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).