optical diffusion (scattering) versus refraction

Question

When an electromagnetic wave meets an interface a part of it is reflected and part of it is refracted (and from the refractive index I can calculate the angles of propagation and the intensities using respectively Snell and Fresnel laws).

Then I know that it could happen another process, the scattering in which the outgouing wave has no a specific direction and can also have a different wavelenght (this is what happens in Raman scattering). So, knowing the physical properties of the 2 media (refractive index, etc...), how can I predict when I the incidend wave will be scattered or refracted?

Answer 1

Let's first discuss phenomena in which the wavelength does not change. These are called linear or elastic.

As you point out, reflection, refraction, and scattering all have their origins in the re-direction of light by a medium. In fact, they all have their origins in scattering. As you point out, scattering often means re-direction into any other direction.

When the medium is uniform or homogeneous over lengths that are much larger than a wavelength, the molecules that comprise the medium are excited coherently, that is, all in step with each other. Each molecule re-radiates in step with all the others. In this case the scattered light from each molecule interferes with the scattered light from all the other molecules. It turns out rather remarkably that the field made up of all that scattered light is coherent with respect to the original beam. A well-defined direction of propagation emerges. Refraction.

If the medium is smaller in size than a wavelength, then there are not enough molecules for the scattered field to form a coherent beam. Light goes of in other directions. Rayleigh scattering.

The in-between case, not much smaller than a wavelength, but not much bigger either, is complicated, but the basic principles still apply. Mie scattering.

When the wavelength changes (nonlinear or inelastic) the same comments apply. The only difference is that the medium allows interactions that can remove energy from the light, changing it's wavelength. If the medium is small, we get, for example, Raman scattering. If the medium is large and homogeneous, we get a host of coherent nonlinear phenomena such as Second Harmonic Generation (SHG), Coherent Anit-Stokes Raman Scattering (CARS), and more, in which the re-radiated light goes off in a single, well-defined direction.

Answer 2

When an electromagnetic wave meets a more or less well-defined interface between media of different refractive indices n1 and n2 we can describe the behaviour in terms of reflection and refraction, as you explain well.

The more general situation: An electromagnetic wave of certain wavelength, traveling in medium with refractive index n1 is incident an object with refractive index n2. Then two things can happen: scattering and absorption. In case of scattering, the wave is redirected in a different direction, in case of absorption the wave is converted to some other form of energy. For a simple system, like a spherical object, the solutions can be analytically derived (see Rayleigh or Mie scattering).

In this view, the conversion from wavelength a to another wavelength b by any nonlinear process, such as Raman scattering or second harmonic generation, is part of the absorption. To calculate the efficiencies of these processes in a medium, we need to know the nonlinear susceptibility (usually a tensor, thus direction-dependent). This quantity depends on symmetries in the material structure. At interfaces, where certain symmetries are broken, some nonlinear processes are therefore more efficient, such as Raman scattering.