Lorentz-invariant topological structures of the electromagnetic field in a Fabry-Perot resonant slit-grating

Abstract

It is commonly assumed that the most correct description of the electromagnetic world is the abstract one, and that topological constructs such as lines of force are not covariant. In the present paper, we show that for a $y$-invariant system with a $p$-polarized electromagnetic field, it is possible to construct absolute (i.e. Lorentz invariant) lines, which we call electric spaghettis (ESs). The electromagnetic field is fully described by the ES topology that transcend the limit between space and time, plus a new invariant, the characteristic parameter $\eta$. In a Fabry-Perot resonant slit-grating, three ES patterns can be distinguished, corresponding to three regions: null straight lines in plane wave regions, rounded rhombuses in the interference region inside the grating, and Bernoulli's logarithmic spiral patterns - the first ever described fractals - in the funneling region.