Vortex astigmatic Fourier-invariant Gaussian beams.

Area of Science:

• Optics and Photonics
• Quantum Optics

Background:

• Optical vortices carry orbital angular momentum (OAM).
• Astigmatic beams possess elliptical symmetry.
• Conventional astigmatic beams may split central intensity nulls.

Purpose of the Study:

• To introduce and characterize a novel family of astigmatic elliptical Gaussian (AEG) optical vortices.
• To analyze the orbital angular momentum properties of these novel beams.
• To investigate the behavior of the central intensity null in AEG vortices.

Main Methods:

• Theoretical derivation of a two-parameter family of AEG optical vortices.
• Calculation of the total normalized orbital angular momentum.
• Analysis of the phase structure and intensity distribution in the transverse plane.

Main Results:

• AEG vortices are free space modes (up to scale and rotation).
• The total normalized OAM can be integer, fractional, or zero.
• OAM is the algebraic sum of vortex and astigmatic contributions.
• A single, n-fold degenerate intensity null exists on the optical axis.
• The central null does not split, unlike in other astigmatic beams.

Conclusions:

• AEG vortices represent a unique class of optical beams with tunable OAM.
• The findings challenge previous assumptions about intensity null splitting in astigmatic beams.
• This work expands the toolkit for generating and controlling light beams with specific OAM properties.