Generating twisted light

One of my first thoughts about twisted light was "It must be very difficult to generate twisted light in the lab!". Talking to others, I found that this is a common misunderstanding.

People tend to think that one requires very particular --and expensive-- laboratory equipment. Fortunately, the experimentalists say that it is not a difficult task to twist conventional laser fields.

There are several techniques that can be use to produce beams of twisted lights. I will first comment on simple ones [1], that will show how easy the beams can be produced. Then, I will briefly talk about one of the more sophisticated technique.

Spiral phase plate

Spiral phase plates are to me the most comprehensible of all elements use to convert an incident plane wave into twisted light [1]. It is simply a piece of transparent material in the form of a disk, that has been additionally shaped into the form of a spiral: the thickness of the disk varies with the angle. This causes that light passing through different portions of the disk gains different phases, due to change in optical path. The phase depends on the angle, and the field coming out of the disk gains the characteristic factor $\large e^{i\, \ell\, \varphi}$.

Computer generated
hologram

A different way to create the twisted field is by means of the so-called Computer Generated Holograms (CGH) [2]. This is diffraction grating that is generated by numerically calculating the intensity profile and transmittance that result from the interference between a tilted plane wave and a twisted wave. This computer-generated pattern, typically fork-like, is then printed and used as a grating. When a plane wave shines on this grating, different beams (orders) are created, having for example values of ℓ=-1,0,1.

A more sophisticated optical device is the Spatial Light Modulator (SLM), which can be used to modulate not only the phase but also the amplitude and polarization of the light, in time and space [3]. It is a high-resolution liquid crystal display that either reflects or refracts an incident light beam, into the desired output beam. The pattern displayed by the SLM is controlled by a computer, and can be modified nowadays at a frequency in the range 60-200 Hz.

References

[1] "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate", Kotlyar VV, Almazov AA, Khonina SN, Soifer VA, Elfstrom H, Turunen J., J Opt Soc Am A Opt Image Sci Vis. 2005 May;22(5):849-61.

[2] "Making optical vortices with computer-generated holograms", Alicia V. Carpentier, Humberto Michinel, José R. Salgueiro, and David Olivieri, Am. J. Phys. 76, 916 (2008)

A nice student project describes how to use SPP and CGH: http://laser.physics.sunysb.edu/~amol/papers/siemens/siemens.pdf

[3] "Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement", Xi-Lin Wang, Jianping Ding, Wei-Jiang Ni, Cheng-Shan Guo, and Hui-Tian Wang, OPTICS LETTERS 3549, Vol. 32 no. 24 (2007).

SLM manufacturer : http://holoeye.com/spatial-light-modulators/
Phase-plate manufacturer: http://www.rpcphotonics.com/vortex.asp