Generalized M2 factor of hard-edged diffracted flattened Gaussian beams

Area of Science:

• Optics and Photonics
• Laser Physics

Background:

• The M2 factor is a critical parameter for characterizing laser beam quality.
• Flattened Gaussian beams are important in various optical applications.
• Understanding beam propagation and diffraction is essential for laser system design.

Purpose of the Study:

• To derive a closed-form expression for the generalized M2 factor of hard-edge diffracted flattened Gaussian beams.
• To analyze the influence of beam order and truncation parameter on the M2 factor.
• To investigate the M2 factor of truncated plane waves.

Main Methods:

• Utilizing generalized truncated second-order moments.
• Deriving a closed-form expression for the generalized M2 factor.
• Analyzing special cases and specific beam parameters.

Main Results:

• A closed-form expression for the generalized M2 factor of hard-edge diffracted flattened Gaussian beams was obtained.
• The M2 factor depends on the beam order and truncation parameter.
• The M2 factor of truncated plane waves was determined to be a constant value (4√3/3).

Conclusions:

• The derived formula provides a valuable tool for assessing the quality of flattened Gaussian beams.
• The M2 factor of truncated plane waves is independent of aperture width, simplifying analysis in certain scenarios.
• This research contributes to a deeper understanding of beam propagation and quality metrics in optical systems.