A differentiated plane wave as an electromagnetic vortex

Differentiating a complex scalar plane wave with respect to its direction produces an isolated straight vortex line and has a natural extension, described in earlier papers, to the vector waves of electromagnetism-a differentiated plane wave (DPW). It epitomizes destructive interference and will be...

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Bibliographic Details
Published in:Journal of Optics 2015-04, Vol.17 (4), p.45603-12
Main Authors: Hannay, J H, Nye, J F
Format: Article
Language:English
Subjects:
diffraction
electromagnetic vortex
Fields (mathematics)
Fluid dynamics
Fluid flow
Functions (mathematics)
Mathematical analysis
optical vortex
Plane waves
Polarization
singular optics
Vortices
wave propagation
wave vortex
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Summary:Differentiating a complex scalar plane wave with respect to its direction produces an isolated straight vortex line and has a natural extension, described in earlier papers, to the vector waves of electromagnetism-a differentiated plane wave (DPW). It epitomizes destructive interference and will be shown to have the local structure of an electromagnetic vortex. In this paper its polarization structure and Poynting vector field are compared and contrasted with that of the family of linear polynomial waves, of which it is a special member. By definition this wider family has a general linear complex vector function of position multiplying a plane wave, but the function must be such that the combination satisfies Maxwell's equations. This forces translational invariance of the function along the wavevector direction-in other words the wave is 'non-diffracting'. In a natural sense all possible polarizations are exhibited once only. But the DPW has a distinctive polarization structure only partly explored previously. Both classes of waves share similar Poynting vector fields, which can be 'elliptic' (helix-like flow lines) or 'hyperbolic', of a repulsive nature, unexpected for a vortex. Both classes can be considered as a limit in the superposition of three closely parallel ordinary plane waves in destructive interference, and this derivation is supplied in full here.
ISSN:2040-8978
2040-8986
1464-4258
DOI:10.1088/2040-8978/17/4/045603