467, 23.535740239681235, 0.22157652716566317
refl:, 0.9575555538987225, 0.4126315789473684, 23.27331242373393, 0.22084351574148542
refl:, 0.9575555538987225, 0.4083333333333333, 23.016851878423925, 0.220057130518136
refl:, 0.9575555538987225, 0.4041237113402062, 22.76615102993319, 0.21921919579654955
refl:, 0.9575555538987225, 0.4, 22.521012118111, 0.21832995493951468
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108004 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00824594 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.17431196343224772 / 0.17431196343224772 = 1.0
field decay(t = 100.01): 1.226599619152291e-12 / 0.17431196343224772 = 7.0368068547919865e-12
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0162461 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.17431196264184795 / 0.17431196264184795 = 1.0
field decay(t = 100.01): 2.9177363356244976e-11 / 0.17431196264184795 = 1.6738589201817764e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.0239400553612397, 0.8, 54.99999999999999, 0.11015750327021501
refl:, 1.0239400553612397, 0.784, 53.39534223243568, 0.12100519786278613
refl:, 1.0239400553612397, 0.7686274509803922, 51.90867481651075, 0.13067356321855755
refl:, 1.0239400553612397, 0.7538461538461539, 50.524208813748004, 0.1393743175816963
refl:, 1.0239400553612397, 0.739622641509434, 49.22931269112476, 0.14718461760941978
refl:, 1.0239400553612397, 0.7259259259259259, 48.013685667151286, 0.15425442212255983
refl:, 1.0239400553612397, 0.7127272727272727, 46.86879216202182, 0.16064116852684127
refl:, 1.0239400553612397, 0.7, 45.787462696319906, 0.1664466525245801
refl:, 1.0239400553612397, 0.6877192982456141, 44.7636047370949, 0.17171830451504444
refl:, 1.0239400553612397, 0.6758620689655173, 43.79198840588911, 0.17651889499651638
refl:, 1.0239400553612397, 0.664406779661017, 42.868084512177944, 0.1808955749197593
refl:, 1.0239400553612397, 0.6533333333333333, 41.98794000564178, 0.18488590864155194
refl:, 1.0239400553612397, 0.6426229508196721, 41.148080731197126, 0.1885334768453189
refl:, 1.0239400553612397, 0.632258064516129, 40.345434464399176, 0.19186399028554912
refl:, 1.0239400553612397, 0.6222222222222222, 39.57726925315509, 0.1949105801621511
refl:, 1.0239400553612397, 0.6124999999999999, 38.841143478370526, 0.19769436000574783
refl:, 1.0239400553612397, 0.6030769230769231, 38.13486500383326, 0.20023789123980396
refl:, 1.0239400553612397, 0.593939393939394, 37.45645745905701, 0.2025624060128163
refl:, 1.0239400553612397, 0.5850746268656717, 36.80413218014341, 0.204680856177325
refl:, 1.0239400553612397, 0.5764705882352942, 36.176264682924305, 0.2066128346051995
refl:, 1.0239400553612397, 0.5681159420289855, 35.57137479946729, 0.20837010840175924
refl:, 1.0239400553612397, 0.56, 34.98810980028866, 0.2099625172331732
refl:, 1.0239400553612397, 0.552112676056338, 34.42522996870841, 0.21140487263605512
refl:, 1.0239400553612397, 0.5444444444444444, 33.881596203503065, 0.2127045522560479
refl:, 1.0239400553612397, 0.536986301369863, 33.35615931039313, 0.21386953098052403
refl:, 1.0239400553612397, 0.5297297297297298, 32.847950708397136, 0.21491013773280657
refl:, 1.0239400553612397, 0.5226666666666667, 32.3560743283589, 0.21583212552616557
refl:, 1.0239400553612397, 0.5157894736842105, 31.87969952142079, 0.2166414381263308
refl:, 1.0239400553612397, 0.509090909090909, 31.41805482739263, 0.21734485598596862
