What is Rayleigh scattering?

Rayleigh scattering is a common optical phenomenon named after the British physicist Lord Rayleigh. It is the linear scattering of light at a scattering center that is much smaller than the wavelength of the light. In this case, the scattering is proportional to the amplitude of the mid-emerging amplitude, provided that the inverse wavelength occurs to the fourth power and to 1 + COS 2 θ, where θ is the scattering angle. Forward and backward scattering (θ = 0 and θ = π, respectively) have the same intensity.

Rayleigh scattering and Mie scattering can be described by Mie scattering theory (named after Gustav Mie) for larger centers. Here, the properties are different. Par exemple, for forward scattering, the scattering amplitude is stronger and has a different wavelength dependence.

The scattering centers for Rayleigh scattering can be individual atoms or molecules. However, one can also describe Rayleigh scattering in the atmosphere due, for example, to microscopic density fluctuations, which are caused by the random distribution of molecules in the air.

Note that for scattering at multiple particles or scattering centers, one cannot simply add up the power scattered by the individual centers because of interference effects: the amplitudes must be added. As a result, Rayleigh scattering of light does not occur in perfectly pure and regular crystals. Moreover, Rayleigh scattering in air is possible only due to the random density fluctuations described above.

Formula for the principle of Rayleigh scattering

In amorphous optical materials such as quartz glass, random density fluctuations always exist due to the irregular microstructure. They are even much stronger than usual at room temperature because the density fluctuations occurring in the fibers near the glass softening temperature are “frozen” during the fiber manufacturing process.

Rayleigh scattering sets a lower limit to the propagation loss in optical fibers. Of course, other losses can also result, e.g. due to irregular core/cladding interfaces (especially with high refractive index contrasts), scattering and absorption of impurities as well as macro- and micro-bending. Quartz fibers optimized for long-haul fiber optic communications have very low propagation losses, close to the limit given by Rayleigh scattering. For wavelengths substantially below the often-used 1.5-μm region, Rayleigh scattering alone will be higher than the actual loss of these fibers at 1.5-μm wavelengths. At essentially longer wavelengths, Rayleigh scattering would be weaker, but the infrared absorption of silica would begin.

In principle, it would be possible to use mid-infrared fibers made of other glasses (e.g., fluoride fibers) with even lower losses, but in practice silica fibers are already at optimum performance.

Most of the Rayleigh-scattered light in an optical fiber comes out of the fiber from the side. Only a small fraction of the scattered light is scattered back and thus guided again in the fiber core. As a result, the return loss of fiber optic devices is usually high. The total return loss of fiber optic devices is usually caused by reflections at interfaces such as fiber ends, mechanical splices or fiber connectors.

Due to the high light intensity that often occurs in optical fibers, nonlinear scattering processes such as Raman scattering and Brillouin scattering may also occur. Rayleigh scattering as a linear process is also important at low light intensities.