Trying to simulate a simple double slit

[Snens98]

Hello,

I'm trying to simulate a simple double-slit with a slit separation of 4 µm and a slit width of 1 µm.

As the incident wave, I'm using a plane wave with a wavelength of 0.457 µm.

I want to calculate the angular far-field interference pattern of the double slit.

But it doesn't work. Then I noticed that no matter what geometry I use, the far-field pattern always looks basically the same.

Could it be that the plane wave is somehow incorrectly defined? Is the resolution too low? I don't know what I'm doing wrong.

My Code is:

import os, tempfile
from pylab import *
from CSXCAD  import ContinuousStructure
from openEMS import openEMS
from openEMS.physical_constants import *
from openEMS.ports  import UI_data
import matplotlib.pyplot as plt



### Setup the simulation
Sim_Path = os.path.join(tempfile.gettempdir(), 'Doubleslit')
unit = 1e-6 # all length in µm

# size of the simulation box
SimBoxX = 9
SimBoxY = 1
SimBoxZ = 9

PW_BoxX = 8
PW_BoxY = 1
PW_BoxZ = 8


### Setup FDTD parameters 
FDTD = openEMS(NrTS=2000, EndCriteria=1e-4)


### Gaussian
f0 = 3e8 / 0.457e-6  # 0.457 µm
bandwidth = 0.05 * f0
FDTD.SetGaussExcite(f0, bandwidth)



### PML
FDTD.SetBoundaryCond( ['PML_8', 'PML_8', 'PML_8', 'PML_8', 'PML_8', 'PML_8'] )


### Setup Mesh
CSX = ContinuousStructure()
FDTD.SetCSX(CSX)
mesh = CSX.GetGrid()
mesh.SetDeltaUnit(unit)


#create mesh
x_lines = np.linspace(-SimBoxX/2, SimBoxX/2, 400)
y_lines = np.linspace(-SimBoxY/2, SimBoxY/2, 400)
z_lines = np.linspace(-SimBoxZ/2, SimBoxZ/2, 400)
 
mesh.SetLines('x', x_lines)
mesh.SetLines('y', y_lines)
mesh.SetLines('z', z_lines)


### Doubleslit geometry
geo = CSX.AddMaterial('block', epsilon=10000)
start = [-PW_BoxX/2 + tx, -PW_BoxY/2, -PW_BoxZ/2]
stop  = [-PW_BoxX/2+1 + tx, PW_BoxY/2, -PW_BoxZ/2+8]
geo.AddBox(start, stop,priority=1)

airSlit1 = CSX.AddMaterial('Block', epsilon=1)
tz = 4 +2
start = [-PW_BoxX/2 + tx, -PW_BoxY/2, -PW_BoxZ/2+tz]
stop  = [-PW_BoxX/2+1 + tx, PW_BoxY/2, -PW_BoxZ/2+1+tz]
airSlit1.AddBox(start, stop, priority=10)

airSlit2 = CSX.AddMaterial('air', epsilon=1)
tz = 4 -2
start = [-PW_BoxX/2 + tx, -PW_BoxY/2, -PW_BoxZ/2+tz]
stop  = [-PW_BoxX/2+1 + tx, PW_BoxY/2 , -PW_BoxZ/2-1+tz]
airSlit2.AddBox(start, stop, priority=10)


# Plane wave excitation
inc_angle = 0 
k_dir = [cos(np.deg2rad(inc_angle)), sin(np.deg2rad(inc_angle)), 0]
E_dir = [0, 0, 1]

pw_exc = CSX.AddExcitation('plane_wave', exc_type=10, exc_val=E_dir)
pw_exc.SetPropagationDir(k_dir)
pw_exc.SetFrequency(f0)

start = np.array([-PW_BoxX/2, -PW_BoxY/2, -PW_BoxZ/2])
stop  = np.array([(-PW_BoxX/2)+1, PW_BoxY/2, PW_BoxZ/2])
pw_exc.AddBox(start, stop)




### nf2ff
nf2ff = FDTD.CreateNF2FFBox()



### Run simulation
CSX_file = os.path.join(Sim_Path, 'Doubleslit.xml')
if not os.path.exists(Sim_Path):
    os.mkdir(Sim_Path)
CSX.Write2XML(CSX_file)
from CSXCAD import AppCSXCAD_BIN
os.system(AppCSXCAD_BIN + ' "{}"'.format(CSX_file))

FDTD.Run(Sim_Path, cleanup=True)





phi = np.array([0]) 
theta = np.linspace(0, 360, 720) 


nf2ff_res = nf2ff.CalcNF2FF(Sim_Path, [f0], theta, phi, center=[0,0,0], verbose = 1)
E_theta = nf2ff_res.E_theta[0] 
E_phi   = nf2ff_res.E_phi[0]

intensity = np.abs(E_theta)**2 + np.abs(E_phi)**2
intensity /= np.max(intensity)


plt.figure()
plt.subplot(111, projection='polar')
plt.polar(np.deg2rad(theta), intensity, 'b-')
plt.title("Radiation Pattern")
plt.show()

Image of the farfield plot and simcell:

Best regards,
Jens

[thliebig]

The plane wave excitation only creates a plane wave on the inside, not the outside. You cannot create a plane wave like I think you are trying here...

[Snens98]

Thank you for your response. So, does that mean it's not possible to define the wave before the double slit in such a way that it passes through the slits, gets diffracted, and then the near-field is recorded after the slit, followed by the calculation of the far-field?

[thliebig]

It is not possible like this using a plane wave excitation I think... But I think you could setup a parallel plate waveguide using the proper boundary conditions etc.? But I think it needs some more thought ...

[gadiLhv]

Instead of a plane wave, try to build a rectengular waveguide that is terminated with your slit wall on the far end. You'll need to terminate it with PML on the other. You will get terrible return loss, but who cares. You just need to excite the slits such that they will be in-phase. The issue with this approach may be long simulation time due to high reflection.