Laguerre-Gaussian-to-Hermite-Gaussian mode conversion revisited

Area of Science:

• Optics and Photonics
• Quantum Optics
• Laser Physics

Background:

• Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes are fundamental solutions in paraxial optics.
• Optical astigmatism is a common aberration that can induce mode conversion.
• Understanding and controlling LG-to-HG mode conversion is crucial for various optical applications.

Purpose of the Study:

• To generalize the theoretical framework for Laguerre-Gaussian-to-Hermite-Gaussian (LG-to-HG) mode conversion.
• To identify distinct conversion scenarios based on astigmatism conditions.
• To explore astigmatic phase profiles for controlled LG-to-HG mode conversion.

Main Methods:

• Theoretical analysis of LG beam diffraction by astigmatic optical elements.
• Investigating three types of astigmatic elements: cylindrical lenses, quadratic curved-line gratings, and elliptical zone plates.
• Exploring two families of astigmatic phase profiles for independent control over mode stretching and orientation.

Main Results:

• Identified three distinct LG-to-HG conversion scenarios based on astigmatism.
• Showed that LG modes of different orders convert to corresponding HG modes at specific distances.
• Demonstrated independent control over the stretching and orientation of converted HG modes using tailored astigmatic phase profiles.

Conclusions:

• The generalized theoretical framework accurately predicts LG-to-HG mode conversion under astigmatism.
• Astigmatic optical elements offer versatile methods for controlling light beam modes.
• Theoretical predictions show good qualitative agreement with experimental observations.