Chromatic Dispersion (CD)
Calculate chromatic dispersion, pulse broadening, and system penalties for single-mode fiber.
D(λ)
17.46 ps/(nm·km)
S(λ) = 0.0582 ps/(nm²·km)
Accumulated Dispersion D·L
1397 ps/nm
β₂ / β₃
-22.27 ps²/km
β₃ = 0.1313 ps³/km
Dispersion Length L_D
40.49 km
T₀ = √2·σ₀ (1/e half-width)
Output rms Width σ
147.39 ps
from σ₀ = 21.23 ps; V_ω = 3.33
Bit-Rate Limit, Optimum Pulse
1.71 Gb/s
4Bσ ≤ 1 with σ₀ chosen to minimise σ (this source)
Limit for σ_λ → 0, β₃ = 0
5.92 Gb/s
B√(|β₂|L) ≤ ¼
Dispersion Penalty at 1 Gb/s
0.90 dB
−5 log₁₀(1 − (4Bσ_b)²), σ_b = √(σ² − σ₀²) the added rms broadening
Dispersion vs Wavelength
Pulse Width & Penalty vs Length
Key Formulas
D(λ) = (S₀/4)(λ − λ₀⁴/λ³) [ITU-T G.652; S₀ ≤ 0.092, 1300 ≤ λ₀ ≤ 1324 nm]
β₂ = −λ²D/(2πc), β₃ = (λ²/2πc)²(S + 2D/λ)
σ²/σ₀² = 1 + (1 + V²)(β₂L/2σ₀²)² + ½(1 + V²)²(β₃L/4σ₀³)², V = 2σ_ωσ₀ [Agrawal §2.4.2, unchirped]
σ_D = √((DLσ_λ)² + ½(SLσ_λ²)²) [broad source]; optimum σ₀, β₃ = 0: σ² = σ_D² + |β₂|L
Penalty = −5 log₁₀(1 − (4Bσ_b)²) dB, σ_b = √(σ² − σ₀²)
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
G.652 Sellmeier D(λ) and Gaussian-pulse broadening with source width, β₂ and β₃ (no chirp). Bit-rate limit 4Bσ ≤ 1 with the optimum input pulse (broad and narrow sources). The penalty uses the added broadening √(σ² − σ₀²).
- ITU-T G.652 (11/2016). Characteristics of a single-mode optical fibre and cable. D(λ) = (S₀/4)(λ − λ₀⁴/λ³) with 1300 ≤ λ₀ ≤ 1324 nm and S₀ ≤ 0.092 ps/(nm²·km). itu.int
- Agrawal G. P. (2010). Fiber-Optic Communication Systems, 4th ed., §2.3–2.4 (β₂, β₃, pulse broadening, bit-rate limits) and §5.4.4 (penalty). Wiley. doi:10.1002/9780470918524
- Marcuse D. (1980). Pulse distortion in single-mode fibers. Appl. Opt. 19, 1653. Gaussian-pulse broadening with source spectral width. doi:10.1364/AO.19.001653