Update docs and examples

[MatthewFilipovich]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.92%. Comparing base (a3062a6) to head (306b8a2).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

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[Copilot]

Pull request overview

This PR refreshes TorchOptics documentation and expands the Sphinx-gallery example set, aiming to provide clearer user guides and richer end-to-end demonstrations (propagation, systems, coherence/polarization, optimization, and quantum).

Changes:

• Reworked multiple user-guide pages and quickstart content for clearer explanations and more complete runnable snippets.
• Added/organized many new Sphinx-gallery examples across optical phenomena, optical systems, aberrations, coherence/polarization, optimization, and quantum.
• Updated lint configuration and minor code/test cleanups around Laguerre–Gaussian notation.

Reviewed changes

Copilot reviewed 41 out of 41 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
tests/profiles/test_laguerre_gaussian_profile.py	Removes inline Ruff suppression tied to ambiguous l variable.
src/torchoptics/profiles/laguerre_gaussian.py	Removes inline Ruff suppression for Laguerre–Gaussian l parameter and helper.
README.md	Updates feature bullets and links README snippets to full docs examples.
pyproject.toml	Updates Ruff ignore list (adds E741).
examples/README.rst	Rewords examples landing page text.
examples/quantum/README.rst	Adds a quantum examples subsection landing page.
examples/quantum/quantum_state_discrimination.py	Adds a quantum state discrimination example using HG modes and Helstrom bound.
examples/optimization/training_petal_beam.py	Adds an optimization/inverse-design example (petal beam training + animation).
examples/optimization/training_multi_plane_focusing.py	Adds an optimization example for multi-plane focusing.
examples/optimization/README.rst	Adds optimization subsection landing page.
examples/optical_systems/README.rst	Adds optical systems subsection landing page.
examples/optical_systems/phase_only_modulators.py	Adds a phase-only hologram example for beam shaping.
examples/optical_systems/mach_zehnder_interferometer.py	Adds a Mach–Zehnder interferometer example using beam splitters.
examples/optical_systems/lens_focusing.py	Adds a lens focusing and beam waist evolution example.
examples/optical_systems/4f_system.py	Adds a 4f system example demonstrating spatial filtering.
examples/optical_phenomena/youngs_double_slit.py	Adds a Young’s double slit interference example.
examples/optical_phenomena/talbot_effect.py	Adds a Talbot effect (self-imaging) example and carpet visualization.
examples/optical_phenomena/README.rst	Adds optical phenomena subsection landing page.
examples/optical_phenomena/polychromatic_light_with_grating.py	Adds a polychromatic dispersion example with RGB visualization.
examples/optical_phenomena/gaussian_beam_propagation.py	Adds a Gaussian beam propagation + theory comparison example.
examples/optical_phenomena/fresnel_zone_plate.py	Adds a Fresnel zone plate construction and focusing example.
examples/optical_phenomena/aperture_limited_psf.py	Adds an aperture-limited PSF gallery example.
examples/optical_phenomena/animate_propagation.py	Adds a propagation animation example using animate_tensor.
examples/coherence_and_polarization/spatial_coherence.py	Adds a spatial coherence propagation comparison example.
examples/coherence_and_polarization/README.rst	Adds coherence/polarization subsection landing page.
examples/coherence_and_polarization/polarized_field.py	Adds a polarized field walkthrough (polarizers/waveplates, Stokes parameters).
examples/coherence_and_polarization/laser_speckle_patterns.py	Adds laser speckle simulation + statistics example.
examples/aberrations/zernike_aberrations.py	Adds Zernike aberration gallery + PSF degradation example.
examples/aberrations/README.rst	Adds aberrations subsection landing page.
examples/aberrations/chromatic_aberration.py	Adds chromatic aberration example using polychromatic phase modulation.
docs/source/user-guide/systems.rst	Clarifies System.forward element skipping behavior at field z.
docs/source/user-guide/spatial_coherence.rst	Expands mutual coherence explanation, memory note, and plotting examples.
docs/source/user-guide/propagation.rst	Adds guidance on Fresnel-variant propagation methods.
docs/source/user-guide/profiles.rst	Reorganizes and expands profile documentation; adds mode galleries and Zernike section.
docs/source/user-guide/polarization.rst	Rewrites polarized-field intro and points to elements guide for details.
docs/source/user-guide/inverse_design.rst	Refines inverse-design narrative and updates training loop example to use overlap loss.
docs/source/user-guide/fields.rst	Adds sample Field.__repr__ output and clarifies geometry requirements for overlap.
docs/source/user-guide/elements.rst	Major expansion: modulators, polychromatic modulators, lenses, detectors, beam splitters, polarization elements, visualization.
docs/source/user-guide/configuration.rst	Clarifies defaults usage and adds explicit torch import in dtype example.
docs/source/quickstart/index.rst	Updates quickstart narrative and parameters; points to new optimization examples.
docs/source/conf.py	Reorders Sphinx-gallery sections to match new examples directory layout.

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