Transmittance and reflectance of a suspended nanolayer

[Dev-linkon]

I followed the example 'Transmittance Spectrum of a Waveguide Bend' given in the Meep tutotial to find out the transmittance and reflectance of a nanolayer (n=2.37) suspended in water (n=1.34) through 3D simulations. I found that that the transmittance is more than 1 over some wavelength range and the loss (=1-reflectance-transmittance) is negative, which is not practical. However, when simulated the same structure with the refractive index altered, I got a nice plot.

Please let me know, what could be the probable solution to this problem.

The python script is as follws-

from __future__ import division

import meep as mp
import numpy as np
import matplotlib.pyplot as plt

resolution = 20 # pixels/um

w = 2 

dpml = 0.2
pml_layers = [mp.PML(dpml)]

sx = (w*0.8)+dpml  # size of cell in X direction
sy = w+dpml  # size of cell in Y direction
sz = w+dpml
cell = mp.Vector3(sx,sy,sz)

# pad = 4  # padding distance between waveguide and cell edge


#wvg_xcen =  0.5*(sx-w-2*pad)  # x center of vert. wvg
#wvg_ycen = -0.5*(sy-w-2*pad)  # y center of horiz. wvg

geometry = [mp.Block(size=mp.Vector3(sx,mp.inf,mp.inf),
                     center=mp.Vector3(0,0,0),
                     material=mp.Medium(index=1.34))]
                     
lambda_min = 2                   # minimum source wavelength
lambda_max = 7                   # maximum source wavelength
fmin = 1/lambda_max
fmax = 1/lambda_min
fcen = 0.5*(fmin+fmax)
df = fmax-fmin

sources = [mp.Source(mp.GaussianSource(fcen,fwidth=df),
                     component=mp.Ez,
                     center=mp.Vector3(-0.5*sx+dpml,0,0),
                     size=mp.Vector3(0,w,w))]

sim = mp.Simulation(cell_size=cell,
                    boundary_layers=pml_layers,
                    geometry=geometry,
                    sources=sources,
                    resolution=resolution)

sim.symmetries.append(mp.Mirror(mp.Y, phase=1))  
sim.symmetries.append(mp.Mirror(mp.Z, phase=-1))

nfreq = 100  # number of frequencies at which to compute flux

# reflected flux
refl_fr = mp.FluxRegion(center=mp.Vector3(-0.5*sx+dpml+0.1,0,0),size=mp.Vector3(0,w,w))
refl = sim.add_flux(fcen,df,nfreq,refl_fr)

# transmitted flux
tran_fr = mp.FluxRegion(center=mp.Vector3(0.5*sx-dpml,0,0),size=mp.Vector3(0,w,w))
tran = sim.add_flux(fcen,df,nfreq,tran_fr)

pt = mp.Vector3(0.5*sx-dpml-0.1,0,0)

sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ez,pt,1e-3))

# for normalization run, save flux fields data for reflection plane
water_refl_data = sim.get_flux_data(refl)
print('FIRST REFLECTION FLUX')
sim.display_fluxes(refl)
# save incident power for transmission plane
water_tran_flux = mp.get_fluxes(tran)
print('FIRST TRANSMISSION FLUX')
sim.display_fluxes(tran)

sim.reset_meep()

geometry = [mp.Block(size=mp.Vector3(sx,mp.inf,mp.inf),
                     center=mp.Vector3(0,0,0),
                     material=mp.Medium(index=1.34))]
                     
geometry.append(mp.Block(mp.Vector3(0.5,mp.inf,mp.inf), center=mp.Vector3(0,0,0), material=mp.Medium(index=2.37)))

sim = mp.Simulation(cell_size=cell,
                    boundary_layers=pml_layers,
                    geometry=geometry,
                    sources=sources,
                    resolution=resolution)

sim.symmetries.append(mp.Mirror(mp.Y, phase=1))  
sim.symmetries.append(mp.Mirror(mp.Z, phase=-1))

# reflected flux
refl = sim.add_flux(fcen, df, nfreq, refl_fr)

tran = sim.add_flux(fcen,df,nfreq,tran_fr)

# for normal run, load negated fields to subtract incident from refl. fields
sim.load_minus_flux_data(refl,straight_refl_data)

sim.run(mp.at_beginning(mp.output_epsilon),
	until_after_sources=mp.stop_when_fields_decayed(50, mp.Ez, pt, 1e-3))

NL_refl_flux = mp.get_fluxes(refl)
NL_tran_flux = mp.get_fluxes(tran)

flux_freqs = mp.get_flux_freqs(refl)

print('SECOND REFLECTION FLUX')
sim.display_fluxes(refl)
print('SECOND TRANSMISSION FLUX')
sim.display_fluxes(tran)

wl = []
Rs = []
Ts = []
for i in range(nfreq):
    wl = np.append(wl, 1/flux_freqs[i])
    Rs = np.append(Rs,-NL_refl_flux[i]/water_tran_flux[i])
    Ts = np.append(Ts,NL_tran_flux[i]/water_tran_flux[i])

if mp.am_master():
    plt.figure()
    plt.plot(wl,Rs,'bo-',label='reflectance')
    plt.plot(wl,Ts,'ro-',label='transmittance')
    plt.plot(wl,1-Rs-Ts,'go-',label='loss')
    plt.axis([2.0, 7.0, 0, 1])
    plt.xlabel("wavelength (μm)")
    plt.legend(loc="upper right")
    plt.show()

I have obtained a plot as attached here.

[smartalecH]

See this FAQ:

https://meep.readthedocs.io/en/latest/FAQ/#why-are-my-reflectancetransmittance-values-less-than-zero-andor-greater-than-one