thz-circular-waveguide-modes

THz Circular Copper Waveguide Modes

A reproducible semi-analytical simulation of a broadband, linearly polarized Gaussian THz beam coupled through a lens into an air-filled circular copper waveguide.

Default physical system

Parameter	Value
Waveguide material	Copper
Inner diameter	2.0 mm
Length	40 cm
Copper conductivity	5.8 × 10⁷ S m⁻¹
Lens focal length	100 mm
Lens clear diameter	50.8 mm (2 inch)
Lens f-number	1.97
Lens numerical aperture	0.246
Frequency sweep	0.10–2.00 THz
Input polarization	Linear, along x

The default Gaussian 1/e electric-field radius on the lens is 25.4 mm, so the beam fills the lens (fill_factor = 1). This matters: focal length and lens diameter alone do not uniquely determine the focused THz spot unless the beam size incident on the lens is known.

What the simulation calculates

• TE and TM cutoff frequencies from the appropriate Bessel-function roots.
• Frequency-dependent propagation constant and relative group delay.
• Full vector eigenfields (E_x,E_y,E_z,H_x,H_y,H_z).
• Diffraction-limited Gaussian waist produced by the specified lens.
• Aperture clipping and Gaussian-to-mode power overlap.
• Copper-wall conductor loss from a surface-resistance perturbation.
• Modal power at the input and after 40 cm propagation.
• Coherent output field maps at 0.20, 0.50, 1.00, and 1.50 THz.
• CSV tables and publication-ready PNG figures.

For a perfectly centered, cylindrically symmetric, x-polarized Gaussian, only one angular orientation of the (m=1) families is symmetry-accessible: TE({1n})-sin and TM({1n})-cos. Other modes remain important in a real experiment when the beam is offset, tilted, distorted, or coupled through a non-ideal flange.

Quick start

Python 3.10 or later is recommended.

python -m venv .venv
source .venv/bin/activate          # Windows: .venv\Scripts\activate
python -m pip install -r requirements.txt
python run_simulation.py

The results are written to results/. Numerical highlights from the supplied default run are collected in RESULTS_SUMMARY.md.

Run the tests with:

PYTHONPATH=src python -m unittest discover -s tests -v

Change the experiment

All important quantities are command-line parameters:

python run_simulation.py \
  --diameter-mm 2.0 \
  --length-cm 40 \
  --focal-length-mm 100 \
  --lens-diameter-mm 50.8 \
  --fill-factor 0.80 \
  --minimum-thz 0.10 \
  --maximum-thz 2.00

If the measured 1/e THz field radius on the lens is (w_L), set

fill_factor = w_L / 25.4 mm

For example, a measured 20 mm radius corresponds to --fill-factor 0.7874.

Output files

File	Contents
cutoff_frequencies.csv	Sorted TE/TM cutoff table
modal_spectrum.csv	Coupling, loss, output power, beta, and delay per mode
total_spectrum.csv	Total aperture, coupled, and output power fractions
simulation_metadata.json	Geometry, settings, and model assumptions
01_mode_cutoffs.png	Cutoffs of Gaussian-accessible modes
02_coupling_and_output.png	Aperture, coupled, and transmitted power
03_output_modal_power.png	Frequency-resolved output modal content
04_copper_loss.png	Copper loss over the 40 cm guide
05_output_field_maps.png	Coherent output fields at four THz frequencies

Model scope

This code is intended for fast physical interpretation and parameter sweeps. It is not a full 3D finite-element model. The eigenfields assume a perfectly circular, air-filled bore with ideal geometry. Copper loss is evaluated using the good-conductor surface resistance

[ R_s=\sqrt{\frac{\pi f\mu_0}{\sigma}} ]

and first-order perturbation of the perfect-conductor fields. The model omits:

• input/output flange reflections and impedance matching;
• finite wall thickness, surface roughness, oxidation, and seams;
• waveguide bends, ellipticity, tapers, and mechanical tolerances;
• lens aberration and measured spatial phase;
• atmospheric absorption;
• offsets and angular misalignment.

Consequently, copper_loss_db is propagation loss from the wall model, whereas the reduction between incident and coupled power is coupling/aperture loss. Experimental insertion loss can be substantially larger than copper propagation loss.

The equations and normalization are documented in docs/model.md.

Citation

If you use this project in research, cite the repository metadata in CITATION.cff and describe any measured beam radius, alignment, surface roughness, and flange geometry added to the default assumptions.

License

MIT License.

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