# Rayleigh Scattering

Rayleigh scattering is an effect of the scattering of light or electromagnetic radiation by particles much smaller in size than the wavelength. For example, when sunlight emits photons which enter the earth’s atmosphere, scattering occurs. The average wavelength for sunlight is around 500nm, which is in the visible light spectrum. However, it is known that the sunlight also emits Infrared waves and of course, ultraviolet radition. Interestingly enough, Rayleigh scattering influences the color of the sky due to diffuse sky radiation.

The reason why a huge wavelength (compare 400 nm with nitrogen and oxygen molecules which are only hundreds of picometers) can scatter on a small particle is because of electromagnetic interractions. When the nitrogen/oxygen molecules vibrate at a certain frequency, the photons interract and vibrate at the same frequency. The molecule essential absorbs and reradiates the energy, scattering it. Because the horizontal direction is the primary direction of vibration, the air scatters the sunlight. The polarization is dependent on the direction of the incoming sunlight. The intensity is proportional to the inverse of the wavelength to the fourth power. The shorter the wavelength, the more scattering. This can explain why the sky is blue because blue is more likely scattered by Raleigh scattering due to higher frequency (smaller wavelength). It is not dark blue because other wavelengths are also scattered, but much less so.

Rayleigh Scattering is quite important in optical fibers. Because the silica glass have microscopic differences in the refractive index within the material, Rayleigh scattering occurs which leads to losses. The following coefficient determines the scattering.

The equation shows that the scattering coefficient is proportional to isothermal compressibility (β), photoelastic coeffecient, the refractive index  as well as fictive Temperatue and is inversely proportional to the wavelength.

Rayleigh scattering accounts for 96% of attenuation in optical fibers. In a perfectly pure fiber, this would not occur. The scattering centers are typically atoms or molecules, so in comparison to the wavelength they are quite small. The Rayleigh scattering sets the lower limit for propagation loss. In low loss fibers, the attenuation is close to the Rayleigh scattering level, such as in Silica Fibers optimized for long distance propagation.