Dispersion and attenuation in optical fibre

Attenuation and dispersion are the two main transmission impairments of an optical fibre. Attenuation reduces the signal power and limits distance; dispersion spreads the pulses and limits bandwidth (bit rate).

Attenuation

Attenuation is the loss of optical power along the fibre, given in dB/km:

$$\alpha\ (\text{dB/km}) = \frac{10}{L}\log_{10}\frac{P_{in}}{P_{out}}$$

Causes:

1. Absorption
   • Intrinsic: absorption by silica itself, ultraviolet (electronic) and infrared (molecular vibration) bands.
   • Extrinsic: impurities such as transition metal ions (Fe, Cu) and OH⁻ ions (water peak near 1383 nm).
2. Scattering
   • Rayleigh scattering from tiny density variations in glass; varies as $1/\lambda^4$, so it is the main loss at short wavelengths.
   • Mie scattering from larger defects.
3. Bending losses
   • Macrobending: large bends let light escape.
   • Microbending: tiny random bends from cabling pressure.
4. Splice and connector losses (in a link).

Low-loss windows: 850 nm (~2.5 dB/km), 1310 nm (~0.35 dB/km), 1550 nm (~0.2 dB/km).

Dispersion

Dispersion is the time spreading of a light pulse as it travels. Spread pulses overlap (inter-symbol interference), limiting the maximum bit rate.

 in: _|^|_|^|_    out: _/^^\/^^\_  (pulses overlap)

1. Intermodal dispersion: different modes in multimode fibre take different paths and arrive at different times. Large in step-index fibre, reduced in graded-index, zero in single mode fibre.
2. Chromatic (intramodal) dispersion: different wavelengths in the source spectrum travel at different speeds.
   • Material dispersion: index of glass varies with wavelength.
   • Waveguide dispersion: propagation depends on core size relative to wavelength.
   • Zero near 1310 nm in standard fibre; shifted to 1550 nm in dispersion-shifted fibre.
3. Polarization mode dispersion: the two polarizations travel at slightly different speeds.