Creating Light with a Twist
Azure Hansen, John Noé, Harold Metcalf
Laser Teaching Center, Stony Brook University
Singularities can be found everywhere in physics, perhaps the
best-known example being black holes in spacetime. Light may also
possess singularities. Over the last decade, singular optics has
exploded into a rich field with numerous useful and potential
applications in communications, astronomy, quantum computing and
medicine. For example, this research was initially motivated by the
possibility of using an optical vortex filter for the direct optical
detection of exoplanets [1]. Optical vortices, an important type of
optical singularity, have a spiral-shaped phase distribution and
therefore a characteristic region of undefined phase where the
amplitude is necessarily zero. These beams with a dark core may be
described by Laguerre-Gaussian (LG) modes, which have an extra phase
term of exp(ilφ), where l, the topological charge, is the number
of 2π windings, and φ is the azimuthal angle. As first
recognized in 1992 [2], LG modes are associated with orbital angular
momentum of light, a phenomenon distinct from the spin angular
momentum of circularly polarized light. Optical vortices may be
created by the transformation of Hermite-Gaussian laser modes [3], by
spiral phase plates, by specialized (forked or spiral zone plate)
diffraction gratings, or by a programmable liquid crystal-based device
called a spatial light modulator (SLM).
We have studied optical vortices experimentally using a "fork"
diffraction grating made by photographing a calculated interference
pattern of plane-wave and LG beams [4]. When illuminated with
collimated laser light the grating produces a diffraction pattern in
which the non-zero orders contain optical singularities. Even orders
of diffraction are suppressed due to the interaction of single- and
multiple-slit diffraction amplitudes; and only a limited number of
orders (m ≤ 7) are produced with any significant intensity. The size
and position of the laser beam incident on the grating greatly affects
the quality of the vortices.
The phase of a beam of light may be visualized via interference
with another light beam. Interferograms were created that combined
Gaussian and LG beams of varying topological charge and the resulting
fringe patterns recorded and studied. Simulations created in the
Mathematica software package closely match the observed patterns.
Future work will involve: measuring the profile and core depth of
the vortices; creating forked gratings that maximize intensity in a
specific diffraction order; producing beams with fractional
topological charge; studying the effect of partially coherent light on
singularity behavior; and selecting and purchasing an SLM.
We wish to thank Kiko Galvez (Colgate University) for providing the
fork grating, and Grover Swartzlander (University of Arizona, Tucson),
Miles Padgett (Glasgow University) and Sir Michael Berry (Bristol
University) for helpful discussions. This research was supported by
NSF grant PHY-98044.
References
1. G. A. Swartzlander, Jr., "Peering Into Darkness," Optics & Photonics
News 34 (Dec 2001)
2. L. Allen, et al., "Orbital angular momentum of light and the
transformation of Laguerre-Gaussian modes," Phys. Rev. A 45, 8185-8189
(1992)
3. Alex Ellis, http://laser.physics.sunysb.edu/~alex
4. E.J. Galvez, et al., "Geometric Phase Associated to Mode Transformations
of Optical Beams Bearing Orbital Angular Momentum," Physical Review
Letters 90, 203901 (2003)
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