Particle scattering of laser beams

The study of the interaction between an electromagnetic wave and (macroscopic) particles has long been an essential part of optics, or more generally, electromagnetism. An important date is 1890, when Lorenz rigorously described the interaction between light and an isolated sphere (under certain assumptions) without recourse to Maxwell's equations, i.e. in fact within the framework of the old aether theory. A more modern formulation, using Maxwell's equations, but equivalent (!), was then produced by Mie, then completed by Debye. The resulting theory, known as Mie's theory, or Lorenz-Mie theory (and its variants), has since been an indispensable reference for the study of the scattering of light (and other electromagnetic waves) by particles. In particular, it provides the rigorous and complete theory of the rainbow.

Other theories, known as limit theories, can be either deduced as special cases of Lorenz-Mie theory, or established independently on the basis of specific first principles. When the scattering objects are small compared to the wavelength, we find Rayleigh theory, which describes the radiation of an excited dipole. On the contrary, when the objects are large compared to the wavelength, scattering can be described by geometrical optics in terms of refraction and reflection. In this geometrical approach stricto sensu, diffraction must be added to model forward radiation.

These theoretical approaches have led to applications in a wide variety of fields. Many atmospheric phenomena can be explained by light scattering theory (often incorporating so-called multiple scattering effects). Rainbows, glows and halos result from the scattering of light by aerosols, ice crystals or water droplets. The visual quality of the atmosphere (its transparency) depends on the nature and concentration of aerosol particles, or the properties of fog droplets. Leaving our planet behind, the study of the light scattered by planetary atmospheres provides us with information on their composition. The so-called zodiacal light results from scattering by interplanetary dust, and can limit the possibilities of space telescopes.

The turbidity of liquids and solids (and sometimes their color) depends on how the light illuminating them is scattered, either by their molecular constituents or by suspended particles. More generally, scattering is essential to our vision of the world, since the light we perceive is, in most cases, light scattered by surrounding objects, illuminated by natural or artificial sources.

Practical applications, both in the laboratory and in industry, are also numerous. Here, however, we shall focus on metrological applications. Laser-Doppler velocimetry, a widely used measurement technique, measures the velocity...