Birefringence Fiber Calculator
Geometric (elliptical-core) and stress-induced birefringence and beat length of a single-mode fiber from core and cladding indices and core shape.
NA and V
0.1211, V = 2.208
Δ = 0.341 %, ellipticity ε = 1 − b/a = 0.020
Geometric B
1.548e-7
ε n₁ Δ² G(V); slow axis along the major axis
Total B
1.548e-7
geometric + stress (0.00e+0)
Beat Length
10.01 m
L_B = λ/|B|
Group Birefringence
4.738e-8
geometric part ε n₁ Δ² d(VG)/dV = 4.74e-8
DGD per Length
0.1580 fs/m
0.1580 ps/km, uncoupled (short) fibre
Model
B_geo = ε n₁ Δ² G(V), ε = 1 − b/a, Δ = (n₁ − n₂)/n₁
G(V) = (W²/V⁴)[U² + (U² − W²)(J₀/J₁)² + UW²(J₀/J₁)³] at U, W of LP01
B_group = ε n₁ Δ² d(VG)/dV (+ stress B); DGD = B_group/c
L_B = λ/|B|
Sakai and Kimura's first-order result for a slightly elliptical step-index core in a weakly guiding fibre. G peaks at ≈ 0.49 near V = 1.8, so B is a few 10⁻⁷ for a telecom core and tens of 10⁻⁵ only with a large Δ and ε. The geometric group birefringence changes sign near V = 2.5. The stress input adds an anisotropic-stress term (from the core or stress rods) with the same axes; enter it negative if its slow axis is the minor axis. Ignored: material dispersion of n₁ and Δ, and random coupling in long fibres (PMD grows as √L there).
Chart: geometric phase and group birefringence against wavelength at the current core shape; the phase value peaks where V ≈ 1.8.
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
Sakai–Kimura first-order geometric birefringence B = εn₁Δ²G(V) of a slightly elliptical step-index core and its group value, plus a stress term you enter; weak guidance (Δ ≪ 1). Not modelled: large ellipticity, material dispersion.
- Sakai J., Kimura T. (1981). Birefringence and polarization characteristics of single-mode optical fibers under elastic deformations. IEEE J. Quantum Electron. 17, 1041. G(V) for an elliptical core, as quoted in Rashleigh (1983). doi:10.1109/jqe.1981.1071213
- Rashleigh S. C. (1983). Origins and control of polarization effects in single-mode fibers. J. Lightwave Technol. 1, 312. doi:10.1109/jlt.1983.1072121