Polarization-Maintaining Fiber
Birefringence, beat length, h-parameter and output extinction ratio of PANDA, bow-tie and elliptical-core PM fibers versus length and input PER.
Presets fill B and h with typical orders of magnitude. Datasheets give a beat length (B = λ/L_B) and a crosstalk XT over a length L (h = artanh(10^(−|XT|/10))/L); use those for your fibre.
Beat Length
4.429 mm
L_B = λ/B
DGD per Length
1.167 ps/m
B/c: group ≈ phase B in stress fibres; for e-core fibre the group value differs from the phase value: it can be several times smaller or larger, depending on V
Fibre Crosstalk
-30.00 dB
10 log tanh(hL), for a perfect launch
Output PER
26.99 dB
from 30 dB in; exact coupled-power solution
Length to 20 dB
9.000 km
ln(r₀/r_t)/(2h)
Meets Requirement
Yes
output 26.99 dB vs 20 dB
Model
dPx/dz = −h(Px − Py), dPy/dz = h(Px − Py)
Py/Px = (1 − r)/(1 + r), r = e^(−2hL)(1 − ε₀)/(1 + ε₀), ε₀ = 10^(−PER_in/10)
ε₀ = 0: Py/Px = tanh(hL); small values add: ε ≈ ε₀ + hL
L_B = λ/B, DGD = B/c
Random coupling between the two polarization modes along the fibre (Noda, Okamoto and Sasaki 1986). h depends on the coating, cabling, bends and temperature, so take it from the datasheet or a measurement. Ignored: splice and connector misalignment (an angle θ adds ≈ tan²θ), polarization-dependent loss, and coherent (non-random) coupling at stress points.
Chart: output polarization extinction ratio against fibre length, with the required PER as a dashed line.
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
Exact solution of the PM-fibre coupled power equations with h-parameter h: Py/Px = (1−r)/(1+r), r = e^(−2hL)(1−ε₀)/(1+ε₀). Beat length λ/B, DGD B/c. B and h are inputs (typical presets).
- Noda J., Okamoto K., Sasaki Y. (1986). Polarization-maintaining fibers and their applications. J. Lightwave Technol. 4, 1071. h-parameter and crosstalk. doi:10.1109/jlt.1986.1074847