refl:, 1.0239400553612397, 0.5025641025641026, 30.97042247873359, 0.2179480717640861
refl:, 1.0239400553612397, 0.4962025316455696, 30.536133536635912, 0.21845549976557374
refl:, 1.0239400553612397, 0.49, 30.114563572550164, 0.21887075023784372
refl:, 1.0239400553612397, 0.4839506172839506, 29.70512882224086, 0.21919941164026552
refl:, 1.0239400553612397, 0.47804878048780486, 29.307282750744406, 0.21944546389616373
refl:, 1.0239400553612397, 0.47228915662650606, 28.920512975908146, 0.21961022544356806
refl:, 1.0239400553612397, 0.4666666666666667, 28.544338505905493, 0.2196984674330614
refl:, 1.0239400553612397, 0.4611764705882353, 28.178307252549438, 0.21971428386147993
refl:, 1.0239400553612397, 0.4558139534883721, 27.821993787605123, 0.21965764862748693
refl:, 1.0239400553612397, 0.4505747126436782, 27.474997313821564, 0.21953193965864698
refl:, 1.0239400553612397, 0.4454545454545454, 27.13693982621647, 0.21934178652625613
refl:, 1.0239400553612397, 0.44044943820224725, 26.80746444237855, 0.21908700093353123
refl:, 1.0239400553612397, 0.43555555555555553, 26.486233883298294, 0.21876853077786598
refl:, 1.0239400553612397, 0.4307692307692308, 26.172929088582443, 0.2183905958409472
refl:, 1.0239400553612397, 0.4260869565217391, 25.867247951913267, 0.21795488284012238
refl:, 1.0239400553612397, 0.421505376344086, 25.56890416433822, 0.21746063743615796
refl:, 1.0239400553612397, 0.41702127659574467, 25.277626154460066, 0.21690850348145124
refl:, 1.0239400553612397, 0.4126315789473684, 24.993156115881433, 0.21630059246127992
refl:, 1.0239400553612397, 0.4083333333333333, 24.715249113370163, 0.21563737630418256
refl:, 1.0239400553612397, 0.4041237113402062, 24.443672260178424, 0.2149184652144797
refl:, 1.0239400553612397, 0.4, 24.178203959791162, 0.2141434469115452
-----------
Initializing structure...
time for choose_chunkdivision = 0.000112057 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.0063448 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.16505586379118362 / 0.16505586379118362 = 1.0
field decay(t = 100.01): 1.6796657955389861e-12 / 0.16505586379118362 = 1.0176347310289891e-11
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000111818 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.020278 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.16505586311279807 / 0.16505586311279807 = 1.0
field decay(t = 100.01): 3.3223715038456985e-11 / 0.16505586311279807 = 2.0128769988468766e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.0825317547305482, 0.8, 59.99999999999999, 0.07360773441443474
refl:, 1.0825317547305482, 0.784, 58.07108488083593, 0.08756183349395384
refl:, 1.0825317547305482, 0.7686274509803922, 56.311309260669624, 0.09993186958234106
refl:, 1.0825317547305482, 0.7538461538461539, 54.69254540505164, 0.11102792920544496
refl:, 1.0825317547305482, 0.739622641509434, 53.19365179333026, 0.12095671757064261
refl:, 1.0825317547305482, 0.7259259259259259, 51.798237196004614, 0.12989111490169047
refl:, 1.0825317547305482, 0.7127272727272727, 50.49327371888257, 0.13795385843502186
refl:, 1.0825317547305482, 0.7, 49.268194122622916, 0.14525656081749277
refl:, 1.0825317547305482, 0.6877192982456141, 48.11428082873218, 0.15187584382721003
refl:, 1.0825317547305482, 0.6758620689655173, 47.024238635081495, 0.15790192109849083
refl:, 1.0825317547305482, 0.664406779661017, 45.99188753936469, 0.16337692994168027
