Roadmap: architecture, ergonomics & physics-generality enhancements

[garrekstemo]

Overview

Tracking epic for enhancements that extend TransferMatrix.jl along two axes: (A) architecture & ergonomics and (B) physics generality & robustness. The physics items draw on the Mackay & Lakhtakia (2020) transfer-matrix treatment (The Transfer-Matrix Method in Electromagnetics and Optics, Springer, DOI 10.1007/978-3-031-02022-3), which covers homogeneous bianisotropic slabs, continuously varying (sculptured / chiral) media via a piecewise-uniform approximation, and corrugated interfaces — most of which the package does not yet implement.

Each linked issue is scoped to a single implementable step (one PR). Some have a dependency on a sibling — see the dependency graph below. Issues that are pure scoping/decision placeholders are marked.

History: the original #86 (matrix-exponential propagator + bianisotropy) and #87 (graded/chiral media) bundled multiple separable deliverables and were each split into four single-step issues. #86 → #86, #91, #92, #93. #87 → #87, #94, #95, #96.

A. Architecture & ergonomics

• Add optional Unitful unit support via a dispatch seam #81 — Optional Unitful unit support via a dispatch seam (removes the bare-μm footgun)
• Move RefractiveIndex.jl to a package extension (optional dependency) #82 — Move RefractiveIndex.jl to a package extension (leaner core; shares ext/ setup with Add optional Unitful unit support via a dispatch seam #81)
• Add built-in dispersion models / materials (Drude, Lorentz) #83 — Built-in dispersion models / materials (Drude, Lorentz) — shipped self-contained / zero-dep (deliberately not routed through CurveFitModels)
• Add circular-polarization basis output to transfer() #84 — Circular-polarization basis output for transfer (good first issue; also a prerequisite for Validate chiral circular-Bragg stopband against literature #96)
• Make Layer broadcast as a scalar (Base.broadcastable) #85 — Make Layer broadcast as a scalar (Base.broadcastable) (good first issue, lowest priority)

B. Physics generality & robustness

Constitutive-tensor generalizations (in the existing Berreman backend; independent, parallelizable):

• Add user-facing API for a full (non-symmetric / gyrotropic) dielectric tensor on a Layer #86 — Full (non-symmetric / gyrotropic) ε tensor API on a Layer (magneto-optic / Faraday media)
• Generalize calculate_γ and dynamical_matrix to an anisotropic (3×3) μ tensor #91 — Generalize calculate_γ + dynamical_matrix to an anisotropic μ tensor (magnetic anisotropy)

Matrix-exponential propagator & bianisotropy:

• Spike + implement a matrix-exponential layer propagator backend #92 — Matrix-exponential propagator spike (M = exp(-iP·d)); may resolve R+T ≈ 0.998 for strongly rotated lossless crystals #70/Anisotropic ambient medium at oblique incidence produces NaN #71, eliminates mode sorting
• Activate magnetoelectric coupling (ρ1/ρ2) for bianisotropic media #93 — Activate magnetoelectric coupling (ρ1/ρ2) for bianisotropic media — depends on Spike + implement a matrix-exponential layer propagator backend #92 (or an equivalent generalized-eigenvector propagator)

Graded / chiral media (piecewise-uniform approximation):

• Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87 — GradedLayer type with piecewise-uniform expansion into homogeneous Layers (rugate, chirped, graded-index)
• Add helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) #94 — Helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) — depends on Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87
• Add nslices auto-refinement helper (refine_slices) #95 — refine_slices auto-refinement helper for nslices convergence — depends on Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87
• Validate chiral circular-Bragg stopband against literature #96 — Validate chiral circular-Bragg stopband against literature — depends on Add helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) #94 and Add circular-polarization basis output to transfer() #84

Robustness & exploratory:

• Add a scattering-matrix backend for numerical stability in thick/absorbing stacks #88 — Scattering-matrix backend for numerical stability in thick / absorbing / high-birefringence stacks (synergistic with Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87, Spike + implement a matrix-exponential layer propagator backend #92; depends on neither)
• Investigate periodically corrugated (grating) interfaces (large / exploratory) #89 — (scoping only) periodically corrugated (grating) interfaces — effectively a second, RCWA-class solver

Dependency graph

#92  →  #93                         (exp-propagator → magnetoelectric coupling)
#87  →  #94  →  #96                 (GradedLayer → chiral preset → validation)
#87  →  #95                         (GradedLayer → refine_slices)
#84  ─────────→  #96                (circular basis also gates the chiral validation)

Everything else is independent. #86, #91, #92, #87, #88 can all proceed in parallel.

Suggested sequencing

1. Add optional Unitful unit support via a dispatch seam #81 + Move RefractiveIndex.jl to a package extension (optional dependency) #82 — establish the ext/ infrastructure; Add optional Unitful unit support via a dispatch seam #81 is the highest value/lowest risk win.
2. Add circular-polarization basis output to transfer() #84, Make Layer broadcast as a scalar (Base.broadcastable) #85 — quick, contained ergonomic wins. (Add circular-polarization basis output to transfer() #84 also unblocks Validate chiral circular-Bragg stopband against literature #96 later.)
3. Add user-facing API for a full (non-symmetric / gyrotropic) dielectric tensor on a Layer #86, Generalize calculate_γ and dynamical_matrix to an anisotropic (3×3) μ tensor #91 — cheap constitutive-tensor generalizations inside the current backend; independently valuable, no propagator rewrite needed.
4. Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87 — GradedLayer expansion; then Add helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) #94, Add nslices auto-refinement helper (refine_slices) #95 in parallel on top of it.
5. Spike + implement a matrix-exponential layer propagator backend #92 — research spike; informs whether the exponential backend supersedes parts of the Berreman path. Activate magnetoelectric coupling (ρ1/ρ2) for bianisotropic media #93 follows if Spike + implement a matrix-exponential layer propagator backend #92 is promising.
6. Add a scattering-matrix backend for numerical stability in thick/absorbing stacks #88 — S-matrix stability; most valuable once Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87/Add helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) #94 produce long layer stacks.
7. Validate chiral circular-Bragg stopband against literature #96 (after Add helicoidal/chiral preset constructor (plain fine-slicing, no Oseen) #94 and Add circular-polarization basis output to transfer() #84), Add built-in dispersion models / materials (Drude, Lorentz) #83 (pending design decision), Investigate periodically corrugated (grating) interfaces (large / exploratory) #89 (scoping only) as capacity allows.

Notes

• Add user-facing API for a full (non-symmetric / gyrotropic) dielectric tensor on a Layer #86, Generalize calculate_γ and dynamical_matrix to an anisotropic (3×3) μ tensor #91, Spike + implement a matrix-exponential layer propagator backend #92, Activate magnetoelectric coupling (ρ1/ρ2) for bianisotropic media #93 all concern layer-propagation / constitutive generality and should be designed with awareness of each other; Add user-facing API for a full (non-symmetric / gyrotropic) dielectric tensor on a Layer #86 and Generalize calculate_γ and dynamical_matrix to an anisotropic (3×3) μ tensor #91 are the cheap, backend-internal wins, while Activate magnetoelectric coupling (ρ1/ρ2) for bianisotropic media #93 is the deepest (true bianisotropy) and rides on Spike + implement a matrix-exponential layer propagator backend #92.
• Add a scattering-matrix backend for numerical stability in thick/absorbing stacks #88 (S-matrix) is independent of Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87/Spike + implement a matrix-exponential layer propagator backend #92 but pays off most once long slice stacks (Add GradedLayer type with piecewise-uniform expansion into homogeneous Layers #87) exist.