An alternative theoretical model for an anomalous hollow beam

Area of Science:

• Optics and Photonics
• Theoretical Physics

Background:

• Anomalous hollow beams with elliptical symmetry have been experimentally observed.
• Existing theoretical models may lack convenience or flexibility for describing these beams.

Purpose of the Study:

• To propose a convenient and flexible theoretical model for anomalous hollow beams of elliptical symmetry.
• To express the electric field of these beams using a finite sum of elliptical Gaussian modes.

Main Methods:

• Developing a theoretical model based on elliptical Gaussian modes.
• Deriving analytical propagation formulas for coherent and partially coherent beams.
• Utilizing numerical examples to demonstrate propagation and focusing properties.

Main Results:

• The proposed model successfully describes flexible anomalous hollow beams with elliptical symmetry.
• The model encompasses flat-topped, dark hollow, and Gaussian beams as special cases.
• Analytical formulas for beam propagation through astigmatic ABCD optical systems were derived.

Conclusions:

• The new theoretical model offers a convenient approach for studying anomalous hollow beams.
• The derived propagation formulas are applicable to both coherent and partially coherent scenarios.
• Numerical calculations validate the model's ability to predict beam behavior.