Symmetric Cross MTS Unit Cell

This project reproduces the symmetric-cross metasurface unit cell from:

Baladi and Hum, "Equivalent Circuit Models for Metasurfaces Using Floquet Modal Expansion of Surface Current Distributions," IEEE TAP, 2021.

The default parameters match Fig. 13 and Table II in the paper.

Geometry

Parameter	Value
l_x	20 mm
l_y	20 mm
w	3 mm
P_x	30 mm
P_y	30 mm
h	1.524 mm
epsilon_r	3.02

Current Model

For x-polarized normal incidence, the paper uses:

I_1x(x) = 0.95 cos(0.12 x) - 0.2 cos(0.64 x)
I_2y(y) = 0.5 I_1x(0) |(|y| - L_y/2) / (L_y/2)|

where x and y are in mm.

Setup in VS Code

Open this folder in VS Code. The workspace is configured to use:

D:\anaconda3\python.exe

This interpreter already includes NumPy and Matplotlib on this machine. If you prefer a virtual environment, run:

python -m venv .venv
.\.venv\Scripts\Activate.ps1
python -m pip install -r requirements.txt
python -m pip install -e .

The .vscode folder includes launch and task configurations for the two main scripts. They set PYTHONPATH=src, so editable installation is optional.

Run

Create the geometry and current plots:

python -m symmetric_cross_mts.plot_current

Run the ECM frequency sweep:

python -m symmetric_cross_mts.run_ecm

By default this writes the current restored ECM candidate. This candidate uses:

TTR variant: TE/TM unit-polarization projection
evanescent branch: decaying branch
high-order substrate loading: disabled for evanescent modal sum
width profile: cosine correction
mode order: 9

This is the closest fully analytical reconstruction found so far. It naturally reproduces the main Fig. 15 features: the reflection peak / transmission null near 5.8 GHz and the reflection minimum near 8 GHz.

To overlay the digitized anchors:

python -m symmetric_cross_mts.run_ecm --anchors

To run the hand-digitized Fig. 15 calibration:

python -m symmetric_cross_mts.run_ecm --mode calibrated --anchors

To run the raw analytical ECM implementation:

python -m symmetric_cross_mts.run_ecm --mode raw

Validate the Fig. 22 width sweep (w = 3, 5, 7 mm):

python -m symmetric_cross_mts.validate_width_sweep

This writes:

outputs/width_sweep_s11.png
outputs/width_sweep_summary.csv

Diagnose why the current analytical implementation does not yet match the published Fig. 15 curve:

python -m symmetric_cross_mts.diagnose_ecm

Outputs are written to:

outputs/geometry.png
outputs/current_distribution.png
outputs/s_parameters.png
outputs/s_parameters.csv

Notes

The ECM implementation follows the paper's Floquet modal projection workflow and uses a normalized current amplitude. It is meant as a reproducible analytical starting point for the symmetric-cross unit cell. Small differences from the published HFSS overlay can be expected because the paper does not publish all implementation details, such as exact metal thickness, loss tangent, modal truncation, numerical normalization choices, the incident-current normalization I0, and the exact normal-incidence TE00 limiting procedure. Without those normalization details, the raw Fourier-integral T00 is too small and the model mostly reproduces the bare dielectric slab response.