Chaos in electromagnetics

There is a superficial paradox to the existence of chaos in electromagnetic wave propagation since Maxwell’s equations are linear with respect to the fields in free space or a linear dielectric medium, while chaos only occurs in non-linear systems. The problem has long been studied in quantum mechanics under the heading of  “quantum chaology” or “quantum chaos”.

In electromagnetics chaos manifests by virtue of the fact that ray propagation, and the eikonal equation describing it, is non-linear. So, for example, rays bouncing around the inside of a container describe a trajectory with non-linear characteristics unless the container has one of a few special forms. Dr Mackay was the first person to recognise that RCS prediction software using ray tracing must recognise this fact and deal with the consequences.

Chaotic spreading of ray paths in a general cross section straight duct

The relationship  between the properties of linear wave fields and non-linear ray characteristics is subtle and, it is safe to say, not properly understood especially in three dimensions. Rather little foundational work has been done in this area of electromagnetics though the fundamental properties of the statistics of wave fields at high frequencies will require an understanding of the subject. This is likely to have engineering consequences for designing optimal data communications in cluttered environments, optimal image processing in cluttered environments, high frequency radar cross section (RCS) prediction software and in the construction of RCS statistics and target detection algorithms.