Polarization Mode Dispersion (PMD)
Calculate PMD-induced differential group delay (DGD), its Maxwellian outage probability, and PMD-limited reach.
Mean DGD (PMD value)
5.00 ps
⟨Δτ⟩ = PMD · √L
RMS DGD
5.43 ps
⟨Δτ²⟩^½ = ⟨Δτ⟩ / 0.921
Mean DGD / bit period
0.0500
within the ≤ 0.1 rule of thumb
PMD-limited length
400 km
mean DGD ≤ 0.1 bit period at 10 Gb/s
Max DGD (3 × mean)
15.0 ps
0.150 bit periods
Probability DGD exceeds it
4.20e-5
≈ 22.1 min/year
DGD Distribution (Maxwellian)
Mean DGD / Bit Period vs Distance
Model
⟨Δτ⟩ = PMD·√L, f(Δτ) = √(2/π) Δτ²/σ³ · exp(−Δτ²/2σ²), σ = ⟨Δτ⟩√(π/8)
P(DGD > Δτ) = erfc(u/√2) + √(2/π) u e^(−u²/2), u = Δτ/σ
The PMD coefficient is the mean DGD per √length (ITU-T G.650.2). In a long, randomly coupled fibre the instantaneous DGD is Maxwellian (Poole 1988), with ⟨Δτ⟩ ≈ 0.921 × the rms DGD; it exceeds 3⟨Δτ⟩ with probability 4.2 × 10⁻⁵, about 22 minutes a year.
Rule of thumb, not a standard: keep ⟨Δτ⟩ ≤ 0.1 bit period, so the DGD stays below 0.3 bit period except for that fraction of the time. For multilevel formats use the symbol period; coherent receivers compensate first-order PMD digitally. Not modelled: second-order PMD, component PMD and the penalty itself. Modern G.652.D cable specifies PMDQ ≤ 0.2 ps/√km; old fibre can exceed 1 ps/√km.
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
First-order PMD of a long, randomly coupled fibre: Maxwellian DGD with mean PMD·√L. The 10 % bit-period limit is a design rule of thumb. Not modelled: second-order PMD, component PMD and the penalty itself.
- Kogelnik H., Jopson R. M., Nelson L. E. (2002). Polarization-mode dispersion. In Optical Fiber Telecommunications IVB.
- Poole C. D. (1988). Statistical treatment of polarization dispersion in single-mode fiber. Opt. Lett. 13, 687. Maxwellian statistics of the DGD. doi:10.1364/ol.13.000687
- ITU-T G.650.2. The PMD value as the mean DGD.
- Duelk M. (2006). IEEE 802.3 HSSG, Nov. 2006, duelk_02_1106. Probability 4.2×10⁻⁵ that the DGD exceeds 3 times its mean.