Hamsa Sridhar, Kings Park High School, Kings Park, NY; Harold Metcalf and John Noe, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University
Laser beams can be described in terms of two independent families of basic spatial patterns, or modes. The Hermite-Gaussian (HG) modes have rectangular symmetry, while the Laguerre-Gaussian (LG) modes have cylindrical symmetry. Many types of LG modes (called optical vortices) have helical wavefronts and carry orbital angular momentum, a property that can be exploited in an optical tweezers to cause micro-particles to rotate. The degree of angular momentum in the light beam is called the order, and higher orders cause greater rotation. The overall goal of this project is to develop a simple method for creating useful higher-order LG modes for use in optical tweezers.
Several methods of creating LG modes have been explored. Conventional "forked" diffraction gratings create high quality modes but spread the light into multiple orders, resulting in poor efficiency. Inexpensive spiral phase plates created by a cracked piece of plastic, a subject of much recent investigation at the LTC, create vortices with high efficiency but relatively poor quality. Fractional order vortices that may be present create gaps in the vortex ring that the particles cannot pass over.
Currently, an alternative energy-efficient method for creating LG modes from HG modes through a cylindrical-lens mode converter  is being investigated, and a converter is being constructed. (The possibility of constructing a tilted spherical lens mode converter is also being explored.) The availability of such a device shifts the problem to one of obtaining suitable HG modes to feed into it. One possibility is to create a quasi-HG mode from an ordinary zero-order Gaussian laser beam. Dissecting the cross-section of the beam with a glass slide creates an optical path length difference (phase shift) between the two halves of the beam. Using a Mach-Zehnder interferometer, the phase difference is set to be pi/2 radians, as in true HG modes.
We would like to thank the Simons Foundation for funding this research.
 M.W.Beijersbergen et al., Optics Commun. 96 (1994) p. 123.