GaussianBeam source intensity pattern not circularly symmetric

[yorickreum]

Describe the bug
When measuring the intensity just above a GaussianBeam source in Tidy3D, the resulting pattern is not circularly symmetric. Instead, it appears elongated along the direction of polarization.

To Reproduce
Steps to reproduce the behavior:

1. Add a GaussianBeam source (e.g., polarized along the x-axis).
2. Place a FieldMonitor a small distance above the source (e.g., 0.1 µm in the z-direction).
3. Measure the electric field intensity |E|² in the x-y plane.
4. Compare the beam expansion along the x and y axes.

Expected behavior
Based on my understanding of electrodynamics, the intensity should expand equally along both x and y axes in the transverse plane, regardless of the polarization direction.

Question
Is my understanding of the physics incorrect? Or is this an expected effect due to vectorial (non-paraxial) behavior in full-wave simulations? A known artifact or limitation of the GaussianBeam implementation in Tidy3D? We've tried increasing the spatial resolution etc., but the asymmetry remains.

[momchil-flex]

Hi, sorry that nobody got back to you earlier.

The beam should indeed be circularly symmetric and we even have tests that (sort of) test for that. We've also seen it in practice. I think there's probably something not quite right in your setup. If you could provide the exact code you used, I could take a look if this is reproducible and why. For example, as you point out in your question, this could be a limitation of the paraxial approximation breaking. If the beam waist is comparable to the wavelength, then indeed that could cause the beam cross-section to not look like an isotropic Gaussian anymore. The isotropic shape should be recovered for larger beam waist though.