Introduction
Bessel beams are a special type of light propagation that does not diffract. The light distribution of a Bessel beam maintains a tight focus with high irradiance over great distances. Bessel beams are also self-healing, which means that the light pattern will regenerate after being partially obstructed. Such properties make this phenomenon useful for optical trapping and tweezing, high-precision drilling, and communication applications. In this example FRED will be used to generate a pseudo-Bessel beam using an axicon. [1][2][3][4][5]
Description of a Bessel beam
Bessel beams are propagating light fields with a distribution described by a Bessel function of the first kind. The cross section of a Bessel beam consists of concentric rings. Each ring (including the central lobe) contains the exact same infinitesimal amount of energy.
Figure 1. Irradiance pattern along the cross-section of a Bessel beam. The Bessel function is shown in the upper right.
Higher-order Bessel beams are modified along the azimuthal direction according to the equation Jl(krr)exp(ilφ), where kr determines ring spacing and l determines azimuthal phase variation. In the far-field, the Bessel beam takes the form of an annular ring.
Axicon generation of a Bessel beam
Practically speaking, the mathematically ideal Bessel beam is impossible to create: it contains an infinite amount of rings over an infinite extent. Pseudo-Bessel beams, on the other hand, are confined to an aperture. The most straightforward way to create a Bessel beam is with an axicon (a cone-shaped refractive material or reflective surface that transforms an incident plane wave into a self-interfering cone of light). Self-interference forms concentric fringes.
It is simple to create an axicon in FRED and can be done by creating a “circular cone” Element Primitive consisting of the Simple Glass material and coated with the Transmit coating. In this example a base semi-aperture of 1 mm and height of 0.1 mm was chosen. Next, a Simplified Optical Source of the type Collimated Source (plane wave) was created and set to be coherent to ensure self-interference. A wavelength of 500 nm is used for the source. Finally, an absorbing surface with attached analysis surface is placed 12 mm from the axicon.
Figure 2. Left: a collimated plane wave illumination passes through a glass axicon. Right: further along the axis, a detector is placed in a region of self-interference where a pseudo-Bessel beam is generated.
To observe the Bessel beam, Coherent Scalar Wave Field is viewed. The field amplitude can be shown by right-clicking the graph and selecting Show Field Amplitude. Over a 0.2 mm diameter observation region, distinct Bessel rings are visible (Figure 3).
The associated FRED file can be downloaded from our Knowledge Base.
[1] Dudly, A., Laverly, M., Padgett, M. , and Forbes, A. “Unraveling Bessel Beams.” http://www.osa-opn.org/home/articles/ volume_24/ june_2013/featurres/unraveling_bessel_beams/#.VkueeCspXS5
[2] “Bessel Beam.” Wikipedia. January 18, 2016. Accessed January 21, 2016. https://en.wikipedia.org/wiki/Bessel_beam
[3] Durnin, J. “Exact Solutions for Nondiffracting Beams. I. The Scalar Theory”, JOSA A 4, 651-654 (1987)
[4] “’Tractor beam’ is possible with lasers, say scientists”. Published 3/3/11. Accessed 1/21/16. http://www.bbc.com/news/science-environment-12620560
[5] Ridden, P. “New microscope captures 3D movies of living cells.” Published 3/15/11. Accessed 1/21/16. http://www.gizmag.com/3d-microscope-movies-living-cells/18138/