Creating
Bessel beams with a 4-f spatial filter
Melia Bonomo, John NoƩ, Marty Cohen Laser Teaching Center,
Stony Brook University
The purpose of this project was to create zero-order Bessel beams by a
recently described 4-f spatial filtering method [1]. This
experience provided a valuable introduction to important broader topics
such as Fourier optics and diffraction theory. A Bessel beam is a
non-diffracting solution to the Helmholtz wave equation; unlike typical
Gaussian laser beams it consists of a narrow core surrounded by concentric
rings. Bessel beams have important research and commercial applications
including optical trapping and extending the working range of barcode
scanners.
A Bessel beam can be visualized as a uniform superposition of plane
waves whose wave vectors propagate on the surface of a cone. The Fresnel
diffraction of a narrow ring of light can produce such a converging
conical wave front [2]. As demonstrated by Kowalczyk et al., a thin
ring of light can be generated by spatially filtering the light diffracted
from a circular aperture to edge-enhance the image [1].
Our 4-f configuration consisted of a 1 mm circular aperture (the
"object"), a 333 mm focal length achromat lens, an annular spatial filter
(outer diameter 20 mm, inner diameter 6 mm), and a second identical lens;
each optical element was separated by 333 mm. We settled upon each
aperture's dimensions based on what produced the clearest edge-enhanced
image of the object. The object was illuminated with a clean uniform
wavefront obtained from a 633-nm HeNe laser.
We used an Electrim EDC-1000N camera (pixel size 7.4 x 7.4 microns) to
record the evolution of the light field from the initial aperture to the
final Bessel beam. As expected, we observed a narrow ring of light at the
4-f focal plane. The ring diffracted into a Bessel beam that formed 21 mm
past the focal plane and propagated a further 47 mm. The central spot size
and intensity varied along the axis of propagation, as expected, due to
the fact that this method generates quasi-Bessel beams.
We are currently working on analyzing the collected images with ImageJ
software to extract the transverse intensity profile of the Bessel beam as
a function of propagation distance and the profile of the thin ring of
light. These results will be compared with a theoretical model that we are
creating with Mathematica.
This work was supported by the Stony Brook Physics and Astronomy REU
program and the Laser Teaching Center.
[1] Jeremy Kowalczyk, Stefanie N. Smith, and Eric B. Szarmes,
"Generation of Bessel beams using a 4-f spatial filtering system,"
Am. J. Phys. {77} 229-236 (2009).
[2] J. Durnin, J. H. Eberly, and J. J. Miceli, "Diffraction Free
Beams," Phys. Rev. Lett. {58} 1499-1501 (1987).
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