Producing Optical Vortices with an Adjustable Spiral Phase Plate
Amol Jain, Herricks High School; Gregory Caravelli, Johns Hopkins University; John Noé and Harold Metcalf, Laser Teaching Center, Department of Physics and Astronomy, Stony Brook University
An optical vortex is characterized by a doughnut-shaped intensity distribution with zero field amplitude, and hence a phase singularity, at the center. Optical vortices feature a screw-shaped topological wavefront dislocation, which can be visualized as a helical phase ramp around the field's dark center. The phase varies linearly with the azimuthal angle φ as described by the phase term exp(ilφ). Consequently, the total phase variation around the circumference of a vortex is 2πl, where l is an integer known as the topological charge. The wide range of possible topological charges (l up to 400 has been reported in laser beams) allows for some interesting applications, including precision optical manipulation (i.e. applying varying torques to particles using laser tweezers), high-speed data transfer, and quantum computing and encryption.
Optical vortices can be created by passing a laser beam through a diffraction pattern imprinted on a transparent surface, otherwise known as a computer-generated hologram (CGH). Because a significant amount of intensity is necessarily lost in the diffraction process, a better means of generating optical vortices is to directly impose the spiral phase shift distribution on the light field by controlling the thickness of a transparent medium through which the light passes. Such spiral phase plates can be manufactured using micro-lithography, but their practicality is limited by production technicalities and their fitness for only one particular wavelength. Computer-controlled spatial light modulators (SLMs) can be used to create vortices with any wavelength of light, but they are very expensive.
In this project, a simple and inexpensive method  for producing a spiral phase plate was investigated experimentally and improved. The phase plate can be adjusted to produce vortices of arbitrary topological charge and functions for any laser wavelength. It consists simply of a 22 mm square, 0.25 mm thick plastic microscope cover slip which has been slit radially from the center to a corner. The phase shift is adjusted by inserting a 2.8 mm thick plastic piece into the cut, which causes the two sides of the material to curve smoothly outwards in opposite directions. The curved shape of the surface creates a spatially varying optical path length (apparent thickness) distribution and hence a varying phase change. Vortices of up to l = 7 were created with a red (632.8 nm) HeNe laser. A 2-dimensional translator was built and used in conjunction with the optical lever method to measure the surface tilt at 430 points on a 508 micron grid around the center of the cover slip. The data are being analyzed to better understand the tilt distribution and further improve the phase plate design.
This work was supported by the Simons Foundation and NSF Grant No. PHY-0243935.
 C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S.G. Lipson, ``Adjustable Spiral Phase Plate,'' Applied Optics, April 2004.