Canonical cylinder papers (Bohren & Huffman's infinite cylinder; coated fibres)

← Verification · Cylinders · Plane wave
Reference
canonical cylinder papers (Bohren & Huffman's infinite cylinder; coated fibres)
Kind
paper: a published number or figure
Calculated
Q_ext, Q_sca
Agreement
plotting precision; printed digits
A non-absorbing cylinder of n = 1.55 in air at 0.6328 µm: scattering per unit volume, Bohren & Huffman Fig. 8.7 Bohren & Huffman, Absorption and Scattering of Light by Small Particles (1983), §8.4: the scattering width over the cross-sectional area, 4 Q_sca / (π d), the book's demonstration that a cylinder scatters the two polarizations differently. Maxima read off the figure to ±0.2 and ±0.03 µm; the book prints the diameters of the highest ones only, so the others are marked where PyStratify's curve peaks. From crosscheck/classics/bohren_huffman_1983.py.
1234560246810diameter [µm]Csca/ V [10⁴ cm⁻¹]
parallel (E along the axis), PyStratify perpendicular, PyStratify parallel, read off Fig. 8.7 perpendicular, read off Fig. 8.7
Hover to read values.
  • largest relative difference from the read values: 0.00978723
  • PyStratify the lines, the reference the circles
A three-layer nanorod with four aligned resonances, lossless: superscattering, Ruan & Fan 2010, Fig. 1 Ruan & Fan, Phys. Rev. Lett. 105, 013901 (2010): Drude core to 0.3485 λ_p, ε = 12.96 shell to 0.5623 λ_p, Drude shell to 0.6370 λ_p, H along the axis. Each channel can scatter at most 2λ/π (the single-channel limit, 1 on this axis); aligning four gives ~8. The m = 3 and 4 resonances are needles about 1e-6 ω_p wide, so the window is computed on 6001 points and drawn on a thinned grid that keeps every peak. From crosscheck/classics/ruan_fan_2010.py.
0.25360.25380.2540.25420.25440.25460.25480.25502468ω / ω_pwidth / (2λ/π)
total scattering, PyStratify channel m = ±1, PyStratify channel m = ±2, PyStratify channel m = ±3, PyStratify channel m = ±4, PyStratify printed peak, 7.94 at ω = 0.2542 ωp
Hover to read values.
  • peak, relative difference from the printed 7.94: 0.00887141
  • PyStratify the lines, the reference the circles
The same nanorod with silver-like loss (γ = 0.004 ω_p core, 0.012 ω_p shell): Ruan & Fan 2010, Fig. 4a With silver's damping the needles broaden and the superscattering drops from ~8 to 1.92 single-channel limits; the paper prints the peak heights (p. 3–4), not their frequencies, so they are marked where PyStratify's curves peak. From crosscheck/classics/ruan_fan_2010.py.
0.250.2520.2540.2560.2580.511.52ω / ω_pwidth / (2λ/π)
scattering, PyStratify absorption, PyStratify scattering peak, printed (1.92) absorption peak, printed (0.73)
Hover to read values.
  • largest relative difference from the printed peaks: 0.00155704
  • PyStratify the lines, the reference the circles
A 1 nm sodium wire in vacuum and a 2 nm one in ε = 2, E across the wire: extinction, Ruppin 2001 (local curves) Ruppin, Opt. Commun. 190, 205 (2001): Drude sodium (ω_p = 8.65e15 s⁻¹, γ = 0.01 ω_p). The calculator draws the paper's dashed local curves; its solid ones add the hydrodynamic response. The printed resonances, ω_p/√(1 + ε_m), fall at 0.7071 (PyStratify 0.707) and 0.5774 (0.576); the heights are read off the log axis. From crosscheck/classics/ruppin_2001.py.
0.40.60.811.21.410⁻⁴10⁻³10⁻²10⁻¹11010²ω / ω_pQext
a = 1 nm, εm = 1, PyStratify a = 2 nm, εm = 2, PyStratify a = 1 nm: read off Fig. 1 (dashed) at the printed resonance ωp/√2
Hover to read values.
  • largest difference in log₁₀ Q_ext from the read values: 0.0116616
  • PyStratify the lines, the reference the circles

Run it yourself: bohren_huffman_1983.py · ruan_fan_2010.py · ruppin_2001.py · figures.py on GitHub, PyStratify 97e52a9