refactor(notebooks): use internal adam for autograd25

[marcorudolphflex]

Summary

This extracts the Autograd25WaveguideCrossing.ipynb changes from #465 into a standalone PR.

• Replaces the direct optax optimizer setup and manual update loop with Tidy3D's internal adam and optimize helpers.
• Removes the notebook-level optax dependency.
• Updates the Gaussian source bandwidth from f0 / 20 to f0 / 5, matching the refactor(notebooks): use internal adam and optimize helper - batch 4 #465 note that this avoided glitchy transmission values above 1.

Autograd25 Result From #465

Objective (max.): develop 9.6852e-01 vs. branch 9.4947e-01 (-1.97%).

develop:

branch:

Validation

• uvx ruff format --check --diff Autograd25WaveguideCrossing.ipynb
• uvx ruff check Autograd25WaveguideCrossing.ipynb
• uv run --no-project python scripts/sync_metadata_tags.py --check
• uv run --no-project python scripts/validate_notebook_metadata.py Autograd25WaveguideCrossing.ipynb
• uv run --no-project python scripts/check_notebook_private_paths.py Autograd25WaveguideCrossing.ipynb
• python3 misc/check_misc_references.py
• uv run spellcheck.py Autograd25WaveguideCrossing.ipynb

---

Note

Low Risk
Documentation-only example refactor with no library or auth changes; the wider source bandwidth only affects this notebook’s simulation numerics.

Overview
Autograd25WaveguideCrossing.ipynb now follows the same autograd optimization pattern as other inverse-design examples: imports adam and optimize from tidy3d.plugins.autograd, builds an adam(learning_rate=...) optimizer, and runs the loop via optimize(...) with bounds, maximize direction, and a step callback instead of a hand-rolled optax update loop. The notebook no longer depends on optax.

The horizontal mode source GaussianPulse bandwidth is widened from fwidth=freq0 / 20 to freq0 / 5 to avoid unphysical transmission above 1; related markdown describes the optimize helper rather than manual optimizer state management.

^{Reviewed by Cursor Bugbot for commit f8cb9ba. Bugbot is set up for automated code reviews on this repo. Configure here.}

[github-actions]

Spell check passed successfully for 1 notebook(s).
Generated by GitHub Action run: https://github.com/flexcompute/tidy3d-notebooks/actions/runs/27749382577

[groberts-flex]

thank you @marcorudolphflex