Bessel Beam Generation

Bessel beam generation

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.

Bessel beam radial profile

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.

Axicon raytrace

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).

Field profile of Bessel beam

Figure 3. Distribution of irradiance (left) and light field (right) in self-interfering region beyond an axicon illuminated by a plane wave with wavelength of 500 nm.

 

The associated FRED file can be downloaded from our knowledgebase.

 

[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/