English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Singularities, i.e. places of discontinuities of parameters are extremelygeneral objects appearing in electromagnetic waves and thus are the key tounderstanding fundamental wave processes. These structures commonly occur inpurely coherent, highly directional waves, such as laser beams, determiningadditional spatial or "`topological"' properties of the wave fieldsindependently of their propagational dynamics. For instance, topologies of wavefronts, called phase singularities, add orbital degrees of freedom toelectromagnetic waves. These singularities are common to all types of scalarwaves described only by their intensity and phase distributions. As theelectromagnetic wave is a vector wave, its topological properties generallydepend on all field components leading to complex field patterns in space andtime. These patterns may contain singular points of undefined instantaneousorientation of the vector field, i.e. the instantaneous field (IF)singularities. In zero-order paraxial approximation of purely transverseelectromagnetic waves, some instantaneous field distributions may carryapparent topological monopoles, when the originally source-free wave exhibitsspatial structure associated with the 2D "virtual" sources of electromagneticfields. Here we present systematic description of topological singularities inboth electric and magnetic field of the electromagnetic waves in a paraxialapproximation. We also consider the important types of paraxial electromagneticwaves with complex transverse field structures containing instantaneous fieldsingularities.

Topological monopoles and currents in electromagnetic waves