UTILIZATION OF RIEMANN-SILBERSTEIN VECTORS IN ELECTROMAGNETICS

Helicity, polarization, and Riemann-Silberstein vortices

Bialynicki-Birula has defined Riemann-Silberstein (RS) vortices as surfaces in spacetime where the complex form of a free electromagnetic field given by F = E + iB is null (F · F = 0) and shown that they can be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of C-lines associated with a monochromat...

Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann–Silberstein vector – a complex combination of the electric and magnetic field vec...

Reply to Silberstein

Statement Aaron Silberstein 1

Anabelian geometry is a grand synthesis of number theory, algebraic geometry, algebraic topology, and group theory. Parallel to the situation in algebraic topology where to a space, one attaches a fundamental group (after fixing a basepoint), in algebraic geometry one attaches to every algebraic variety X (and a geometric point x) its étale fundamental group πét 1 (X,x). Similar to the topologi...

Metamaterials in electromagnetics

This article takes a look at metamaterials in electromagnetics from a general point of view. The terminology of complex electromagnetic materials is discussed critically. A unique definition for metamaterials does not exist, but certain salient points can be distinguished in the ongoing discussion within the research community and in various formal suggestions for this definition in the literat...