refl:, 1.0825317547305482, 0.6533333333333333, 45.01193662107726, 0.16837576220748254
refl:, 1.0825317547305482, 0.6426229508196721, 44.07981414374115, 0.1729308563822558
refl:, 1.0825317547305482, 0.632258064516129, 43.191537588393835, 0.17709787538099556
refl:, 1.0825317547305482, 0.6222222222222222, 42.34361264736431, 0.18090702518494378
refl:, 1.0825317547305482, 0.6124999999999999, 41.53295361356457, 0.18439374819992094
refl:, 1.0825317547305482, 0.6030769230769231, 40.756819839298586, 0.1875864032458676
refl:, 1.0825317547305482, 0.593939393939394, 40.01276444425686, 0.1905057507798468
refl:, 1.0825317547305482, 0.5850746268656717, 39.298592486049785, 0.19318030905511865
refl:, 1.0825317547305482, 0.5764705882352942, 38.61232652957572, 0.1956239605857035
refl:, 1.0825317547305482, 0.5681159420289855, 37.9521780657052, 0.19785784772625742
refl:, 1.0825317547305482, 0.56, 37.31652360111115, 0.19989839276598212
refl:, 1.0825317547305482, 0.552112676056338, 36.70388451304266, 0.2017547526768604
refl:, 1.0825317547305482, 0.5444444444444444, 36.112909964600526, 0.20344360330889855
refl:, 1.0825317547305482, 0.536986301369863, 35.54236232752769, 0.20497480625666326
refl:, 1.0825317547305482, 0.5297297297297298, 34.991104674473426, 0.20635699484209216
refl:, 1.0825317547305482, 0.5226666666666667, 34.4580899908132, 0.20760151265764157
refl:, 1.0825317547305482, 0.5157894736842105, 33.94235182430718, 0.20871528450622134
refl:, 1.0825317547305482, 0.509090909090909, 33.442996144127704, 0.20970524738496094
refl:, 1.0825317547305482, 0.5025641025641026, 32.95919422270091, 0.2105783514069682
refl:, 1.0825317547305482, 0.4962025316455696, 32.4901763870572, 0.2113414215404359
refl:, 1.0825317547305482, 0.49, 32.035226512949734, 0.21200027362523924
refl:, 1.0825317547305482, 0.4839506172839506, 31.593677156370052, 0.21255807961996584
refl:, 1.0825317547305482, 0.47804878048780486, 31.164905234389202, 0.21302071809138926
refl:, 1.0825317547305482, 0.47228915662650606, 30.748328181342448, 0.21339356617448996
refl:, 1.0825317547305482, 0.4666666666666667, 30.343400517915825, 0.2136782430141135
refl:, 1.0825317547305482, 0.4611764705882353, 29.949610780196405, 0.21387969509149066
refl:, 1.0825317547305482, 0.4558139534883721, 29.566478763613983, 0.2140025648813409
refl:, 1.0825317547305482, 0.4505747126436782, 29.193553043244272, 0.21404664550288702
refl:, 1.0825317547305482, 0.4454545454545454, 28.830408737409662, 0.2140158741099825
refl:, 1.0825317547305482, 0.44044943820224725, 28.47664548610104, 0.2139163515040305
refl:, 1.0825317547305482, 0.43555555555555553, 28.131885619609587, 0.213747755347228
refl:, 1.0825317547305482, 0.4307692307692308, 27.79577249602797, 0.2135103221579689
refl:, 1.0825317547305482, 0.4260869565217391, 27.46796898905743, 0.21320790783224955
refl:, 1.0825317547305482, 0.421505376344086, 27.14815610992485, 0.2128440342182022
refl:, 1.0825317547305482, 0.41702127659574467, 26.836031749237822, 0.21242171734687695
refl:, 1.0825317547305482, 0.4126315789473684, 26.531309526343414, 0.21193780892543815
refl:, 1.0825317547305482, 0.4083333333333333, 26.23371773525153, 0.21138950860192895
refl:, 1.0825317547305482, 0.4041237113402062, 25.94299837747481, 0.21078013578978685
refl:, 1.0825317547305482, 0.4, 25.65890627325528, 0.2101171783272214
-----------
Initializing structure...
