Parametric characterization of rotationally symmetric hard-edged diffracted beams

Area of Science:

• Optics and Photonics
• Laser Physics
• Beam Propagation

Background:

• Second-order moments and M2 factor are crucial for characterizing laser beams.
• Previous studies focused on 2D Cartesian systems, limiting analysis of complex beam structures.

Purpose of the Study:

• To extend the analysis of truncated second-order moments and the generalized M2 factor (M(G)2 factor) to 3D rotationally symmetric hard-edged diffracted beams.
• To derive a closed-form expression for the M(G)2 factor of flattened Gaussian beams.
• To ensure consistency with existing theoretical frameworks.

Main Methods:

• Extension of 2D Cartesian coordinate formalisms to 3D cylindrical coordinates.
• Derivation of propagation equations for truncated moments and the M(G)2 factor.
• Development of a closed-form expression for the M(G)2 factor of specific beam types.

Main Results:

• Propagation equations for truncated moments and the M(G)2 factor exhibit similarities to non-truncated cases.
• A closed-form expression for the M(G)2 factor of rotationally symmetric hard-edged diffracted flattened Gaussian beams was derived.
• The M(G)2 factor approaches a constant value for high beam orders, consistent with truncated plane waves.

Conclusions:

• The developed formalism is consistent and applicable to 3D hard-edged diffracted beams.
• The M(G)2 factor provides a robust metric for beam quality in complex diffraction scenarios.
• This work advances the understanding of light beam propagation and characterization in optical systems.