Parallel Plate Waveguide

The simplest possible openEMS simulation: a parallel-plate waveguide excited with a sinusoidal TEM mode, showing the core workflow of geometry setup, field dump and result visualization.

Introduction

This tutorial covers:

FDTD setup with a sinusoidal excitation and mixed boundary conditions
Geometry and mesh definition with CSXCAD
A time-domain E-field dump written as VTK files
Geometry inspection with AppCSXCAD and animation in Paraview

Python Script

Get the latest version from git.

Import Libraries

import os, tempfile
import numpy as np

from CSXCAD  import ContinuousStructure
from openEMS import openEMS

Setup the simulation

Sim_Path = os.path.join(tempfile.gettempdir(), 'Parallel_Plate_WG')
print(f'{Sim_Path=}')

FDTD Parameters and Boundary Conditions

Run 200 time steps with a 10 MHz sinusoidal excitation to reach steady state quickly. PEC boundaries on +/-y model the conducting plates; PMC on +/-x makes the structure periodic in x; Mur ABCs on +/-z absorb outgoing waves.

FDTD = openEMS(NrTS=200, EndCriteria=0, OverSampling=50)
FDTD.SetSinusExcite(10e6)
FDTD.SetBoundaryCond(['PMC', 'PMC', 'PEC', 'PEC', 'MUR', 'MUR'])

CSXCAD Geometry and Mesh

All coordinates are in metres. The uniform 1 m mesh spans +/-10 m in x and y (the plate aperture) and -10 to 30 m in z, giving 30 cells of propagation distance beyond the source plane.

CSX = ContinuousStructure()
FDTD.SetCSX(CSX)
mesh = CSX.GetGrid()
mesh.SetDeltaUnit(1)

mesh.SetLines('x', np.arange(-10, 11, 1))
mesh.SetLines('y', np.arange(-10, 11, 1))
mesh.SetLines('z', np.arange(-10, 31, 1))

Excitation

A y-polarised (E_y) uniform-field source at z = 0 launches the TEM mode. The excitation box covers the full cross-section to produce a spatially uniform plane-wave front.

exc = CSX.AddExcitation('excitation', exc_type=0, exc_val=[0, 1, 0])
exc.AddBox([-10, -10, 0], [10, 10, 0])

Field Dump

Record the time-domain E-field in the xz mid-plane (y = 0) so Paraview can animate wave propagation along z after the simulation completes.

Et = CSX.AddDump('Et', dump_mode=1)
Et.AddBox([-10, 0, -10], [10, 0, 30])

Run the simulation

if 0:  # debugging only
    CSX_file = os.path.join(Sim_Path, 'parallel_plate_wg.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, verbose=3)

print('use Paraview to visualize the FDTD result...')

Visualizing the Results

The simulation writes the E-field dump to Et_*.vtr in the simulation directory. To animate the propagating wave in Paraview:

File → Open and select the Et_..vtr group.
Click Apply in the Properties panel.
Set Color by to E-Field.
Press Play in the Animation toolbar.
Use Rescale to Data Range occasionally to tune the colour mapping.

For a clearer view of the wave propagation, apply a Warp By Vector filter (Filters → Alphabetical → Warp By Vector, then Apply).