time for choose_chunkdivision = 0.000109911 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00752401 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.15668265201002152 / 0.15668265201002152 = 1.0
field decay(t = 100.01): 2.2446823295144107e-12 / 0.15668265201002152 = 1.4326297779098349e-11
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000112057 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0143809 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.1566826516265948 / 0.1566826516265948 = 1.0
field decay(t = 100.01): 3.452976998428892e-11 / 0.1566826516265948 = 2.2038030136597423e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.1328847337958123, 0.8, 64.99999999999999, 0.037170886043112084
refl:, 1.1328847337958123, 0.784, 62.645633431180784, 0.05362783985573467
refl:, 1.1328847337958123, 0.7686274509803922, 60.547811567584965, 0.06875709351287543
refl:, 1.1328847337958123, 0.7538461538461539, 58.65172469781183, 0.082354616478198
refl:, 1.1328847337958123, 0.739622641509434, 56.919780417243786, 0.09462755396270182
refl:, 1.1328847337958123, 0.7259259259259259, 55.32480276439999, 0.10557645638030469
refl:, 1.1328847337958123, 0.7127272727272727, 53.84635215217889, 0.11544950273548941
refl:, 1.1328847337958123, 0.7, 52.468573108244414, 0.1243168343725702
refl:, 1.1328847337958123, 0.6877192982456141, 51.17885777022349, 0.13235703881433808
refl:, 1.1328847337958123, 0.6758620689655173, 49.96697533403755, 0.139626360552005
refl:, 1.1328847337958123, 0.664406779661017, 48.82448244349733, 0.14625471025031767
refl:, 1.1328847337958123, 0.6533333333333333, 47.744310665402864, 0.1522788790416092
refl:, 1.1328847337958123, 0.6426229508196721, 46.720469815981424, 0.1577852862490647
refl:, 1.1328847337958123, 0.632258064516129, 45.7478295128327, 0.16280555175366354
refl:, 1.1328847337958123, 0.6222222222222222, 44.82195500406973, 0.167398621072885
refl:, 1.1328847337958123, 0.6124999999999999, 43.93898156096055, 0.17159777718924688
refl:, 1.1328847337958123, 0.6030769230769231, 43.09551684594588, 0.17544391308281032
refl:, 1.1328847337958123, 0.593939393939394, 42.288563952640665, 0.1789701508099767
refl:, 1.1328847337958123, 0.5850746268656717, 41.51545997434592, 0.18219866439447
refl:, 1.1328847337958123, 0.5764705882352942, 40.77382641078957, 0.185160771243366
refl:, 1.1328847337958123, 0.5681159420289855, 40.06152872079658, 0.18786997681737858
refl:, 1.1328847337958123, 0.56, 39.37664302675111, 0.19035022781311492
refl:, 1.1328847337958123, 0.552112676056338, 38.717428473384835, 0.19261993394590182
refl:, 1.1328847337958123, 0.5444444444444444, 38.08230410219336, 0.19469110743273724
refl:, 1.1328847337958123, 0.536986301369863, 37.4698293655767, 0.1965812755931606
refl:, 1.1328847337958123, 0.5297297297297298, 36.87868759977799, 0.19830004161335185
refl:, 1.1328847337958123, 0.5226666666666667, 36.307671922074825, 0.19985824848269654
refl:, 1.1328847337958123, 0.5157894736842105, 35.75567312877807, 0.20126711563403166
refl:, 1.1328847337958123, 0.509090909090909, 35.22166925577522, 0.20253568251243403
refl:, 1.1328847337958123, 0.5025641025641026, 34.70471652928195, 0.2036726801968963
refl:, 1.1328847337958123, 0.4962025316455696, 34.203941485939055, 0.20468320295652365
refl:, 1.1328847337958123, 0.49, 33.7185340819115, 0.20557517176695547
refl:, 1.1328847337958123, 0.4839506172839506, 33.247741642788455, 0.20635542059630924
refl:, 1.1328847337958123, 0.47804878048780486, 32.790863531764046, 0.2070277254966668
refl:, 1.1328847337958123, 0.47228915662650606, 32.347246434236666, 0.20759964094140226
refl:, 1.1328847337958123, 0.4666666666666667, 31.91628017368787, 0.20807496149136276
refl:, 1.1328847337958123, 0.4611764705882353, 31.497393987322308, 0.20845469225613245
refl:, 1.1328847337958123, 0.4558139534883721, 31.090053201105746, 0.20874562394291427
refl:, 1.1328847337958123, 0.4505747126436782, 30.693756253024553, 0.20895386380475825
refl:, 1.1328847337958123, 0.4454545454545454, 30.308032020994055, 0.20908023176898172
refl:, 1.1328847337958123, 0.44044943820224725, 29.9324374181665, 0.209125738596599
refl:, 1.1328847337958123, 0.43555555555555553, 29.5665552236732, 0.20909456295065154
