7e407dd1ac
Update examples for sampled-interface tapers, explicit physical CPML spacing, copied SCPML widths, and the consolidated complex mode solver. Document breaking API changes, overlap measures, and PML convergence.
91 lines
4.4 KiB
Markdown
91 lines
4.4 KiB
Markdown
# waveguides
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::: meanas.fdfd.waveguide_2d
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::: meanas.fdfd.waveguide_3d
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::: meanas.fdfd.waveguide_cyl
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## Overlap measures and normalization
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`waveguide_2d.inner_product(..., measure="physical", conj_h=True)` uses real
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Yee widths for physical Poynting power. `measure="stretched"` keeps complex
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widths for coordinate reaction. `lorentz_metric` and `lorentz_overlap` default
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to the stretched measure. Use the same grid and measure when constructing and
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using dual fields. A real overlap grid still defines a consistent constructed
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dual basis, even when the eigenproblem uses a separate PML grid.
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`normalized_fields_e/h(..., normalization="lorentz")` normalizes unconjugated
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self-reaction to one. This fixes phase up to a sign and is distinct from unit
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forward power, which remains the default. Zero-power or self-orthogonal modes
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raise `ValueError`; open self-orthogonal modes require paired primal/dual
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normalization through `ModeBasis`.
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## Targeted and reproducible mode solving
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For modes near an effective index guess, use `solve_modes_near` with
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`target_wavenumbers=[omega * n_guess]`. It targets the electric beta-squared
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operator at `(omega * n_guess)**2`; `solve_modes_near_beta` instead targets the
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first-order signed-beta operator. Both use the LU shift-invert backend and
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support `eigensolver_opts={"v0": starting_vector}`. Factorization cost and
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memory depend on the grid, so this is not universally faster than indexed
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solving. `solve_modes` keeps its global mode-number semantics and now accepts
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`rng` or `v0` for reproducible initialization.
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`waveguide_3d.mode_from_2d` accepts a supplied transverse electric eigenvector
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and reuses field reconstruction, normalization, numerical-dispersion
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correction, Yee staggering, rotation, and full-grid embedding without solving
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an eigenproblem.
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## Interface and sampled-taper scattering
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All scattering matrices use outgoing rows and incoming columns, ordered
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`[left, right]`:
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```text
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[b_left ] [R_left T_right_to_left] [a_left ]
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[b_right] = [T_left_to_right R_right] [a_right]
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```
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`get_s` and `get_abcd` require explicit `dxes`. Mixed Petrov-Galerkin testing is
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the default: left electric duals test H continuity, and right magnetic duals
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test E continuity. Both incidence directions are solved together with full
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projection matrices. Mixed scattering supports unequal mode counts.
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`formulation="galerkin"` selects equal-count left testing of both equations.
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Neither formulation silently clips transmission. The optional `force_nogain`
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and `force_reciprocal` flags are numerical projections, not general physical
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tests for arbitrary open or evanescent modal coordinates.
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`get_taper_s` replaces finite-difference CMT with half propagation in the left
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basis, a midpoint interface, and half propagation in the right basis for each
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sampled interval. Redheffer composition avoids growing passive backward
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transfer branches. Refine section sampling and modal/PML bases to establish
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convergence. The ineffective `rtol`, `atol`, and `max_step` arguments have been
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removed. The existing `eme_taper_cmt.py` example filename is retained.
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```python
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prepared = eme.prepare_taper(sections, dxes)
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s_original = eme.evaluate_taper_s(prepared)
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s_longer = eme.evaluate_taper_s(prepared, z_coords=prepared.z_coords * 1.2)
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s_changed_beta = eme.evaluate_taper_s(
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prepared, wavenumber_matrices=beta_matrices,
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)
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```
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`PreparedTaper` owns read-only copies of phase-aligned interface data. Beta
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matrix overrides have shape `(section, mode, mode)` in the original supplied
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section bases; recorded basis transforms are applied automatically. Explicit
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backward branches require backward beta overrides when forward beta is changed.
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Evaluation performs no field overlaps or eigensolves. Length sweeps reuse the
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sampled model; wavelength sweeps with reused fields are explicitly frozen-basis
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approximations. Reprepare when fields, duals, grids, or formulations change.
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`cascade_s(left, right, internal_modes=...)` connects spatially ordered S
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matrices, including unequal external ports. Public `abcd_to_s` and `s_to_abcd`
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use `[f_right, b_right] = ABCD @ [f_left, b_left]` and require equal port counts.
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`get_taper_abcd` converts the stable S result; zero transmission or an
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unrepresentable transfer matrix raises `LinAlgError`. Prefer S for long lossy
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devices. Singular interface and cascade systems also raise contextual errors
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rather than silently substituting pseudoinverses.
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::: meanas.fdfd.eme
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