Producing Optical Vortices with an Adjustable Spiral Phase Plate

Gregory Caravelli, Johns Hopkins University; Amol Jain, Herricks High
School; John Noe and Harold Metcalf, Laser Teaching Center, Department
of Physics and Astronomy, Stony Brook University

An optical vortex (OV) is an example of a phase singularity in a wave
field, that is, a point in space where the phase of the field is
undefined and the amplitude is necessarily zero. A loosely related but
more familiar example would be trying to identify directions such as
East or West while standing on the earth's North Pole. In recent years
the study of such optical singularities has emerged as an exciting new
discipline, both on account of its inherent theoretical interest and
applications in diverse fields such as optical manipulation (laser
tweezers), quantum computing and encryption. The most common type of
OV is characterized by a spiral phase distribution in which the phase
of the light field steadily increases in proportion to the azimuthal
angle phi as one moves around the vortex center (phase = exp^{il
phi}). After one complete revolution the phase has advanced by an
integer multiple l times 2 pi; this integer is called the topological
charge of the vortex. OV's are commonly created by passing a laser
beam through a type of diffraction pattern called a computer-generated
hologram (CGH). A more effective method is to directly impose a spiral
phase-shift distribution on the light beam by varying the thickness of
a transparent material through which it passes. A fixed spiral phase
plate can be made by micro- lithography, a technically difficult
process. Such a device is also limited to a specific wavelength.  A
variable (computer controlled) phase plate can be created using a
spatial-light modulator (SLM), but such devices are quite expensive.

In the current project an extremely simple and inexpensive method [1]
for creating a spiral phase plate was investigated experimentally. The
device can be easily adjusted to produce OV's of varying topological
charge at any laser wavelength. (We observed vortices up to charge 7
with a HeNe laser.) Our version consists of a 22 mm square, 0.25 mm
thick, plastic miscroscope cover slip which has been cut along a line
running radially outwards from the center to one corner. It is "tuned"
by inserting a thin plastic wedge part way into the cut; this causes
the material on either side of the cut to curve smoothly outwards in
opposite directions. The resulting surface tilt creates a spatially
varying optical path length distribution and hence a varying phase
shift. It is of great interest to know what the tilt angle
distribution is, as this information can be used to model and refine
the device.  A simple optical-lever method was developed to accurately
measure the surface tilt at 441 points on a 500 micron grid. The spot
diameter of the scanning HeNe laser beam was estimated to be 200
microns. Analysis of the data to extract the tilt distribution is in
progress.

This work was supported by NSF Grant No. PHY-0243935.

1) C. Rotschild, S. Zommer, S. Moed, O. Hershcovitz, and S.G. Lipson, 
   "Adjustable Spiral Phase Plate," Applied Optics, April 2004.