refl:, 1.1328847337958123, 0.4307692307692308, 29.209992121269647, 0.20899049887482632
refl:, 1.1328847337958123, 0.4260869565217391, 28.86237692208816, 0.2088190433084917
refl:, 1.1328847337958123, 0.421505376344086, 28.523358950864424, 0.2085833129971406
refl:, 1.1328847337958123, 0.41702127659574467, 28.192606577687982, 0.2082742041204916
refl:, 1.1328847337958123, 0.4126315789473684, 27.86980587961545, 0.2078930131964556
refl:, 1.1328847337958123, 0.4083333333333333, 27.554659418441407, 0.20745662776433935
refl:, 1.1328847337958123, 0.4041237113402062, 27.246885122601544, 0.20697561960434535
refl:, 1.1328847337958123, 0.4, 26.946215262627685, 0.20643519600186538
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00959396 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.14944315649486126 / 0.14944315649486126 = 1.0
field decay(t = 100.01): 4.987937476864823e-12 / 0.14944315649486126 = 3.3376820952228335e-11
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.0218339 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.14944315644072245 / 0.14944315644072245 = 1.0
field decay(t = 100.01): 3.807851695141726e-11 / 0.14944315644072245 = 2.548026812222836e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.1746157759823854, 0.8, 70.0, 0.008715934286147569
refl:, 1.1746157759823854, 0.784, 67.05783140972835, 0.024210799209089452
refl:, 1.1746157759823854, 0.7686274509803922, 64.53417775149677, 0.04029873111181387
refl:, 1.1746157759823854, 0.7538461538461539, 62.31059707934406, 0.0555678814867085
refl:, 1.1746157759823854, 0.739622641509434, 60.31629899672389, 0.06970125775811391
refl:, 1.1746157759823854, 0.7259259259259259, 58.50481213939229, 0.08255524971343331
refl:, 1.1746157759823854, 0.7127272727272727, 56.843594941553754, 0.09413263635827869
refl:, 1.1746157759823854, 0.7, 55.30875739675561, 0.10463698983404623
refl:, 1.1746157759823854, 0.6877192982456141, 53.88211612099151, 0.11407493400247079
refl:, 1.1746157759823854, 0.6758620689655173, 52.54943143507829, 0.1226472707657511
refl:, 1.1746157759823854, 0.664406779661017, 51.29929235382265, 0.13039930819744874
refl:, 1.1746157759823854, 0.6533333333333333, 50.122379445158494, 0.13744242808130103
refl:, 1.1746157759823854, 0.6426229508196721, 49.010959419193355, 0.1438468426182844
refl:, 1.1746157759823854, 0.632258064516129, 47.958527855818005, 0.14968921112177416
refl:, 1.1746157759823854, 0.6222222222222222, 46.9595500055931, 0.1550186900782557
refl:, 1.1746157759823854, 0.6124999999999999, 46.00926848902442, 0.15990623687364083
refl:, 1.1746157759823854, 0.6030769230769231, 45.103557823882895, 0.1643748532843572
refl:, 1.1746157759823854, 0.593939393939394, 44.23881248012816, 0.16847752780425043
refl:, 1.1746157759823854, 0.5850746268656717, 43.41185942214757, 0.1722356163059057
refl:, 1.1746157759823854, 0.5764705882352942, 42.619888854495166, 0.17567897390885354
refl:, 1.1746157759823854, 0.5681159420289855, 41.860398715356425, 0.17883996497200733
refl:, 1.1746157759823854, 0.56, 41.131149701242414, 0.18173480153232927
refl:, 1.1746157759823854, 0.552112676056338, 40.430128463310105, 0.18439121641848574
refl:, 1.1746157759823854, 0.5444444444444444, 39.75551721886283, 0.18682378756973045
refl:, 1.1746157759823854, 0.536986301369863, 39.10566845306894, 0.18904674104030247
refl:, 1.1746157759823854, 0.5297297297297298, 38.479083699202135, 0.19107686788902303
refl:, 1.1746157759823854, 0.5226666666666667, 37.87439561623927, 0.19292625454975332
refl:, 1.1746157759823854, 0.5157894736842105, 37.29035275442276, 0.19460884663783543
refl:, 1.1746157759823854, 0.509090909090909, 36.72580652885898, 0.1961345571897698
refl:, 1.1746157759823854, 0.5025641025641026, 36.179700019842116, 0.1975122933988443
refl:, 1.1746157759823854, 0.4962025316455696, 35.651058294458764, 0.19875051751344916
refl:, 1.1746157759823854, 0.49, 35.138980002927255, 0.19985541870413245
refl:, 1.1746157759823854, 0.4839506172839506, 34.64263004924646, 0.20083789883449643
refl:, 1.1746157759823854, 0.47804878048780486, 34.161233172132036, 0.2017049645889793
refl:, 1.1746157759823854, 0.47228915662650606, 33.69406830116886, 0.20245751259203246
refl:, 1.1746157759823854, 0.4666666666666667, 33.24046357629389, 0.20310354230391978
