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

TL;DR

This paper introduces Lorentz-invariant topological lines of the electromagnetic field called electric spaghettis, revealing new invariant structures in a Fabry-Perot resonant slit-grating with three distinct pattern regions.

Contribution

It demonstrates the construction of Lorentz-invariant electromagnetic field lines and identifies new topological structures in a specific resonant system.

Findings

Identification of three distinct ES patterns in different regions

Introduction of the invariant parameter η

Description of fractal spiral patterns in the funneling region

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.