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Light Tied in Knots

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BRISTOL, GLASGOW & SOUTHAMPTON, UK, Jan. 18, 2010 -- A branch of abstract mathematics inspired by knots that occur in shoelaces and rope has been used to design holograms capable of creating knots in optical vortices.

The colored circles represent the hologram, out of which the knotted optical vortex emerges. (Images: University of Bristol)

The remarkable feat of tying light in knots has been achieved by a team of physicists working at the universities of Bristol, Glasgow and Southampton.

Understanding how to control light in this way has important implications for laser technology used in wide a range of industries.

"In a light beam, the flow of light through space is similar to water flowing in a river. Although it often flows in a straight line - out of a torch, laser pointer, etc - light can also flow in whirls and eddies, forming lines in space called optical vortices," said Dr. Mark Dennis of the University of Bristol and lead author on a paper published this week on the work. "Along these lines, or optical vortices, the intensity of the light is zero (black). The light all around us is filled with these dark lines, even though we can't see them."

Optical vortices can be created with holograms which direct the flow of light. In this work, the team designed holograms using knot theory – a branch of abstract mathematics inspired by knots that occur in shoelaces and rope and which was previously considered completely abstract. Using these specially designed holograms they were able to create knots in optical vortices.

Professor Miles Padgett of Glasgow University, who led the experiments, said, "The sophisticated hologram design required for the experimental demonstration of the knotted light shows advanced optical control, which undoubtedly can be used in future laser devices."

"The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms," added Dennis, who began to study knotted optical vortices with professor Sir Michael Berry at Bristol University in 2000. "This work opens a new chapter in that history."

The paper, "Isolated optical vortex knots," by Mark R. Dennis (a Royal Society research fellow), Robert P. King, Barry Jack, Kevin O'Holleran and Miles J. Padgett, was published online Jan. 17 in the journal Nature Physics.

The research was funded by the Leverhulme Trust.

For more information, visit:

Jan 2010
Electromagnetic radiation detectable by the eye, ranging in wavelength from about 400 to 750 nm. In photonic applications light can be considered to cover the nonvisible portion of the spectrum which includes the ultraviolet and the infrared.
atomsBristolGlasgowhologramsknot theorylightlight sourcesMark DennisMikes PadgettNature Physicsoptical vorticesopticsResearch & TechnologySouthamptonUKlasersLEDs

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