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Knots of Light

  1. Dec 17, 2011 #1

    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.


    Natural and artificially created light fields in three-dimensional space contain lines of zero intensity, known as optical vortices1, 2, 3. Here, we describe a scheme to create optical beams with isolated optical vortex loops in the forms of knots and links using algebraic topology. The required complex fields with fibred knots and links4 are constructed from abstract functions with braided zeros and the knot function is then embedded in a propagating light beam. We apply a numerical optimization algorithm to increase the contrast in light intensity, enabling us to observe several optical vortex knots. These knotted nodal lines, as singularities of the wave’s phase, determine the topology of the wave field in space, and should have analogues in other three-dimensional wave systems such as superfluids5 and Bose–Einstein condensates6, 7.


    Last edited: Dec 17, 2011
  2. jcsd
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