Hermite-Gaussian modal laser beams with orbital angular momentum

Area of Science:

• Optics and Photonics
• Quantum Optics

Background:

• Hermite-Gaussian (HG) beams are fundamental solutions in paraxial wave optics.
• Understanding generalized HG beams is crucial for advanced optical applications.

Purpose of the Study:

• To deduce a relationship for the complex amplitude of generalized paraxial HG beams.
• To investigate the transformation of these beams into familiar and elegant HG modes.
• To calculate and analyze the orbital angular momentum (OAM) of specific combinations of generalized HG beams.

Main Methods:

• Derivation of a relationship for the complex amplitude of generalized paraxial HG beams.
• Analysis of beam transformations under specific parameter conditions.
• Calculation of OAM for linear combinations of generalized HG beams with phase shifts.

Main Results:

• Generalized HG beams can transform into familiar and elegant HG modes.
• The OAM modulus of combined HG modes can be an integer, unity, or fractional.
• A specific linear combination yields a non-rotating mode with nonzero OAM and broken radial symmetry.

Conclusions:

• The study provides a framework for understanding generalized HG beam behavior.
• The OAM characteristics of these beams offer potential for novel optical manipulations.
• The discovery of non-rotating OAM modes opens new avenues in beam propagation research.