refl:, 1.1746157759823854, 0.4611764705882353, 32.79979193741594, 0.2036476720462249
refl:, 1.1746157759823854, 0.4558139534883721, 32.37146720614281, 0.20409307625590972
refl:, 1.1746157759823854, 0.4505747126436782, 31.954940593960732, 0.20445096223605416
refl:, 1.1746157759823854, 0.4454545454545454, 31.549697581364857, 0.20471845410715214
refl:, 1.1746157759823854, 0.44044943820224725, 31.155255120816925, 0.20489444063169535
refl:, 1.1746157759823854, 0.43555555555555553, 30.771159123350074, 0.2049889592193817
refl:, 1.1746157759823854, 0.4307692307692308, 30.396982194426784, 0.20500542736591415
refl:, 1.1746157759823854, 0.4260869565217391, 30.032321589495837, 0.20495768982428397
refl:, 1.1746157759823854, 0.421505376344086, 29.67679736376329, 0.20483056853588974
refl:, 1.1746157759823854, 0.41702127659574467, 29.33005069412437, 0.20461216911883964
refl:, 1.1746157759823854, 0.4126315789473684, 28.991742354111988, 0.2043374679527374
refl:, 1.1746157759823854, 0.4083333333333333, 28.66155132518973, 0.20400220026620766
refl:, 1.1746157759823854, 0.4041237113402062, 28.339173529827534, 0.2036399273981529
refl:, 1.1746157759823854, 0.4, 28.024320673604695, 0.20318419566870832
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00775695 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.14355855111904026 / 0.14355855111904026 = 1.0
field decay(t = 100.01): 9.667874474337293e-12 / 0.14355855111904026 = 6.734446954901761e-11
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.017272 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.1435585513271557 / 0.1435585513271557 = 1.0
field decay(t = 100.01): 5.780725980413138e-11 / 0.1435585513271557 = 4.0267374719040156e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.2074072828613354, 0.8, 75.0, 0.002279010064127535
refl:, 1.2074072828613354, 0.784, 71.19254305121969, 0.004052585814133056
refl:, 1.2074072828613354, 0.7686274509803922, 68.13230108184366, 0.017669454881364767
refl:, 1.2074072828613354, 0.7538461538461539, 65.5329128763873, 0.03336169435169541
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refl:, 1.2074072828613354, 0.664406779661017, 53.3416232015308, 0.11670121483117171
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refl:, 1.2074072828613354, 0.5297297297297298, 39.76196420912173, 0.18502119081455226
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refl:, 1.2074072828613354, 0.5157894736842105, 38.51854903626071, 0.18904214560856375
refl:, 1.2074072828613354, 0.509090909090909, 37.928677376424204, 0.190789263829168
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refl:, 1.2074072828613354, 0.49, 36.272732803336254, 0.19509368153538312
refl:, 1.2074072828613354, 0.4839506172839506, 35.755353950220794, 0.19624859910356954
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refl:, 1.2074072828613354, 0.47228915662650606, 34.76733773550362, 0.19818701041137332
refl:, 1.2074072828613354, 0.4666666666666667, 34.295192516152845, 0.19897646054575882
refl:, 1.2074072828613354, 0.4611764705882353, 33.83670362811667, 0.19965889435875267
refl:, 1.2074072828613354, 0.4558139534883721, 33.391239589169516, 0.20023796589376308
refl:, 1.2074072828613354, 0.4505747126436782, 32.95821020943854, 0.20072106469864034
refl:, 1.2074072828613354, 0.4454545454545454, 32.537063046367535, 0.2011073384968122
refl:, 1.2074072828613354, 0.44044943820224725, 32.12728023870626, 0.2013932866552523
refl:, 1.2074072828613354, 0.43555555555555553, 31.728375671037586, 0.20159478768644698
refl:, 1.2074072828613354, 0.4307692307692308, 31.33989242755132, 0.20171671281423958
refl:, 1.2074072828613354, 0.4260869565217391, 30.96140049976025, 0.20176796051792995
refl:, 1.2074072828613354, 0.421505376344086, 30.592494717856905, 0.20173546160628877
refl:, 1.2074072828613354, 0.41702127659574467, 30.23279287960783, 0.2015919333831556
refl:, 1.2074072828613354, 0.4126315789473684, 29.88193405422147, 0.20140043913698885
refl:, 1.2074072828613354, 0.4083333333333333, 29.539577041619506, 0.20116952947891878
refl:, 1.2074072828613354, 0.4041237113402062, 29.2053989700849, 0.2008832766544487
refl:, 1.2074072828613354, 0.4, 28.879094017427605, 0.200502480384686
-----------
Initializing structure...
