Generation of an elliptic hollow beam using Mathieu and Bessel functions

Area of Science:

• Optics and Photonics
• Laser Physics
• Beam Shaping

Background:

• Propagation-invariant beams, such as Bessel beams, are crucial for applications requiring stable beam profiles over distance.
• Elliptic vortex beams offer unique properties for optical manipulation and microscopy.
• Existing methods for generating elliptic beams can be mathematically complex.

Purpose of the Study:

• To report a new, mathematically simpler technique for generating propagation-invariant elliptic hollow beams.
• To demonstrate an alternative to methods relying on radial Mathieu functions.
• To explore the generation of elliptic beams using Bessel functions and holographic masks.

Main Methods:

• Utilized Bessel functions with arguments defining an elliptic locus to create a holographic mask.
• Employed both angular Mathieu functions (elliptic vortex term) and circular vortex expressions separately.
• Illuminated the generated mask with a plane beam and filtered its Fourier transform to obtain the elliptic beam.

Main Results:

• Successfully generated propagation-invariant elliptic hollow beams.
• Observed satisfactory results using both elliptic and circular vortex terms.
• Confirmed that vortices remain stable and do not separate, even at higher ellipticity.

Conclusions:

• The developed technique provides a mathematically simpler and potentially more accessible method for generating propagation-invariant elliptic hollow beams.
• The use of Bessel functions and holographic masks offers a viable alternative to traditional methods.
• The stability of the generated beams, particularly the non-separation of vortices at higher ellipticity, is a significant finding.