Letter abstract
Nature Physics 4, 716 - 720 (2008)
Published online: 31 August 2008 | doi:10.1038/nphys1056
There is an Erratum (October 2008) associated with this Letter.
Linked and knotted beams of light
William T. M. Irvine1,2 & Dirk Bouwmeester2,3
Maxwell's equations allow for curious solutions characterized by the property that all electric and magnetic field lines are closed loops with any two electric (or magnetic) field lines linked. These little-known solutions, constructed by Rañada1, are based on the Hopf fibration. Here we analyse their physical properties to investigate how they can be experimentally realized. We study their time evolution and uncover, through a decomposition into a spectrum of spherical harmonics, a remarkably simple representation. Using this representation, first, a connection is established to the Chandrasekhar–Kendall curl eigenstates2, which are of broad importance in plasma physics and fluid dynamics. Second, we show how a new class of knotted beams of light can be derived, and third, we show that approximate knots of light may be generated using tightly focused circularly polarized laser beams. We predict theoretical extensions and potential applications, in fields ranging from fluid dynamics, topological optical solitons and particle trapping to cold atomic gases and plasma confinement.
- Center for Soft Condensed Matter Research, Department of Physics, New York University, New York 10003, USA
- Department of Physics, University of California, Santa Barbara, California 93106, USA
- Huygens Laboratory, Leiden University, PO Box 9504, 2300 RA Leiden, The Netherlands
Correspondence to: William T. M. Irvine1,2 e-mail: wi1@nyu.edu
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