Multi-Core Fiber Crosstalk
Inter-core coupling coefficient, bend-averaged power coupling and crosstalk of a multi-core fiber versus core pitch, bend radius, core mismatch and length.
Coupling coefficient κ
4.45e-3 m⁻¹
V = 2.208, κ/β = 7.49e-10
Power coupling h̄
1.48e-8 m⁻¹
bend- and twist-averaged
Crosstalk, one neighbour
-38.3 dB
tanh(h̄L) after 10 km
Worst core
-30.5 dB
6 nearest neighbours, first-order sum
Critical bend radius R_pk
∞ (Δβ = 0)
βΛ/Δβ: bends tighter than this phase-match the cores
Cladding diameter
150 µm
7 cores, hexagonal, centre core
Crosstalk vs Core Pitch (10 km, R_b = 100 mm)
Model
κ = (NA/(n₁a)) · (U²/V³) · K₀(WΛ/a) / K₁²(W)
h̄ = 2κ²d · Re[1/√((1 + i dΔβ)² + (dβΛ/R_b)²)] → 2κ²R_b/(βΛ) for Δβ = 0, d ≫ R_b/(βΛ)
XT = tanh(h̄L)
κ is Snyder's coupled-mode coefficient for two identical step-index cores, using the exact LP01 eigenvalues U and W. Random bends and twists sweep the phase mismatch between cores through Δβ + (βΛ/R_b) cos θ. Averaging over the twist angle θ, with an exponential autocorrelation of correlation length d, gives Koshiba's h̄. For identical cores (Δβ = 0) and d ≫ R_b/(βΛ) it is Hayashi's 2κ²R_b/(βΛ), independent of d. For cores that differ by Δβ, bends gentler than R_pk never phase-match them, and the crosstalk drops by orders of magnitude.
κ is computed for identical cores; Δβ enters only through phase matching, which is fine while the cores differ slightly. Not included: LP11 and other higher-order modes, trench-assisted profiles, and coupling to cores beyond the nearest neighbours. The worst-core value adds the neighbour pairs, which holds while each pair is well below −10 dB. R_b is the physical bend radius, as in Hayashi's equivalent-index model; the elasto-optic effect makes silica act as if it were about 1.26× larger (Nagano et al. 1978), which would raise the Δβ = 0 crosstalk by about 1 dB.
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
Snyder κ (exact LP01); Koshiba h̄ → Hayashi 2κ²R/(βΛ) for Δβ = 0; XT = tanh(h̄L). LP01 only, no trenches, worst core sums neighbours; physical R, no ≈ 1.27× elasto-optic factor (+1 dB).
- Snyder A. W. (1972). Coupled-mode theory for optical fibers. J. Opt. Soc. Am. 62, 1267. Coupling coefficient of two identical step-index cores. doi:10.1364/josa.62.001267
- Hayashi T. et al. (2011). Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber. Opt. Express 19, 16576. h = 2κ²R/(βΛ), XT = tanh(hL). doi:10.1364/oe.19.016576
- Koshiba M., Saitoh K., Takenaga K., Matsuo S. (2012). Analytical expression of average power-coupling coefficients for estimating intercore crosstalk in multicore fibers. IEEE Photonics J. 4, 1987. doi:10.1109/jphot.2012.2221085