Transcript Chris_Poster - Deveney-BSU

Optical Vortices: The Orbital Angular Momentum of Light
Christopher Cepero
Department of Physics, Bridgewater State College -- Bridgewater MA, 02325
Mentor: Dr. Edward Deveney
Results
Abstract
Methods
It was not realized until 1992 that light could possess angular momentum – plane wave
light twisted in a corkscrew. Due to resemblance with a similar phenomenon seen in fluids,
this momentum is called an Optical Vortex. While optical vortices are still under
investigation, they are already a crucial component of optical tweezers which are used in
biomedical applications to trap neutral particles. Our work centers on the first investigation
of optical vortices here at BSC performing an experiment described in an American Journal
of Physics (AJP) article called “Making optical vortices with computer-generated
holograms.” Using software, we take analytic interference patterns to generate a
holographic mask – laser light impingent on the mask ‘picks up’ angular momentum and the
projections of the momentum can be measured using a modified CCD camera. Our goal in
recreating this experiment is to learn more about both the theory and experimental
outcomes of optical vortices.
Our experiment is a reproduction of the experiment performed in the AJP article “Making
optical vortices with computer-generated holograms.” The method of creating optical vortices
described in this paper involves generating an interference pattern and condensing it accurately
into a 0.5cm by 0.5cm square on film.
The interference pattern is created by the interference of the following two waves, and
the calculation of the resulting function.
Our experimental procedure begins with the characterization of our optics
equipment. The beam splitters and polarizers we have were manufactured for a 780nm
laser., and the AJP article utilizes a 633nm He-Ne laser. Using a power meter, we measured
our 633nm He-Ne laser to have a power of 0.566W. After shining it through the 50/50
beam splitter, we measured a power between 0.238W and .315W for the transmitted
beam; about 60% of the initial power. The reflected beam was measured to have a power
40% the initial, at 0.120W to 0.230W.
Once we characterized our equipment, we moved on to generating the orbital
angular momentum. With the help of Professor Nunez from the photography department,
we photographed the interference patterns and developed the film to act as our
holographic mask.
Introduction
When dealing with light waves, it all begins with Maxwell’s Equations:
Figure 4: The film used as an optical mask.
Our most recent progress has been in encoding the angular momentum from the
optical mask into the laser beam. The interference pattern is approximately 0.5cm by
0.5cm, and the laser must hit the very center of the interference pattern as it is
transmitted. Once it is properly centered, the angular momentum is observable in the
interference pattern the laser creates.
From these equations you can determine that light is an electromagnetic wave which
travels at 300,000,000 m/s in a vacuum, and has the general form:
Furthermore, out of Maxwell’s Equations we can derive the Poynting vector:
Figure 5: The first optical vortices generated at BSC
For an electromagnetic plane wave, the Poynting vector points in the direction of the
waves propagation, and describes the magnitude and direction of the momentum carried in
the wave. For light waves with a helical polarization, the pointing vector contains a
component of the momentum in the azimuthal direction. This component of the momentum
causes an angular momentum parallel to the axis of propagation. This angular momentum
rotates around the beam axis, and has been dubbed an Optical Vortex. The vortex can visibly
be seen when you interfere a plane wave at the center of a helical wave, while both are
coherent.
Current Status
Now that we have successfully coded the laser beam with an angular
momentum, we must cause it to interfere with another coherent laser beam, using
beam splitters. Once we are able to accurately interfere the two laser beams, we will
be able to image the optical vortex.
(a)
(b)
Figure 2:Interference patterns (a) m=2 and (b) m=3, generated using Maple.
Apparatus
• A Class II 633nm He-Ne Laser is our light source, and a CCD camera records the images.
• We use black and white film as our Holographic Mask (HM)
Figure 6: Viewing the optical vortex requires basic optics equipment such as : 50/50 Beam
Splitters (BS), Mirrors (M), Polarizers (P), and slits/diaphrams (S). (image from Carpentier et al.)
After imaging the optical vortices, there are lots of other exciting applications and
experiments this research can be applied to for future research topics.
Acknowledgements
• We are very appreciative of the BSC Photography Department for their assistance
with photographing and developing the film for the holographic mask.
• Many thanks to Dale Smith for help with resizing the interference patterns for
printing.
(a)
(b)
Figure 1 – (a) Light wave with a helical wave front and the Poynting Vector, alongside
the optical vortex. (b) Diffracted pattern caused by the holographic mask. (Images
from Padgett, Courtial, Allen paper)
References
Figure 3: Initial set-up to image the angular momentum.
•A.V. Carpentier et al., “Making optical vortices with computer-generated
holograms,” Am. J.Phys. 76, 916-921 (2008).
•Miles Padgett, Johannes Courtial, Les Allen; “Lights Orbital Angular Momentum,”
Physics Today. 76, 35-40 (2004).