Custom Material Import with Arbitrary Permittivity and Conductivity Distribution

[cyasing]

I want to import data of a complex material (with arbitrary permittivity and conductivity) defined over a uniformly distributed set of grid points. The two data files have permittivity / conductivity values w.r.t 2D coordinates. Coordinates are mentioned since the material does not extend beyond these coordinates (essentially geometry and material data in one). The only two options that came close were:

1. material_function: Does not seem viable, since the values are arbitrary.
2. epsilon_input_file: Only applicable for region without geometry. Also, no option for conductivity file.

What should I do?

[smartalecH]

I would use a material_function and just wrap your discrete samples with some arbitrary interpolator (eg linear interpolation is what meep uses everywhere).

Remember, meep's philosophy is to promote an illusion of continuity. So it expects continuous representations as inputs, even if you have to fake it with interpolation (as that's what meep does under the hood using pervasive interpolation)

[cyasing]

Yeah, that did seem like the only way out.

[cyasing]

@smartalecH I tried getting this to work, but the problem is that my data is too large (~16,000 entries). This is what I am doing:

def custom_material(p):
    BR_con_pd = pd.read_excel('conductivity.xlsx') #Data has columns for x, y, conductivity values
    BR_per_pd = pd.read_excel('permittivity.xlsx') #Data has columns for x, y, permittivity values
    bcon = np.array(BR_con_pd)
    bper = np.array(BR_per_pd)

    if round(p.x, 2) in bcon[:,0].round(2) and round(p.y, 2) in bcon[:,1].round(2):
      #Rounded because MEEP and my data have different precision and step size between entries
        con_val_here = bcon[idx,2]
        per_val_here = bper[idx,2]
        return mp.Medium(epsilon=per_val_here, D_conductivity=2*np.pi*freq*con_val_here/per_val_here)
    else:
     #Interpolation code here
        return mp.Medium(epsilon=per_val_here, D_conductivity=2*np.pi*freq*con_val_here/per_val_here)

Please tell me what I can do differently to make it faster.

[smartalecH]

What do you mean, "too large"? As in, it takes too long to build the geometry? Why not just downsample your original data?

[cyasing]

Yes, the geometry does take too long to build. I cannot down-sample it too much. The 'custom material' is actually a brain's dielectric profile.

[tulchhi-ram]

Did you found a way to improve this. I am simulating a media with space dependent media. When i insert as a slab with each slab a grid point,
when I simulate this its working but too may objects taking very high time to geometry set. So pass the media as function its taking the epsilon value but not complex values.

"The code in which it ignoring the conductivity term"
def epsi(p):
i=int(p.x)

if abs(p.x)>7000:
    ep=mp.Medium(index=1)
else: 
    epsr=sigme[i+6999,0]
    epsim=sigme[i+6999,1]
    D_conductivity=epsim
    susceptibilities = [mp.LorentzianSusceptibility(
        frequency=fcen, gamma=0, sigma=D_conductivity)]
    #ep=epsr+1j*epsim
    ep=mp.Medium(epsilon=epsr, E_susceptibilities=susceptibilities)
return ep

geometry=[mp.Block(size=mp.Vector3(14000,sy-0*dpml,0), center=mp.Vector3(0,0,0),material=epsi)]

sim = mp.Simulation(cell_size=cell, boundary_layers=pml_layers, sources=sources,
resolution=resolution,geometry=geometry,symmetries=symmetries,Courant=0.2)"

"here its working"
geometry = []
sigm=np.zeros((14000))
for i in range(14000):

D_conductivity=2*np.pi*fcen*sigme[i,1]/sigme[i,0]
sigm[i]=D_conductivity
susceptibilities = [mp.LorentzianSusceptibility(
    frequency=fcen, gamma=0, sigma=D_conductivity)]

geometry.append(mp.Block(size=mp.Vector3(1,sy-0*dpml,0), center=mp.Vector3(-7000+i,0,0),
                            material=mp.Medium(epsilon=sigme[i,0],E_susceptibilities=susceptibilities)))

#sim = mp.Simulation(cell_size=cell, boundary_layers=pml_layers, sources=sources,

resolution=resolution, geometry=geometry,symmetries=symmetries,Courant=0.1)

sim = mp.Simulation(cell_size=cell, boundary_layers=pml_layers, sources=sources,
resolution=resolution,geometry=geometry,symmetries=symmetries,Courant=0.1)

Also i have tried to pass it to material function but not working

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