We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a part
icular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.
We examine, both experimentally and theoretically, an interaction of tightly focused polarized light with a slit on a metal surface supporting plasmon-polariton modes. Remarkably, this simple system can be highly sensitive to the polarization of the
incident light and offers a perfect quantum-weak-measurement tool with a built-in post-selection in the plasmon-polariton mode. We observe the plasmonic spin Hall effect in both coordinate and momentum spaces which is interpreted as weak measurements of the helicity of light with real and imaginary weak values determined by the input polarization. Our experiment combines advantages of (i) quantum weak measurements, (ii) near-field plasmonic systems, and (iii) high-numerical aperture microscopy in employing spin-orbit interaction of light and probing light chirality.
It is well known that oscillations at the electron plasma frequency may appear due to instability of the plasma sheath near a positively biased electrode immersed in plasma. This instability is caused by transit-time effects when electrons, collected
by this electrode, pass through the sheath. Such oscillations appear as low-power short spikes due to additional ionization of a neutral gas in the electrode vicinity. Herein we present first results obtained when the additional ionization was eliminated. We succeeded to prolong the oscillations during the whole time a positive bias was applied to the electrode. These oscillations could be obtained at much higher frequency than previously reported (tens of GHz compared to few hundreds of MHz) and power of tens of mW. These results in combination with presented theoretical estimations may be useful, e.g., for plasma diagnostics.
We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented.
We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.
The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A fundamental
nature of this effect is related to the spin-orbit interaction and topological monopoles. Here we report a unified theory and a direct observation of two mutual phenomena: a spin-dependent deflection (the spin Hall effect) of photons and the precession of the Stokes vector along the coiled ray trajectory of classical geometrical optics. Our measurements are in perfect agreement with theoretical predictions, thereby verifying the dynamical action of the topological Berry-phase monopole in the evolution of light. These results may have promising applications in nano-optics and can be immediately extrapolated to the evolution of massless particles in a variety of physical systems.