time for choose_chunkdivision = 0.000110865 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
time for set_epsilon = 0.00754905 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.1392134275610875 / 0.1392134275610875 = 1.0
field decay(t = 100.01): 1.3144200424788948e-11 / 0.1392134275610875 = 9.441761944278838e-11
run 0 finished at t = 100.01 (10001 timesteps)
-----------
Initializing structure...
time for choose_chunkdivision = 0.000108957 s
Working in 3D dimensions.
Computational cell is 0.02 x 0.02 x 12 with resolution 50
     block, center = (0,0,3)
          size (1e+20,1e+20,6)
          axes (1,0,0), (0,1,0), (0,0,1)
          dielectric constant epsilon diagonal = (12.25,12.25,12.25)
time for set_epsilon = 0.019413 s
-----------
Meep: using complex fields.
field decay(t = 50.01): 0.13921342793500532 / 0.13921342793500532 = 1.0
field decay(t = 100.01): 9.871965144118156e-11 / 0.13921342793500532 = 7.091244925544889e-10
run 0 finished at t = 100.01 (10001 timesteps)
refl:, 1.23100969126526, 0.8, 79.99999999999994, 0.028667884842985224
refl:, 1.23100969126526, 0.784, 74.82079670263325, 0.0021347453734021486
refl:, 1.23100969126526, 0.7686274509803922, 71.11813585396203, 0.0041164349187047915
refl:, 1.23100969126526, 0.7538461538461539, 68.12392493650243, 0.017504855468406976
refl:, 1.23100969126526, 0.739622641509434, 65.57213417097068, 0.03282494395652445
refl:, 1.23100969126526, 0.7259259259259259, 63.331955818023665, 0.04792423816150501
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refl:, 1.23100969126526, 0.7, 59.508764013939604, 0.07458578833476998
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refl:, 1.23100969126526, 0.664406779661017, 54.87424701948212, 0.10612404031633497
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refl:, 1.23100969126526, 0.552112676056338, 42.81677180338089, 0.17222042834178233
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refl:, 1.23100969126526, 0.536986301369863, 41.378881661291835, 0.1779352569426369
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refl:, 1.23100969126526, 0.5157894736842105, 39.41567103836258, 0.18483861166276766
refl:, 1.23100969126526, 0.509090909090909, 38.806766338771496, 0.18675601688212784
refl:, 1.23100969126526, 0.5025641025641026, 38.218439871701385, 0.1884996414001091
refl:, 1.23100969126526, 0.4962025316455696, 37.64955065969264, 0.19008080645459632
refl:, 1.23100969126526, 0.49, 37.099048958377544, 0.1915079168724047
refl:, 1.23100969126526, 0.4839506172839506, 36.56596657389412, 0.19279885897563126
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refl:, 1.23100969126526, 0.47228915662650606, 35.54854542021205, 0.19498186511670068
refl:, 1.23100969126526, 0.4666666666666667, 35.062607663064846, 0.19588322966927102
refl:, 1.23100969126526, 0.4611764705882353, 34.59087921692149, 0.19666472127374038
refl:, 1.23100969126526, 0.4558139534883721, 34.13269294834013, 0.19734835806450404
refl:, 1.23100969126526, 0.4505747126436782, 33.6874261758209, 0.197930496667696
refl:, 1.23100969126526, 0.4454545454545454, 33.25449677173539, 0.19840503576945626
refl:, 1.23100969126526, 0.44044943820224725, 32.83335969046958, 0.19877805012361263
refl:, 1.23100969126526, 0.43555555555555553, 32.42350386700291, 0.19904737688450852
refl:, 1.23100969126526, 0.4307692307692308, 32.0244494386133, 0.19925404758581897
refl:, 1.23100969126526, 0.4260869565217391, 31.63574524940934, 0.1993954429097289
refl:, 1.23100969126526, 0.421505376344086, 31.2569666032255, 0.19942422718572894
refl:, 1.23100969126526, 0.41702127659574467, 30.887713235292672, 0.1993498431053417
refl:, 1.23100969126526, 0.4126315789473684, 30.527607477190394, 0.19917542826890433
refl:, 1.23100969126526, 0.4083333333333333, 30.176292593038497, 0.19903411145233238
refl:, 1.23100969126526, 0.4041237113402062, 29.83343126780691, 0.19890224385206828
refl:, 1.23100969126526, 0.4, 29.498704231103652, 0.1984945592268268

Two-dimensional plots of the angular reflectance spectrum based on the simulated data and the analytic Fresnel equations are generated using the script below. The plots are shown in the accompanying figure with four insets. The top left inset shows the simulated and analytic reflectance spectra at a wavelength of 0.6 μm. The top right inset shows the simulated reflectance spectrum as a function of the source wavelength λ and Bloch-periodic wavevector $k_x$: $R(\lambda, k_x)$. The lower left inset is a transformation of $R(\lambda, k_x)$ into $R(\lambda, \theta)$. Note how the range of angles depends on the wavelength. For a particular angle, the reflectance is a constant for all wavelengths due to the dispersionless dielectric. The lower right inset is the analytic reflectance spectrum computed using the Fresnel equations. There is agreement between the simulated and analytic results. The Brewster's angle, where the transmittance is 1 and the reflectance is 0, is tan-1(3.5/1)=74.1°. This is also verified by the simulated results.

