Fiber Bundle Design
Calculate bundle diameter, cladding and core fill, packing-fraction loss and étendue for hexagonal or square fiber bundles.
Bundle Ø
0.875 mm
3 ring(s); full at 37 fibres
Cladding Fill
75.5 %
N·(d_clad/D)²
Core Fill
18.88 %
N·(d_core/D)²: light-guiding area
Packing-Fraction Loss
7.24 dB
uniform spot filling the bundle circle
Total Étendue
1.726e-2 mm²·sr
N·π·A_core·NA²
Infinite-Array Core Fill
22.67 %
π/(2√3)·(d_core/d_clad)²
Formulas
Hexagonal rings: n full rings hold 3n(n + 1) + 1 fibres (1, 7, 19, 37, 61, …)
Bundle diameter: D = (2n + 1)·d_clad (hex); D = ((m − 1)√2 + 1)·d_clad, m = ⌈√N⌉ (square)
Core fill: N·(d_core/D)²; packing loss = −10·log₁₀(core fill)
Étendue: G = π·A_core·NA² per fibre (in air)
Touching fibres with no glue or buffer. A partly filled outer ring is taken as needing the full ring diameter (a model assumption; edge sites sit closer in). Full hexagonal rings fill 75–78 % of their circle, tending to 3/4, so for large bundles a circular close packing is about 10 % smaller in diameter.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Equal touching round fibres in full-diameter hexagonal rings or a square grid, no adhesive or buffer; packing loss for a uniform spot filling the bundle circle.
- OEIS A003215. Hex (centered hexagonal) numbers 3n(n + 1) + 1: fibres in n full hexagonal rings. oeis.org
- Kosterin A., Temyanko V., Fallahi M., Mansuripur M. (2004). Tapered fiber bundles for combining high-power diode lasers. Appl. Opt. 43, 3893. Étendue conservation, taper NA. doi:10.1364/AO.43.003893