Many layers, graded profiles, rainbow, Luneburg lens [W97, WW91, Y24]

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Reference
many layers, graded profiles, rainbow, Luneburg lens [W97, WW91, Y24]
Kind
paper / analytic: a published number or figure
Calculated
Q, S(θ)
Agreement
report
A sphere of m = 1.33 + 0.001i cut into 100 identical layers [W97] Wu & Wang's and Yang's test for a layered recursion: 99 interfaces between identical media must change nothing. The report repeats it with 1000 layers at x = 1000, and checks graded (Kai–Massoli, Luneburg) profiles absorb nothing.
2040608010001234size parameter xQext
Qext, 100 identical layers (PyStratify) Qext, one sphere
Hover to read values.
  • largest relative difference: 1.15×10⁻¹⁶
  • PyStratify the lines, the reference the circles
The rainbow of a 250 µm droplet with a graded index (128 layers, n = 1.33 → 1.36), 514.5 nm [W97] x ≈ 1527 and 128 shells: the primary rainbow near 138° and its supernumerary fringes, from PyStratify's own truncation against 200 orders more. A truncation that stopped too early would move the fringes.
1301321341361381401421441461481501010²10³10⁴scattering angle [°]|S₁|
|S₁|, PyStratify (1574 orders) |S₁|, 1774 orders
Hover to read values.
  • largest relative difference: 7.91×10⁻⁹
  • PyStratify the lines, the reference the circles

Run it yourself: convergence.py · figures.py · RESULTS.md on GitHub, PyStratify 97e52a9