February 2015
Spotlight Summary by Richard Bowman
Adjustable diffractive spiral phase plates
Light beams with a twisted spatial structure have many intriguing properties; their characteristic feature is that they carry orbital angular momentum, meaning they exert a torque on objects they illuminate in addition to any angular momentum associated with the light's spin. These beams have found uses from the manipulation of micro-objects to the search for extra-solar planets, and are being investigated for communication technology. Microscopy is another area where these twisted beams can bring benefits, enhancing contrast in phase microscopy and enabling higher resolution through STED imaging.
One of the main challenges when working with orbital angular momentum-carrying beams is generating them: their helical spatial structure is most often produced using a computer-generated hologram or diffraction grating. Such a grating is designed to impart a phase shift that varies around the axis of the beam such that, on completing a circuit around the centre, the phase will have increased by an integer multiple of 2 pi. This integer is usually referred to as the helical charge l of the beam. Beams with non-zero helical charge focus to a ring instead of the usual point, and the radius of the ring increases as the charge gets further from zero. The difficulty with using a diffraction grating, which is common to most methods of producing helical beams, is that it is hard to change the charge of the output beam: generally this requires a new hologram or grating. Dynamic liquid crystal devices exist that can do this, though they are often polarisation-sensitive and wavelength-specific. Harm and co-workers neatly get around this problem by using two computer generated holographic elements, such that the angle between them sets the helical charge of the transmitted beam.
The new phase plates exploit Moiré fringes, which arise when two patterns of similar periodicity are overlaid. This is similar to the "beating" observed when two waves of nearly the same frequency interfere. Often, shifting the angle or position of one of the two patterns results in a dramatic change in the Moiré fringes, and it is this effect that the paper discusses. By using two phase plates where the phase varies as the square of the azimuthal angle around the beam axis, the team get a phase variation linearly proportional to azimuthal angle-perfect for generating helically phased beams. Changing the angle between the two plates varies the rate at which phase advances around the beam, allowing them to get a helical charge anywhere from -15 to +15. This is a similar approach to earlier work by the same group, where they used two phase plates to produce a variable focal length lens.
The phase plates are produced using gray scale lithography, and in order to keep them very thin they are phase-wrapped, i.e. the phase pattern is written modulo 2 pi. Provided the plates are used at the design wavelength, this should not affect their operation and makes them much easier to fabricate. In principle, if a broadband device were required, it should be possible to make it with thicker, non-wrapped phase plates. The other limitation of this technique is that a small region of the transmitted beam does not have the correct phase. This region is an angular wedge, with a size that is the same as the angle between the two phase plates (taking zero as the position that gives no helical charge, i.e. the plates cancel exactly). Even at the highest helical charges (l=+/-20) this is still only a small portion of the beam.
Beams produced by this method are not quite Laguerre-Gaussian beams, as the intensity is not shaped by the phase plates. However, they have many of the useful properties of L-G beams, and will be useful for creating dark-centred depletion beams for STED as well as enhancing contrast in microscopes. Crucially, this can be done without the expense and complication of a dynamic diffractive element. At the design wavelength the helical beams have very good (94%) efficiency and beam quality, and there's no reason in principle the system couldn't be made broad-band. Their performance is in good agreement with the theory, and they are a very useful addition to the array of optical tools for generating and measuring twisted light.
You must log in to add comments.
One of the main challenges when working with orbital angular momentum-carrying beams is generating them: their helical spatial structure is most often produced using a computer-generated hologram or diffraction grating. Such a grating is designed to impart a phase shift that varies around the axis of the beam such that, on completing a circuit around the centre, the phase will have increased by an integer multiple of 2 pi. This integer is usually referred to as the helical charge l of the beam. Beams with non-zero helical charge focus to a ring instead of the usual point, and the radius of the ring increases as the charge gets further from zero. The difficulty with using a diffraction grating, which is common to most methods of producing helical beams, is that it is hard to change the charge of the output beam: generally this requires a new hologram or grating. Dynamic liquid crystal devices exist that can do this, though they are often polarisation-sensitive and wavelength-specific. Harm and co-workers neatly get around this problem by using two computer generated holographic elements, such that the angle between them sets the helical charge of the transmitted beam.
The new phase plates exploit Moiré fringes, which arise when two patterns of similar periodicity are overlaid. This is similar to the "beating" observed when two waves of nearly the same frequency interfere. Often, shifting the angle or position of one of the two patterns results in a dramatic change in the Moiré fringes, and it is this effect that the paper discusses. By using two phase plates where the phase varies as the square of the azimuthal angle around the beam axis, the team get a phase variation linearly proportional to azimuthal angle-perfect for generating helically phased beams. Changing the angle between the two plates varies the rate at which phase advances around the beam, allowing them to get a helical charge anywhere from -15 to +15. This is a similar approach to earlier work by the same group, where they used two phase plates to produce a variable focal length lens.
The phase plates are produced using gray scale lithography, and in order to keep them very thin they are phase-wrapped, i.e. the phase pattern is written modulo 2 pi. Provided the plates are used at the design wavelength, this should not affect their operation and makes them much easier to fabricate. In principle, if a broadband device were required, it should be possible to make it with thicker, non-wrapped phase plates. The other limitation of this technique is that a small region of the transmitted beam does not have the correct phase. This region is an angular wedge, with a size that is the same as the angle between the two phase plates (taking zero as the position that gives no helical charge, i.e. the plates cancel exactly). Even at the highest helical charges (l=+/-20) this is still only a small portion of the beam.
Beams produced by this method are not quite Laguerre-Gaussian beams, as the intensity is not shaped by the phase plates. However, they have many of the useful properties of L-G beams, and will be useful for creating dark-centred depletion beams for STED as well as enhancing contrast in microscopes. Crucially, this can be done without the expense and complication of a dynamic diffractive element. At the design wavelength the helical beams have very good (94%) efficiency and beam quality, and there's no reason in principle the system couldn't be made broad-band. Their performance is in good agreement with the theory, and they are a very useful addition to the array of optical tools for generating and measuring twisted light.
Add Comment
You must log in to add comments.
Article Information
Adjustable diffractive spiral phase plates
Walter Harm, Stefan Bernet, Monika Ritsch-Marte, Irina Harder, and Norbert Lindlein
Opt. Express 23(1) 413-421 (2015) View: Abstract | HTML | PDF