Bohren & Huffman d₁, c₁ (only l = 1 survives at r = 0)

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Reference
Bohren & Huffman d₁, c₁ (only l = 1 survives at r = 0)
Kind
analytic: a closed form, limit or conservation law: independent of any code
Calculated
E(0), H(0) of four homogeneous spheres, incl. ±0.0 inputs
Agreement
1e-13; observed ≤ 1.1e-14
The field at the centre of a sphere of m = 3 + 0.01i in air, 600 nm: Bohren & Huffman's d₁ and c₁ Only the order ℓ = 1 survives at the centre, so E(0) = d₁ x̂ and H(0) = m c₁ ŷ exactly (Bohren & Huffman Eq. 4.53); PyStratify sums its full near field at r = 0. The peaks are the sphere's internal resonances.
0.511.522.533.54024681012size parameter x|field at the centre|
|E(0)|, PyStratify |H(0)|, PyStratify |d₁|, Bohren & Huffman |m c₁|, Bohren & Huffman
Hover to read values.
  • largest relative difference (complex fields): 2.68×10⁻¹⁴
  • PyStratify the lines, the reference the circles

Run it yourself: mie_codes.py · test_mie_codes.py · figures.py · MIE_CODES.md on GitHub, PyStratify 97e52a9