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 [1,2]. 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 [3], LG modes are associated with orbital angular momentum of light, a phenomenon distinct from the spin angular momentum associated with circularly polarized light. Optical vortices may be created by the transformation of Hermite-Gaussian laser modes [4], by spiral phase plates, or by specialized (forked or spiral zone plate) diffraction gratings.

We have studied optical vortices experimentally using a "fork" diffraction grating made by photographing a calculated interference pattern of plane-wave and LG beams [5]. 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. In the course of the measurements it was observed that a magnified image of the grating could be created with a lens. As the lens was moved away from the optimum focal point, fractal patterns similar to those produced in the Talbot effect [6] were observed.

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; and studying the effect of partially coherent light on singularity behavior. Other Laser Teaching Center students plan to pursue the use of LG modes as high-efficiency optical tweezers capable of rotating small objects (Anirudh Ramesh); and in quantum computing (Yaagnik Kosuri).

We wish to thank Kiko Galvez (Colgate University) for providing the fork grating, and Grover Swartzlander (University of Arizona, Tucson) for helpful discussions. This research was supported by NSF grant PHY-98044.

References

1. Azure Hansen, http://laser.physics.sunysb.edu/~azure

2. G. A. Swartzlander, Jr., "Peering Into Darkness," Optics & Photonics News 34 (Dec 2001)

3. L. Allen, et al., "Orbital angular momentum of light and the transformation of Laguerre-Gaussian modes," Phys. Rev. A 45, 8185-8189 (1992)

4. Alex Ellis, http://laser.physics.sunysb.edu/~alex

5. E.J. Galvez, et al., "Geometric Phase Associated to Mode Transformations of Optical Beams Bearing Orbital Angular Momentum," Physical Review Letters 90, 203901 (2003)

6. Allison Schmitz, http://laser.physics.sunysb.edu/~allison