Optical Network Impairments

Chromatic dispersion occurs because different wavelengths of light travel at different speeds through the fiber. This causes pulse broadening, resulting in intersymbol interference and signal degradation.

CD increases linearly with distance and is a major limiting factor in high-speed and long-haul optical communication systems.

Typical Values:

• Standard Single-Mode Fiber (SSMF): 16-18 ps/(nm·km) at 1550 nm
• Dispersion-Shifted Fiber (DSF): ~0 ps/(nm·km) at 1550 nm
• Non-Zero Dispersion-Shifted Fiber (NZDSF): 2-8 ps/(nm·km) at 1550 nm
• Dispersion limit for 10 Gbps NRZ: ~1000 ps/nm (~60 km of SSMF)
• Dispersion limit for 40 Gbps NRZ: ~60 ps/nm (~3-4 km of SSMF)

PMD results from the difference in propagation speeds between two orthogonal polarization modes within the fiber. This birefringence causes signal spreading and distortion that varies randomly over time.

Unlike CD, PMD is a statistical phenomenon that changes with environmental conditions like temperature and mechanical stress, making it more challenging to compensate.

Typical Values:

• Modern fibers (post-2000): 0.02-0.1 ps/√km
• Older fibers (pre-2000): 0.1-2.0 ps/√km
• PMD limit for 10 Gbps: ~10 ps DGD (Differential Group Delay)
• PMD limit for 40 Gbps: ~2.5 ps DGD
• PMD limit for 100 Gbps: ~1.0 ps DGD
• Maximum tolerable PMD: ~10% of bit period

Attenuation is the gradual loss of optical power as light propagates through the fiber. It is caused by absorption, scattering, and bending losses. Standard single-mode fibers have attenuation of approximately 0.2 dB/km at 1550 nm wavelength.

The power loss follows an exponential decay with distance and affects the signal-to-noise ratio (SNR) at the receiver.

Typical Values:

• SSMF at 1310 nm: 0.30-0.35 dB/km
• SSMF at 1550 nm: 0.18-0.22 dB/km
• Ultra-low-loss fiber: 0.16-0.17 dB/km at 1550 nm
• Submarine cables: 0.15-0.16 dB/km at 1550 nm
• Connector loss: 0.2-0.5 dB per connector
• Splice loss: 0.05-0.1 dB per splice
• Typical span length between amplifiers: 80-120 km

Four-Wave Mixing is a nonlinear effect where three wavelengths interact to generate a fourth wavelength. In WDM systems, this creates new frequency components that can interfere with existing channels, causing crosstalk and signal degradation.

FWM is particularly problematic in systems using equally spaced channels and is more severe in fibers with low dispersion.

Typical Values:

• Number of FWM products: N(N-1)(N-2)/2 for N channels
• FWM efficiency in DSF: Up to 0 dB (100% efficient) with perfect phase matching
• FWM efficiency in SSMF: -20 to -40 dB at 100 GHz spacing
• FWM threshold power: ~3 dBm per channel in DSF
• FWM-induced crosstalk: Can exceed -20 dB in low-dispersion fibers
• Critical channel spacing: <100 GHz in DSF, <50 GHz in NZDSF

Self-Phase Modulation occurs when the phase of an optical signal is modulated by its own intensity due to the Kerr effect in the fiber. This intensity-dependent phase shift leads to spectral broadening of the signal.

SPM causes frequency chirping across the pulse, with the leading edge shifting toward lower frequencies and the trailing edge toward higher frequencies. This interaction with dispersion can lead to pulse distortion.

Typical Values:

• Nonlinear coefficient (n₂): ~2.6×10⁻²⁰ m²/W for silica fibers
• Nonlinear refractive index change: Δn ≈ n₂·I (intensity dependent)
• SPM-induced phase shift: ϕₛₚₘ = γPL, where γ = 2πn₂/(λAₑₑₑ)
• Typical γ values: 1-3 W⁻¹·km⁻¹ for SSMF
• Critical power for 1 radian phase shift: ~5-10 mW in 100 km SSMF
• SPM-induced spectral broadening: ~ 0.1-1 nm at 10 dBm over 100 km

Cross-Phase Modulation is similar to SPM but occurs when the phase of an optical signal is modulated by the intensity of other co-propagating signals in WDM systems. XPM causes intensity-dependent phase shifts between channels.

XPM is typically stronger than SPM in multi-channel systems and can lead to timing jitter and spectral broadening that varies with the bit patterns of adjacent channels.

Typical Values:

• XPM is twice as strong as SPM: ϕₓₚₘ = 2γP₂L for two channels
• XPM-induced phase shift: Up to 2π radians in high-power systems
• XPM-induced jitter: 2-10 ps in 10 Gbps systems
• Channel walk-off length: L_w = T/(D·Δλ) ≈ 50-200 km for 100 GHz spacing
• XPM impact scales with: γP₂L·exp(-α·L_w)
• Maximum XPM-induced crosstalk: -15 to -20 dB

Stimulated Brillouin Scattering is a nonlinear process where high-intensity light generates acoustic waves in the fiber, causing backward scattering of the incident light with a frequency shift.

SBS has the lowest threshold of all nonlinear effects and can limit the maximum optical power that can be launched into the fiber. It is particularly problematic in narrow-linewidth systems.

Typical Values:

• SBS threshold power: 5-10 mW for narrow linewidth (< 10 MHz)
• Brillouin gain coefficient: 4-5×10⁻¹¹ m/W at 1550 nm
• Brillouin frequency shift: 10-11 GHz at 1550 nm
• Brillouin gain bandwidth: 10-100 MHz
• Threshold equation: Pₜₕ ≈ 21·Aₑₑₑ/(g_B·L_eff) for typical SSMF
• Threshold increase with source linewidth: ~1 dB per doubling of linewidth

Stimulated Raman Scattering is a nonlinear process where optical power is transferred from lower wavelength channels to higher wavelength channels. This causes power depletion in shorter wavelength channels and amplification in longer wavelength channels.

SRS is particularly important in wideband WDM systems where the wavelength spread is large. It has a higher threshold than SBS but can cause significant power tilt across the spectrum.

Typical Values:

• SRS threshold power: ~500-1000 mW in SSMF at 1550 nm
• Raman gain coefficient: 6-7×10⁻¹⁴ m/W at 1550 nm
• Raman frequency shift: ~13 THz (100 nm at 1550 nm)
• Raman gain bandwidth: ~6 THz (48 nm at 1550 nm)
• Power tilt in C-band (35 nm): ~0.5 dB/km at 20 dBm total power
• Power transfer efficiency: Up to 25-30% over 100 km
• Critical wavelength separation: >30 nm for significant effect