Transmittance over 1 of gold metasurface

[2213411860]

Recently I'm trying to reproduce the transmittance-wavelength curve from the paper "Frequency Selective Surface Bandpass Filters Applied to Thermophotovoltaic Generators，https://doi.org/10.1063/1.1841894" .

I use gaussian source and k-point (0,0,0). I calculated the flux power with and without metasurface in two runs and divided the first run by the second.
I compared the results(red line) with the paper and lumerical and found it is rather strange that some transmittances are over 1. (or totally wrong)

I would be appreciate if someone can help me out.
Here is my code:
`import matplotlib.pyplot as plt
import numpy as np
import meep as mp
from meep.materials import Au
import sys
l=0.55 # side length of the filter
w=0.2 # width of the cell
a=0.45
b=0.1
dpml = 1
resolution = 60
h1=3 #distance between source and filter
h2=-3 #distance between probe and filter
cell=mp.Vector3(l, l, 8)

#geometry defination
B1= mp.Block(
size=mp.Vector3(a, b, w),
center=mp.Vector3(0, 0, 0),
material=mp.Medium(epsilon=1),
)
B2= mp.Block(
size=mp.Vector3(b, a, w),
center=mp.Vector3(0, 0, 0),
material=mp.Medium(epsilon=1),
)
B3=mp.Block(
size=mp.Vector3(l, l, w),
center=mp.Vector3(0, 0, 0),
material=Au,
)
geometry1=[B3,B2,B1]
geometry2=[B1]

#source defination
w1=0.5
w2=2
fcen = (1/w1-1/w2)/2 # pulse center frequency
df = (1/w1-1/w2) # pulse width (in frequency)
nfreq = 100
k_point = mp.Vector3(0,0,0)
sources = [
mp.Source(
mp.GaussianSource(fcen, fwidth=df),
component=mp.Ex,
center=mp.Vector3(0, 0, h1),
size=mp.Vector3(l, l, 0),
)
]

#pml layer
pml_layers=[mp.PML(thickness=dpml,direction=mp.Z)]

#simulation1
sim = mp.Simulation(
cell_size=cell,
boundary_layers=pml_layers,
k_point=k_point,
sources=sources,
dimensions=3,
resolution=20,
)

tran_fr = mp.FluxRegion(
center=mp.Vector3(0, 0, h2), size=mp.Vector3(l, l, 0)
)
tran = sim.add_flux(fcen,df , nfreq, tran_fr)
pt = mp.Vector3(0, 0, h2) # Reference point

#round 1
sim.run(until_after_sources=mp.stop_when_fields_decayed(20, mp.Ex, pt, 1e-3))

no_cell_tran_flux = mp.get_fluxes(tran)
empty_data = sim.get_flux_data(tran)
sim.reset_meep()

#simulation2
sim = mp.Simulation(
cell_size=cell,
boundary_layers=pml_layers,
geometry=geometry1,
sources=sources,
k_point=k_point,
dimensions=3,
resolution=resolution,
eps_averaging = False
)
tran_fr = mp.FluxRegion(
center=mp.Vector3(0, 0, h2), size=mp.Vector3(1, 1, 0)
)
tran = sim.add_flux(fcen,df , nfreq, tran_fr)
pt = mp.Vector3(0, 0, h2) # Reference point
#round 2
sim.run(until_after_sources=mp.stop_when_fields_decayed(20, mp.Ex, pt, 1e-3))
with_cell_tran_flux = mp.get_fluxes(tran)

#print(with_cell_tran_flux/ no_cell_tran_flux)
op=open("output.txt","w")
sys.stdout=op
for i in range(nfreq):
print(with_cell_tran_flux[i],no_cell_tran_flux[i],with_cell_tran_flux[i] / no_cell_tran_flux[i])
op.close()
`

[stevengj]

Have you checked convergence with resolution? Metals at IR wavelengths often require extraordinarily high resolution in order to resolve the skin depth (which is important to surface-plasmon resonances). I would also be careful of the material model — you might want to fit your own Drude model based on the parameters cited in the paper, for example …

[2213411860]

Thanks for your reply.
I did reset resolution to 120 but only tiny change was seen compared to resolution=60 curve.
I also checked the epsilon in wavelength range 0.5-2um which seems quite normal.

As for Drude model, I think the original one from meep library could be OK for me.
Maybe I should set resolution even higher? I've been struggling for several days. If there is any other possible resolution to this problem, please just let me know.

[2213411860]

By the way, when I ran the simulation, "DFT frequency 0.0 is out of material's range of 0.16131113692089302-4.0327458966810505" was warned, maybe this had something to do with the problem?

[theogdoctorg]

Hi 2213411860,

Nice write-up and interesting problem. Here are the issues that I noticed.

1. That warning you noticed was a good hint -- frequency range was off. As written, "fcen" was 0.75 with a "df" of 1.5, so your frequency range went from 0 up to 1.5. This caused a nonphysical "spike" in the transmittance at freq=0. In the plot of transmittance vs. wavelength on your original post, this showed up at lambda = 0.5, so I'm assuming that you plotted the data against the intended frequency range instead of actual. A helpful check when setting up a simulation like this is to confirm with sim.get_flux_frequs(...) Fixed by changing (fmax-fmin)/2 to (fmax+fmin)/2.

2. For the fluxes between your "empty" and "with geometry" simulations be comparable, you must use the same resolution and the same size flux region. The first was more obvious in your case: you defined a variable "resolution" but only used it in your "with geometry" sim run, and the "empty" simulation has a value of 20 hard-coded. The latter was much more difficult to pin down, which is why it's generally a good idea to a) avoid single-letter variable names especially with "i" or "l", and b) define things in only one location if possible. The first time you defined "tran_fr" you had the size as a Vector3(l,l,0), but the second time, it was Vector3(1,1,0). Note the "1" and and "l". You didn't have to re-define "tran_fr" for your 2nd simulation at all though, and the only way I found it was by commenting out unneeded things in your code until it worked.

Unfortunately I don't have access to that paper from home, so I can't confirm if it matches or not, but at least it's not showing a transmittance > 1 any more.

[2213411860]

I deeply appreciate your detailed replying! Actually it was my first time doing such a difficult project as an undergraduate so I messed up all the things. The misspelling of l and 1 was really stupid and rediculous. But for your help, I would never figure out the mistake. Recently we Chinese are celebrating upcoming Chinese lunar new year and I sincerely wish you a happy new year!