Free space has no transverse index structure: a weak graded medium, waiting on a use case

Aperta
  • Qualcosa non va?
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I maintainer di solito rispondono entro 1 giorno

Nessuno ha ancora preso questa issue.

Valutazione

Difficoltà
5/5
Tempo stimato
Più di una settimana
Idoneità per principianti
5/100
Tipo di issue
Funzionalità
Chiarezza
Da chiarire
Stato di attività
Attiva
Stack tecnologico
numpy, python
Ambito
backend

Direzione di ricerca

The issue is parked until a maintainer names a use case, so there is no code to change yet. Read the SpatialMedium class in src/solprop/spatial.py, which takes one gas state per z, and the free-space model and flux pages under docs/guide/free-space/ to see the current uniform-index assumption. Done means either a SEP under docs/dev/seps/ that takes this over, following SEP 0, or the issue closed with the reason it is not wanted.

Scritto dal modello di indicizzazione a partire dal testo della issue.

Descrizione

area: free space enhancement priority: low
What is missing

On the free-space routes the medium's refractive index is uniform across the beam. A SpatialMedium has one gas state at each z, so a transverse gas-density profile, a prescribed weak thermal lens or a weakly graded region cannot be modelled. This differs from variation along z, which is #206. It is not on the list of refusals, because no interface takes such an index. Other codes take this route, such as 3D-UPPE, which splits a transversely varying index between a homogeneous spectral operator and a physical-space residual.

Why it matters

Nothing needs this today. It would matter for a free-space problem whose transverse index structure sets the result, such as a gas jet's density profile. It is waiting on a use case: without one, nothing here should start.

Things to get right if it is taken up

These are derived here, not run in solprop, except for the small check below.

  • Treating the index as a source is a different model. At one frequency let B = sqrt(k_ref^2 - q^2) be the positive transverse operator and V the index residual in the same basis. The weak-contrast forward-source model is de/dz = G e with G = -i (B + B^-1 V / 2). Even integrated exactly, that is not propagation by -i sqrt(B^2 + V). For a commuting constant residual v, the two differ from the term v^2 / (8 B^3) on. A tighter tolerance cannot close that gap, so it has to be stated as a model error.
  • The conserved quantity is not the ordinary norm. For that model with V Hermitian, G^dagger B + B G = 0, so e^dagger B e is conserved and e^dagger e is not. So a stepper must not rescale the field to hold the ordinary norm. The check below gives the size.
  • A dense matrix across the pixels does not scale. The small coupled-mode machinery is not a route here: its storage would grow as the square of the number of transverse columns.
import numpy as np
from scipy.linalg import expm

B = np.diag([1.0, 2.0])
V = np.array([[0.0, 0.4], [0.4, 0.0]])
e0 = np.array([1.0, 1.0j])
e = expm(-1j * (B + 0.5 * np.linalg.inv(B) @ V) * 0.7) @ e0
print((e.conj() @ e).real / (e0.conj() @ e0).real - 1)        # 0.06633116371809611
print((e.conj() @ B @ e).real / (e0.conj() @ B @ e0).real - 1)  # -3.3306690738754696e-16
Context
  • #206 (media varying along z on Cartesian and line grids), #193 (radial paths outside the adiabatic certificate) and #194 (high numerical aperture) touch the same model.
  • The free-space model and its flux page. The conserved form above is proportional to the scalar axial flux at a fixed frequency (SEP 34).
  • This is a new model, so it starts as a SEP (SEP 0). Keep weak scalar structure apart from full structured-vector propagation and crystal interfaces (SEP 8, #118).
To do
  • Name a concrete use case. Without one, leave this open and parked.
  • If there is one, write a SEP that compares evaluating the residual inside the existing Runge-Kutta stages, under one controller, with an operator-action method.
  • Qualify on a constant residual with its expected model error, small problems diagonalised independently, contrast and grid refinement, radial against Cartesian for symmetric profiles, and a scalar flux balance.

Needs a decision: whether a use case justifies it, by a maintainer. As of 2026-11-01 none is named.

Done when

A SEP takes this over, or this closes with the reason it is not wanted.

Checked against commit 8a9f764. Read, not run, apart from the check above.

Lingua principale
Python
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3
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3
Merge medio
8h 37m
PR unite (30g)
159

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