Are Optical Vortex Knots the Future of Light Manipulation?

[PatrickPowers]

http://www.nature.com/nphys/journal/v4/n9/abs/nphys1056.html

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.

http://www.nature.com/nphys/journal/v6/n2/abs/nphys1504.html

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.

Wikipedia

http://en.wikipedia.org/wiki/Optical_vortex

 

[eljose79]

Optical vortices are regions in a light field where the phase of the electromagnetic wave is singular, resulting in a helical wavefront. This creates a spiral-shaped intensity pattern, with a dark region in the center where the phase is undefined. These vortices can be created artificially using techniques such as holography or spiral phase plates, or they can occur naturally in light fields, such as in the patterns of sunlight passing through a pinhole.

The forum post describes a novel way of creating optical vortices in the form of knots and links using algebraic topology. This approach allows for the creation of complex and unique optical vortex patterns that have potential applications in various fields, including fluid dynamics, particle trapping, and plasma confinement.

I find this research to be both fascinating and promising. The ability to control and manipulate optical vortices opens up new possibilities for studying the behavior of light in three-dimensional space. The use of algebraic topology to create these structures is a creative and innovative approach, and the predicted extensions and potential applications are exciting.

One potential area where this research could have a significant impact is in the study of cold atomic gases. These gases are often used as a model system for studying quantum effects, and the ability to create and control intricate optical vortex patterns could provide new insights into the behavior of these systems. Additionally, the potential for creating knotted beams of light could have applications in quantum computing and communication.

In conclusion, the forum post highlights a groundbreaking research study on the creation of optical vortex knots and links. This research has the potential to advance our understanding of light and its behavior in three-dimensional space, and could have practical applications in various fields. I am eager to see the further developments and potential applications of this research in the future.