When do knots in light stay knotted?
arXiv:1706.06175 · doi:10.1088/1751-8121/aa9749
Abstract
An initially knotted light field will stay knotted if it satisfies a set of nonlinear, geometric constraints, i.e. the null conditions, for all space-time. However, the question of when an initially null light field stays null has remained challenging to answer. By establishing a mapping between Maxwell's equations and transport along the flow of a pressureless Euler fluid, we show that an initially analytic null light field stays null if and only if the flow of the initial Poynting field is shear-free, giving a design rule for the construction of persistently knotted light fields. Furthermore we outline methods for constructing initially knotted null light fields, and initially null, shear-free light fields, and give sufficient conditions for the magnetic (or electric) field lines of a null light field to lie tangent to surfaces. Our results pave the way for the design of persistently knotted light fields and the study of their field line structure.
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Cited by in corpus (7)
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- Stable knots and links in electromagnetic fields
- On spacetime foliations and electromagnetic knots
- Knotted nodal lines in superpositions of Bessel-Gaussian light beams
- Knotted surfaces as vanishing sets of polynomials