In order to generate results for the missing portion of the reflectance spectrum (i.e., the white region), we will need to rerun the simulations for different wavelength spectra.

In [3]:
plt.figure(dpi=200)
plt.pcolormesh(kxs, wvls, Rmeep, cmap='inferno', shading='gouraud', vmin=0, vmax=Rmeep.max())
plt.axis([kxs[0,0], kxs[0,-1], wvl_min, wvl_max])
plt.yticks([t for t in np.linspace(0.4,0.8,5)])
plt.xlabel(r"Bloch-periodic wavevector (k$_x$/2π)")
plt.ylabel("wavelength (μm)")
plt.title("reflectance (meep)")
cbar = plt.colorbar()
cbar.set_ticks([t for t in np.linspace(0,0.4,5)])
cbar.set_ticklabels(["{:.1f}".format(t) for t in np.linspace(0,0.4,5)])
In [4]:
plt.figure(dpi=200)
plt.pcolormesh(thetas, wvls, Rmeep, cmap='inferno', shading='gouraud', vmin=0, vmax=Rmeep.max())
plt.axis([thetas.min(), thetas.max(), wvl_min, wvl_max])
plt.xticks([t for t in range(0,100,20)])
plt.yticks([t for t in np.linspace(0.4,0.8,5)])
plt.xlabel("angle of incident planewave (degrees)")
plt.ylabel("wavelength (μm)")
plt.title("reflectance (meep)")
cbar = plt.colorbar()
cbar.set_ticks([t for t in np.linspace(0,0.4,5)])
cbar.set_ticklabels(["{:.1f}".format(t) for t in np.linspace(0,0.4,5)])
In [5]:
n1=1
n2=3.5

# compute angle of refracted planewave in medium n2
# for incident planewave in medium n1 at angle theta_in
theta_out = lambda theta_in: math.asin(n1*math.sin(theta_in)/n2)

# compute Fresnel reflectance for P-polarization in medium n2
# for incident planewave in medium n1 at angle theta_in
Rfresnel = lambda theta_in: math.fabs((n1*math.cos(theta_out(theta_in))-n2*math.cos(theta_in))/(n1*math.cos(theta_out(theta_in))+n2*math.cos(theta_in)))**2

Ranalytic = np.empty((nfreq, theta_in.size))
for m in range(wvl.size):
    for n in range(theta_in.size):
        Ranalytic[m,n] = Rfresnel(math.radians(thetas[m,n]))

plt.figure(dpi=200)
plt.pcolormesh(thetas, wvls, Ranalytic, cmap='inferno', shading='gouraud', vmin=0, vmax=Ranalytic.max())
plt.axis([thetas.min(), thetas.max(), wvl_min, wvl_max])
plt.xticks([t for t in range(0,100,20)])
plt.yticks([t for t in np.linspace(0.4,0.8,5)])
plt.xlabel("angle of incident planewave (degrees)")
plt.ylabel("wavelength (μm)")
plt.title("reflectance (analytic)")
cbar = plt.colorbar()
cbar.set_ticks([t for t in np.linspace(0,0.4,5)])
cbar.set_ticklabels(["{:.1f}".format(t) for t in np.linspace(0,0.4,5)])