Glossary entry

Rayleigh scattering

Elastic scattering of light by particles much smaller than the wavelength. Produces the fundamental attenuation floor of optical fibers and the dominant backscatter in OTDR measurement.

Rayleigh scattering arises from light interacting with refractive-index inhomogeneities (density fluctuations, thermally frozen-in compositional variations) on length scales much smaller than the wavelength. The scattering process is elastic — the scattered photon has the same frequency as the incident photon, only its direction changes.

The scattering cross-section per unit volume scales steeply with frequency:

\alpha_R(\lambda) \;\propto\; \frac{1}{\lambda^4}.

This $\lambda^{-4}$ dependence has wide-reaching consequences. In silica fiber:

Wavelength	Rayleigh loss
850 nm	$\sim$ 1.8 dB/km
1310 nm	$\sim$ 0.32 dB/km
1550 nm	$\sim$ 0.16 dB/km
1625 nm	$\sim$ 0.13 dB/km
2000 nm	$\sim$ 0.05 dB/km

Rayleigh scattering sets the fundamental attenuation floor of silica fiber — it cannot be reduced by improved manufacturing because it arises from thermodynamic density fluctuations frozen in during fiber drawing. The strong wavelength dependence is one of the main reasons telecom moved to 1310 nm and then 1550 nm operating wavelengths.

Phase function. Rayleigh-scattered light is largely angularly isotropic but slightly biased — the intensity-vs-angle distribution is

I(\theta) \;\propto\; 1 + \cos^2\theta,

producing equal forward- and back-scattered intensity, with a minimum at 90°.

Why the sky is blue. Sunlight scattering off air molecules follows the Rayleigh law: blue light (450 nm) scatters $\sim$ 5× as strongly as red light (650 nm), so blue dominates the diffuse sky background.

OTDR measurement. Optical time-domain reflectometers exploit Rayleigh backscatter to map fiber attenuation along its length. A short input pulse produces a continuous time-resolved trace of backscatter; the slope of the trace gives the local fiber attenuation, and discontinuities indicate splices, connectors, and breaks. Typical OTDR backscatter coefficient for SMF-28: $\sim -82$ dB/m, meaning the backscattered power from a 1-meter section is 82 dB below the forward-launched power.

Mie regime crossover. When the scattering particle size approaches or exceeds the wavelength, Rayleigh's $\lambda^{-4}$ law breaks down and the more general Mie scattering theory applies. The transition typically occurs at particle diameters of $\sim \lambda / 10$ .

Distinguished from inelastic Raman and Brillouin scattering, which exchange energy with vibrational or acoustic modes of the medium and produce frequency-shifted output.