Vortex knots in light

Optical vortices generically arise when optical beams are combined. Recently, we reported how several laser beams containing optical vortices could be combined to form optical vortex loops, links and knots embedded in a light beam (Leach et al 2004 Nature 432 165). Here, we describe in detail the experiments in which vortex loops form these structures. The experimental construction follows a theoretical model originally proposed by Berry and Dennis, and the beams are synthesized using a programmable spatial light modulator and imaged using a CCD camera.

[1]  S. Barnett,et al.  Orbital angular momentum of light , 2007 .

[2]  Jeffrey P. Mower,et al.  Plant genetics: Gene transfer from parasitic to host plants , 2004, Nature.

[3]  J. Leach,et al.  Laser beams: Knotted threads of darkness , 2004, Nature.

[4]  Stephen M. Barnett,et al.  Uncertainty principle for angular position and angular momentum , 2004 .

[5]  Miles J. Padgett,et al.  Observation of the vortex structure of a non-integer vortex beam , 2004 .

[6]  Z. Dutton,et al.  Transfer and storage of vortex states in light and matter waves. , 2004, Physical review letters.

[7]  John F Nye,et al.  Local solutions for the interaction of wave dislocations , 2004 .

[8]  M. Dennis.  Braided nodal lines in wave superpositions , 2003, physics/0307139.

[9]  I. V. Basistiy,et al.  Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam. , 2003, Optics letters.

[10]  A. Winfree,et al.  Stability of knots in excitable media. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Stephen M. Barnett,et al.  Optical Angular Momentum , 2003 .

[12]  M. Vasnetsov,et al.  Laser beams with screw dislocations in their wavefronts , 2003 .

[13]  Mark R. Dennis,et al.  Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime , 2001 .

[14]  M. Berry,et al.  Knotted and linked phase singularities in monochromatic waves , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  J. Ruostekoski,et al.  Creating vortex rings and three-dimensional skyrmions in Bose-Eeinstein condensates. , 2001, Physical review letters.

[16]  Mark R. Dennis,et al.  Topological Singularities in Wave Fields , 2001 .

[17]  Mark R. Dennis,et al.  Phase singularities in isotropic random waves , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  Miles J. Padgett,et al.  IV The Orbital Angular Momentum of Light , 1999 .

[19]  John F Nye,et al.  Natural focusing and fine structure of light: caustics and wave dislocations , 1999 .

[20]  Michael V. Berry,et al.  Much ado about nothing: optical distortion lines (phase singularities, zeros, and vortices) , 1998, Other Conferences.

[21]  Kishan Dholakia,et al.  The Production Of Multiringed Laguerre-Gaussian Modes By Computer-Generated Holograms , 1998 .

[22]  Grover A. Swartzlander,et al.  Propagation dynamics of optical vortices , 1997 .

[23]  Antti J. Niemi,et al.  Stable knot-like structures in classical field theory , 1997, nature.

[24]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[25]  Andrew G. White,et al.  Generation of optical phase singularities by computer-generated holograms. , 1992, Optics letters.

[26]  H. Aref,et al.  Linking of vortex rings , 1991, Nature.

[27]  J Turunen,et al.  Realization of general nondiffracting beams with computer-generated holograms. , 1989, Journal of the Optical Society of America. A, Optics and image science.

[28]  Miceli,et al.  Diffraction-free beams. , 1987, Physical review letters.

[29]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions: III. Knotted waves , 1983 .

[30]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions , 1983 .

[31]  G. Budworth.  The Knot Book , 1983 .

[32]  John F Nye,et al.  The elliptic umbilic diffraction catastrophe , 1979, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[33]  M. Berry,et al.  Dislocations in wave trains , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[34]  H. K. Moffatt,et al.  The degree of knottedness of tangled vortex lines , 1969, Journal of Fluid Mechanics.

[35]  Sir William Thomson F.R.S..  II. On vortex atoms , 1867 .