Exploring vortex structures in orbital-angular-momentum beams generated from planar geometric modes with a mode...

Area of Science:

• Optics and Photonics
• Laser Physics
• Quantum Optics

Background:

• Geometric modes in lasers are crucial for various applications.
• Understanding vortex structures is key to controlling laser beam properties.
• Previous studies have explored different laser modes, but circularly geometric modes require specific investigation.

Purpose of the Study:

• To theoretically demonstrate the circularly geometric mode using the inhomogeneous Helmholtz equation.
• To analyze the factors determining the vortex structures of these modes.
• To experimentally generate and verify the vortex structures of circularly geometric modes.

Main Methods:

• Theoretical analysis solving the inhomogeneous Helmholtz equation with pump distribution.
• Numerical calculations of transverse lasing modes and cavity degeneracy.
• Experimental generation using a selectively pumped solid-state laser and a π/2 mode converter.
• Interferometric analysis using a Mach-Zehnder interferometer to probe vortex structures.

Main Results:

• The circularly geometric mode can be theoretically solved from the inhomogeneous Helmholtz equation.
• Vortex structures are determined by the minimum order, total number, and degeneracy of transverse lasing modes.
• Experimentally generated circularly geometric modes exhibit vortex structures consistent with theoretical predictions.
• Interference patterns confirm the predicted vortex structures, validating the theoretical analysis.

Conclusions:

• The theoretical framework accurately describes the generation and properties of circularly geometric modes.
• Experimental validation confirms the ability to generate and analyze these modes in solid-state lasers.
• The findings provide a foundation for controlling and utilizing laser vortex structures in optical systems.