Vortex beams

  • Liquid crystal devices are used to create digital holograms.
  • Light diffracted off a liquid crystal splits into its many orders.
Date:31 October 2008 Tags:,

The South African scientists are putting a new twist on light, manipulating photons to create vortices with some very weird properties.

Evidence of angular momentum – that bodies can be made to spin and rotate – is very familiar to us from everyday life: twist a rubber band by applying a torque to it and hold it in tension; release it and it will unwind very fast, gaining angular momentum in the process.

Even our timekeeping is in some sense based on angular momentum: each new day arrives courtesy of the spin of the Earth about its axis (spin angular momentum), while the years are measured in the orbit of the Earth about our Sun (orbital angular momentum). Now scientists know that even photons can be twisted, forming so-called “twisted” light in the process. As with the released rubber band, this “twisted” light carries angular momentum.

For over a century now, scientists have known that light can be viewed as either a particle (photon) or a wave. If you could freeze a wave of ordinary light, you would see a series of crests and troughs, moving forward as a series of planes known as wavefronts. The energy transfer is in a straight line in the direction of the travelling planes.

The wavefronts of “twisted” light no longer look like those of ordinary light; but instead transform into a corkscrew-like pattern, with the direction of energy transfer spiralling around the axis of propagation. The waves are still moving forward in a straight line, but twisting as they move, much like water spiralling down a drain.

Near the central propagation axis, the velocity of the spiralling waves becomes infi nite, causing the intensity of the light in the centre to vanish, forming an optical vortex.  is is one of the visual distinctions between “twisted” and ordinary light: if both are focused by a lens, “twisted” light appears as a ring of light, with the optical vortex manifesting itself as a dark centre; an ordinary laser beam appears as a bright spot with no dark centre.

There are an infinite number of possible twists that can be put on the light, for example, a simple single helix, a DNA-like double helix, or a triple helix akin to fusilli pasta. The more twists put on the light, the larger the dark centre of the beam becomes. When light is twisted in this manner, the twist is imparted to each photon, creating “twisted” photons. The result is that each photon carries a well-defined amount of orbital angular momentum.

As the twist is increased, so the amount of orbital angular momentum carried by each photon increases. Creating laser beams with multiple twists – so-called vortex beams – is the key ingredient in many emerging research fields, most notably optical tweezing, quantum computing and quantum information transfer, and is made possible in the laboratory by a fusion of the optical and digital worlds through digital holography.

Digital holography
When holography was first discovered in 1947 by Dennis Gabor (by serendipity; he was actually trying to improve the resolution of an electron microscope), he could not have imagined how all-pervasive the technique would become, nor how important it would become to modern optics in the 21st century. It was only after the invention of the laser in the early 1960s that holography became a serious tool in the armoury of optical scientists.

Waves can be described by both an amplitude and a position, and whereas photographs store information by recording the amplitude of a wave, holograms store information by recording the phase, or position of the wave. But light waves travel very fast, so to store information on the position of the many waves requires that we slow them down – all the way to a standstill.

To do this, we create so-called “standing waves” – waves that don’t move, so that we can record the phase of the waves at every point using conventional photographic techniques. You can think of holography as taking a photograph of the phase of light and storing this information in some conventional medium, such as photographic film.

For many years, these standing waves were created by interference of two waves: a reference wave and an object wave that carries information about the object of which you intend to create a hologram. This is achieved in the laboratory by splitting a laser beam into two parts, reflecting one part off the object that one wishes to make a hologram of, and then recombining the two waves on some photographic film.

The recombining creates standing waves by interference, and the resulting hologram stores information about the object using the phase of the waves. Once the phase information is stored in the hologram, it may be retrieved to create the original object by illuminating the hologram with the reference beam again. This may also be done with white light rather than a laser beam, and the result is the holograms we see on bank cards and some paper currencies.

But what if we want to make a hologram of something that does not exist as a physical object – for example, a vortex beam? In conventional holography, this would be impossible, as an object wave is crucial to the process. Today we get around this inconvenience by using a technique called Computer Generated Holograms (CGHs), otherwise known as digital holography.

Rather than let nature calculate the hologram using interference as described earlier, we use computers to do this, then write the hologram to a liquid crystal display device. If this device is illuminated with a suitable laser beam to act as the reference beam, then the outgoing laser beam will carry the information from the hologram as before. The required hologram for creating a vortex beam takes the form of a fork–like pattern.

A non-vortex reference beam is used to illuminate a digital hologram of a forklike dislocation; the number of forks in the hologram determines the amount of twists put on to the out coming vortex beam: two forks means two twists, with photons carrying 2h- (pronounced h-bar) of orbital angular momentum, three forks means three twists, with 3h- of orbital angular momentum, and so on. This is how optical vortices, which are virtual objects, are created in the laboratory.

Quantum information and quantum computing
Previously in quantum communications systems, information was encoded in the spin angular momentum (polarisation) states of photons. In using the spin to encode information, one is restricted to only two options, “spin clockwise” and “spin anticlockwise”, and so is similar to conventional communication methods of “on” and “off” modulated signals.

The orbital angular momentum state of light – its twisted nature – opens the way for an unlimited number of possible states to be used in a “twisted alphabet”. Rather than use many photons to create the letter “A” through an on-off sequence, “twisted” light can function as a form of communication by encoding the alphabet directly: a flash of single-helix light represents the letter “A” , a double-helix the letter “B”, and so on all the way to “Z”.

Vortex beams thus hold the key to dramatically increased bandwidth for the future. This is still some way off in practice, though, as unfortunately vortex beams with a large number of twists tend to spread out very quickly, an
d so for the moment cannot be used for long-distance communication.

Twisted photons are also making groundbreaking advances in the world of quantum computing. The growing interest in quantum computing stems from the fact that it outperforms conventional, everyday computing by exploiting the principle of quantum superposition (see “The Schizophrenic Atom”, Popular Mechanics, February 2008).

In quantum computing, the number of calculations that can be performed in a given time depends on the number of superposition states a photon can possess. Considering the spin state of a photon, and taking clockwise to be denoted by 1 and anticlockwise by 0, we see that we have a superposition of four states: 00, 01, 10 and 11. Ideally, the number of superposition states needs to be increased, and this can be achieved by using the orbital angular momentum state of photons. Since there is no physical limit to the number of twists that can be put on the light, it’s theoretically possible to create an infinite number of superposition states – the holy grail of quantum computing!

Optically driven motors
The ability to produce light carrying angular momentum may not seem to be an achievement of great importance, since the effects are visible only on the microscopic scale. However, for the past 30 years, there has existed a technique that specialises in the manipulation of microscopic particles – optical tweezers. In an optical tweezer, laser beams are used to produce pico-Newton forces to control microscopic samples in three dimensions: particles are “trapped” by the laser beam and then easily manipulated by steering the laser beam.

If the beam used in the tweezing is a vortex beam, the transfer of orbital angular momentum to the particle will cause it to rotate. Once rotating, optical tweezers can also control the rate of rotation by simply controlling the amount of angular momentum carried by the beam. By using vortex beams to drive micro gears, it’s possible to control fluid flow in microfluidic channels. By placing a number of these gears in series, a chain of rotating gears can be generated, which could make possible an optical pump by imparting angular momentum to one gear. Today we are seeing the first demonstrations of integrated optical-mechanical systems – photon-driven motors using twisted light!

  • Angela Dudley and Melanie McLaren are PhD and MSc students respectively in the Mathematical Optics group at the CSIR National Laser Centre. Both are under the supervision of the group’s leader, Dr Andrew Forbes.

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